{"id":289934,"date":"2021-07-29T12:02:45","date_gmt":"2021-07-29T05:02:45","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=289934"},"modified":"2023-02-07T15:25:58","modified_gmt":"2023-02-07T08:25:58","slug":"bilangan-bulat","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/bilangan-bulat\/","title":{"rendered":"Bilangan Bulat &#8211; Pengertian, Jenis, Operasi Hitung"},"content":{"rendered":"<p><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-289938\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-6.png\" alt=\"\" width=\"800\" height=\"533\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-6.png 800w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-6-300x200.png 300w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-6-768x512.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Halo Quipperian, apa kabar? Semoga tetap semangat belajar ya, meskipun pandemi Covid-19 belum juga berakhir.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Selama belajar dari rumah, pelajaran apa sih yang paling kamu sukai? Apakah kamu suka Matematika?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Saat kamu mendengar istilah Matematika, jangan ciut nyali, ya. Matematika itu mudah kok untuk dipelajari, contohnya saja materi bilangan bulat&nbsp; yang akan dibahas Quipper Blog pada artikel kali ini. Penasaran? Yuk, ikuti pembahasan berikut!<\/span><\/p>\n<h2><strong>Pengertian Bilangan Bulat<\/strong><\/h2>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-289943\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-1.jpg\" alt=\"\" width=\"800\" height=\"533\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-1.jpg 800w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-1-300x200.jpg 300w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-1-768x512.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Bilangan bulat (selanjutnya disingkat menjadi bil. bulat) adalah semua bilangan yang tidak dalam bentuk pecahan atau desimal. Artinya, semua bilangan cacah beserta negatifnya termasuk anggota bil. bulat. Adapun contohnya adalah, -5, -6, -7, -8, 8, 7, 6, 2, dan lainnya.&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Kira-kira, siapa penemu bilangan ini, ya? Adakah di antara Quipperian yang bisa menebaknya? Ya, dialah matematikawan asal Italia yang bernama Leonardo da Pisa atau biasa dikenal sebagai Fibonacci.&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Sejak berusia 27 tahun, Fibonacci sudah berhasil menulis buku perhitungan, <\/span><em><span style=\"font-weight: 400;\">lho<\/span><\/em><span style=\"font-weight: 400;\">. Apakah Quipperian tertarik mengikuti jejaknya?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Jika tertarik, kamu harus lebih giat belajarnya ya!!<\/span><\/p>\n<h2><strong>Jenis-Jenisnya<\/strong><\/h2>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-289942\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-2.jpg\" alt=\"\" width=\"800\" height=\"533\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-2.jpg 800w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-2-300x200.jpg 300w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-2-768x512.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Secara umum, bilangan ini terdiri dari tiga macam, yaitu sebagai berikut.<\/span><\/p>\n<h3><strong>1. Bilangan bulat positif<\/strong><\/h3>\n<p><span style=\"font-weight: 400;\">Bilangan bulat positif adalah bilangan yang dimulai dari angka satu dan seterusnya. Contohnya adalah 1, 2, 3, 4, 5, 6, 7, \u2026, dan seterusnya. Jika diteruskan, nilainya semakin besar.<\/span><\/p>\n<h3><strong>2. Bilangan bulat negatif<\/strong><\/h3>\n<p><span style=\"font-weight: 400;\">Bilangan bulat negatif adalah bilangan yang dimulai dari angka negatif satu (-1) dan seterusnya. Contohnya adalah -1, -2, -3, -4, -5, -6, -7, \u2026, dan seterunya. Jika diteruskan, nilainya semakin kecil.<\/span><\/p>\n<h3><strong>3. Bilangan bulat nol<\/strong><\/h3>\n<p><span style=\"font-weight: 400;\">Bilangan bulat nol adalah bilangan yang hanya terdiri dari angka 0.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Dari ketiga poin di atas, dapat disimpulkan bahwa bil. bulat terdiri dari beberapa jenis bilangan, yaitu bilangan cacah (0, 1, 2, 3, \u2026, dst), bilangan asli (1, 2, 3, 4, \u2026, dst), bilangan prima (2, 3, 5, 7, 11, \u2026, dst), bilangan ganjil (1, 3, 5, 7, 9, \u2026, dst), dan bilangan genap (2, 4, 6, 8, \u2026, dst).<\/span><\/p>\n<h2><strong>Operasi Hitung&nbsp;<\/strong><\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-289941\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-3.jpg\" alt=\"\" width=\"800\" height=\"533\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-3.jpg 800w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-3-300x200.jpg 300w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-3-768x512.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Secara umum, operasi hitung bilangan ini ada empat, yaitu sebagai berikut.<\/span><\/p>\n<h3><strong>1. Operasi hitung penjumlahan<\/strong><\/h3>\n<p><span style=\"font-weight: 400;\">Pada penjumlahan, berlaku beberapa sifat berikut.<\/span><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">&nbsp;Sifat asosiatif, yaitu (<\/span><em><span style=\"font-weight: 400;\">a<\/span><\/em><span style=\"font-weight: 400;\"> + <\/span><em><span style=\"font-weight: 400;\">b<\/span><\/em><span style=\"font-weight: 400;\">) + <\/span><em><span style=\"font-weight: 400;\">c<\/span><\/em><span style=\"font-weight: 400;\"> = <\/span><em><span style=\"font-weight: 400;\">a<\/span><\/em><span style=\"font-weight: 400;\"> + (<\/span><em><span style=\"font-weight: 400;\">b <\/span><\/em><span style=\"font-weight: 400;\">+<\/span><em><span style=\"font-weight: 400;\"> c<\/span><\/em><span style=\"font-weight: 400;\">)<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Sifat komutatif, yaitu <\/span><em><span style=\"font-weight: 400;\">a<\/span><\/em><span style=\"font-weight: 400;\"> + <\/span><em><span style=\"font-weight: 400;\">b<\/span><\/em><span style=\"font-weight: 400;\"> = <\/span><em><span style=\"font-weight: 400;\">b<\/span><\/em><span style=\"font-weight: 400;\"> + <\/span><em><span style=\"font-weight: 400;\">a<\/span><\/em><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Unsur identitas, yaitu <\/span><em><span style=\"font-weight: 400;\">a<\/span><\/em><span style=\"font-weight: 400;\"> + 0 = 0 + <\/span><em><span style=\"font-weight: 400;\">a<\/span><\/em><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400;\">Contoh bil. bulat penjumlahan adalah sebagai berikut.<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">(2 + 5) + 4 = 2 + (5 + 4) = 11<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">6 + 7 = 7 + 6 = 13<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">8 + 0 = 0 + 8 = 8<\/span><\/li>\n<\/ul>\n<h3><strong>2. Operasi hitung pengurangan<\/strong><\/h3>\n<p><span style=\"font-weight: 400;\">Pada pengurangan tidak berlaku sejumlah sifat seperti halnya penjumlahan. Adapun sifat pengurangan adalah sebagai berikut.<\/span><\/p>\n<p><em><span style=\"font-weight: 400;\">a<\/span><\/em><span style=\"font-weight: 400;\"> \u2013 <\/span><em><span style=\"font-weight: 400;\">b<\/span><\/em><span style=\"font-weight: 400;\"> = <\/span><em><span style=\"font-weight: 400;\">a<\/span><\/em><span style=\"font-weight: 400;\"> + (-<\/span><em><span style=\"font-weight: 400;\">b<\/span><\/em><span style=\"font-weight: 400;\">)<\/span><\/p>\n<p><em><span style=\"font-weight: 400;\">a<\/span><\/em><span style=\"font-weight: 400;\"> \u2013 (-<\/span><em><span style=\"font-weight: 400;\">b<\/span><\/em><span style=\"font-weight: 400;\">) = <\/span><em><span style=\"font-weight: 400;\">a<\/span><\/em><span style=\"font-weight: 400;\"> + <\/span><em><span style=\"font-weight: 400;\">b<\/span><\/em><\/p>\n<p><span style=\"font-weight: 400;\">Contoh bil. bulat pengurangan adalah sebagai berikut.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">12 \u2013 20 = 12 + (-20) = -8, dengan nilai -8 tersebut adalah bilangan bulat negatif.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">1 \u2013 (-2) = 1 + 2 = 3<\/span><\/p>\n<h3><strong>3. Operasi hitung perkalian<\/strong><\/h3>\n<p><span style=\"font-weight: 400;\">Pada perkalian, berlaku sejumlah sifat seperti berikut.<\/span><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li><span style=\"font-weight: 400;\">Hasil perkalian antara dua bilangan bulat atau lebih harus mengikuti ketentuan berikut.<\/span>\n<ul>\n<li><span style=\"font-weight: 400;\">Perkalian antarbilangan bulat positif = positif. Contoh perkaliannya 2 x 3 = 6.<\/span><\/li>\n<li><span style=\"font-weight: 400;\">Perkalian antarbilangan bulat negatif = positif. Contoh perkaliannya (-2) x (-3) = 6.<\/span><\/li>\n<li><span style=\"font-weight: 400;\">Perkalian antara bilangan bulat positif dan negatif = negatif. Contoh perkaliannya (-2) x 3 = -6.<\/span><\/li>\n<\/ul>\n<\/li>\n<li><span style=\"font-weight: 400;\">Sifat asosiatif, yaitu (<\/span><em><span style=\"font-weight: 400;\">a<\/span><\/em><span style=\"font-weight: 400;\"> x <\/span><em><span style=\"font-weight: 400;\">b<\/span><\/em><span style=\"font-weight: 400;\">) x <\/span><em><span style=\"font-weight: 400;\">c<\/span><\/em><span style=\"font-weight: 400;\"> = <\/span><em><span style=\"font-weight: 400;\">a<\/span><\/em><span style=\"font-weight: 400;\"> x (<\/span><em><span style=\"font-weight: 400;\">b<\/span><\/em><span style=\"font-weight: 400;\"> x <\/span><em><span style=\"font-weight: 400;\">c<\/span><\/em><span style=\"font-weight: 400;\">)<\/span><\/li>\n<li><span style=\"font-weight: 400;\">Sifat komutatif, yaitu (<\/span><em><span style=\"font-weight: 400;\">a <\/span><\/em><span style=\"font-weight: 400;\">x<\/span><em><span style=\"font-weight: 400;\"> b<\/span><\/em><span style=\"font-weight: 400;\">)<\/span> <span style=\"font-weight: 400;\">x<\/span><em><span style=\"font-weight: 400;\"> c<\/span><\/em><span style=\"font-weight: 400;\"> = <\/span><em><span style=\"font-weight: 400;\">a <\/span><\/em><span style=\"font-weight: 400;\">x<\/span> <span style=\"font-weight: 400;\">(<\/span><em><span style=\"font-weight: 400;\">b<\/span><\/em><span style=\"font-weight: 400;\"> x<\/span><em><span style=\"font-weight: 400;\"> c<\/span><\/em><span style=\"font-weight: 400;\">)<\/span><\/li>\n<li><span style=\"font-weight: 400;\">Sifat distributif, yaitu <\/span><em><span style=\"font-weight: 400;\">a<\/span><\/em><span style=\"font-weight: 400;\"> x (<\/span><em><span style=\"font-weight: 400;\">b<\/span><\/em><span style=\"font-weight: 400;\"> +<\/span><em><span style=\"font-weight: 400;\">c<\/span><\/em><span style=\"font-weight: 400;\">) = (<\/span><em><span style=\"font-weight: 400;\">a<\/span><\/em><span style=\"font-weight: 400;\"> x<\/span><em><span style=\"font-weight: 400;\"> b<\/span><\/em><span style=\"font-weight: 400;\">) <\/span><span style=\"font-weight: 400;\">&nbsp;<\/span><span style=\"font-weight: 400;\">(<\/span><em><span style=\"font-weight: 400;\">a <\/span><\/em><span style=\"font-weight: 400;\">x<\/span><em><span style=\"font-weight: 400;\"> c<\/span><\/em><span style=\"font-weight: 400;\">)<\/span><\/li>\n<\/ol>\n<h3><strong>4. Operasi hitung pembagian<\/strong><\/h3>\n<ol style=\"list-style-type: lower-alpha;\">\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Hasil pembagian antara dua bilangan bulat atau lebih, harus mengikuti ketentuan berikut.<\/span>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Pembagian antarbilangan bulat positif menghasilkan bilangan positif. Contoh pembagiannya adalah 6 : 3 = 2.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Pembagian antarbilangan bulat negatif menghasilkan bilangan positif. Contoh pembagiannya adalah (-6) : (-2) = 3.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Pembagian antara bilangan bulat positif dan negatif menghasilkan bilangan negatif. Contoh pembagiannya adalah 6 : (-2) = -3.&nbsp;<\/span>Perlu diingat bahwa hasil bagi antara dua bil. bulat tidak selalu bil. bulat, contohnya 6 : 4 = 1,5 (angka 1,5 tidak termasuk bilangan bulat).<\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Tidak berlaku sifat komutatif, contohnya 6 : 3 <\/span><span style=\"font-weight: 400;\">\u2260<\/span><span style=\"font-weight: 400;\"> 3 : 6.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Tidak berlaku sifat asosiatif, contohnya (6 : 1) : 3 <\/span><span style=\"font-weight: 400;\">\u2260<\/span><span style=\"font-weight: 400;\"> 6 : (1 : 3).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Jika dibagi dengan nol atau nol sebagai nilai yang dibagi, menghasilkan nilai tak berhingga dan tidak terdefinisi. Contohnya adalah sebagai berikut.<\/span>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">2 : 0 = <\/span><span style=\"font-weight: 400;\">~<\/span><span style=\"font-weight: 400;\"> dan&nbsp; 3 : 0 = <\/span><span style=\"font-weight: 400;\">~<\/span><span style=\"font-weight: 400;\"> , sementara 2 <\/span><span style=\"font-weight: 400;\">\u2260<\/span><span style=\"font-weight: 400;\"> 3<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">0 : 2 = 0 dan 0 : 3 = 0, sementara 2 <\/span><span style=\"font-weight: 400;\">\u2260<\/span><span style=\"font-weight: 400;\"> 3.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<h2><strong>Bagaimana Mengurutkan Bilangan Bulat dengan Garis?<\/strong><\/h2>\n<p><span style=\"font-weight: 400;\">Jika Quipperian diberi sejumlah bilangan, lalu kamu diminta untuk mengurutkannya menggunakan garis bilangan, maka hal pertama yang harus kamu lakukan adalah membuat garis bilangan itu sendiri. Adapun contoh garis bilangan adalah sebagai berikut.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-289937\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/bilangan-bulat-a.png\" alt=\"\" width=\"526\" height=\"224\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/bilangan-bulat-a.png 526w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/bilangan-bulat-a-300x128.png 300w\" sizes=\"(max-width: 526px) 100vw, 526px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Berdasarkan garis bilangan di atas, yang termasuk bil. bulat negatif, yaitu semua bil. bulat di sebelah kiri nol (ditunjuk panah warna merah). Semakin ke kiri, nilai bilangannya semakin kecil. Sementara itu, yang termasuk bil. bulat positif, yaitu semua bil. bulat di sebelah kanan nol (ditunjuk panah warna biru). Semakin ke kanan, nilai bilangannya semakin besar.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Untuk mengurutkan, kamu juga harus berpedoman pada garis bilangan di atas. Agar kamu tidak bingung bagaimana cara bilangan bulat diurutkan, perhatikan dua contoh soal berikut.<\/span><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Urutkan bilangan -4, -8, -3, 6, 5, 7 mulai dari terkecil sampai terbesar!<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Tulislah bilangan bulat yang kurang dari 3 dan lebih dari -5.<\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400;\">Jawaban:<\/span><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Berdasarkan garis bilangan, angka yang letaknya paling kiri adalah -8 dan paling kanan adalah 7. Dengan demikian, urutannya adalah -8, -4, -3, 5, 6, 7.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Bilangan bulat yang kurang dari 3 dan lebih dari -5 adalah -4, -3, -2, -1, 0, 1, 2.<\/span><\/li>\n<\/ol>\n<h2><strong>Cara Membandingkan Bilangan Bulat<\/strong><\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-289940\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-4.jpg\" alt=\"\" width=\"800\" height=\"533\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-4.jpg 800w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-4-300x200.jpg 300w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-4-768x512.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Mungkin Quipperian bertanya-tanya, bagaimana cara membandingkan bilangan bulat itu? Sebelumnya, kamu akan dikenalkan dengan beberapa tanda berikut.<\/span><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">&gt; yang berarti lebih besar dari<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">&lt; yang berarti lebih kecil dari<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">= yang berarti sama dengan<\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400;\">Agar kamu semakin paham, simak contoh berikut.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Suhu Kota London saat ini adalah -3 <\/span><sup><span style=\"font-weight: 400;\">o<\/span><\/sup><span style=\"font-weight: 400;\">C. Sementara itu, suhu di Kota Manchester adalah 2 <\/span><sup><span style=\"font-weight: 400;\">o<\/span><\/sup><span style=\"font-weight: 400;\">C. Nyatakan suhu Kota London terhadap kota Manchester dalam bentuk perbandingan.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Kota London = -3&nbsp;<\/span><sup><span style=\"font-weight: 400;\">o<\/span><\/sup><span style=\"font-weight: 400;\">C (berada di sebelah kiri nol)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Kota Manchester = 2 <\/span><sup><span style=\"font-weight: 400;\">o<\/span><\/sup><span style=\"font-weight: 400;\">C (berada di sebelah kanan nol)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Artinya, suhu Kota London lebih kecil dari suhu Kota Manchester. Secara matematis, dapat ditulis sebagai berikut.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Suhu Kota London &lt; Suhu Kota Manchester<\/span><\/p>\n<p><span style=\"font-weight: 400;\">-3 <\/span><sup><span style=\"font-weight: 400;\">o<\/span><\/sup><span style=\"font-weight: 400;\">C &lt; 2 <\/span><sup><span style=\"font-weight: 400;\">o<\/span><\/sup><span style=\"font-weight: 400;\">C<\/span><\/p>\n<h2><strong>Penerapan dalam Kehidupan Sehari-Hari<\/strong><\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-289939\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-5.jpg\" alt=\"\" width=\"800\" height=\"533\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-5.jpg 800w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-5-300x200.jpg 300w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/Bilangan-Bulat-5-768x512.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Apakah Quipperian tahu jika materi ini dekat sekali dengan kehidupan kamu sehari-hari?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Contoh bilangan bulat dalam kehidupan sehari-hari bisa kamu temukan saat membeli lampu, televisi, kulkas, HP, komputer, kipas angin, telur, dan lainnya.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Saat kamu membeli barang-barang di atas, pasti kamu akan mengatakan \u201cPak, beli 2 lampu atau 2 TV atau 2 komputer\u201d karena tidak mungkin kamu mengatakan \u201cPak, beli 2,5 lampu atau 2,5 TV atau \u00bc komputer\u201d.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Apakah Quipperian sudah paham dengan materi kali ini?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Agar pemahamanmu semakin terasah, coba kerjakan contoh soal berikut ini.<\/span><\/p>\n<h2><strong>Contoh Soal 1<\/strong><\/h2>\n<p><span style=\"font-weight: 400;\">Perhatikan pernyataan berikut.<\/span><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Andi memiliki uang Rp20.000. Uang itu ia gunakan untuk membeli beras 2,5 kg. Ternyata harga beras per kilonya adalah Rp10.000. Mengingat jarak antara rumah Andi dan toko beras jauh, akhirnya Andi memutuskan berhutang dahulu terkait kekurangannya.<\/span><\/li>\n<li><span style=\"font-weight: 400;\">Hani melelehkan es batu pada suhu ruang 20 <\/span><sup><span style=\"font-weight: 400;\">o<\/span><\/sup><span style=\"font-weight: 400;\">C. Jika suhu es batu mula-mula -1 <\/span><sup><span style=\"font-weight: 400;\">o<\/span><\/sup><span style=\"font-weight: 400;\">C, tentukan selisih suhu ruang dan es batu.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Di suatu permainan terdapat ketentuan skor seperti berikut.<\/span>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Jika menang mendapatkan skor 5.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Jika kalah mendapatkan skor -2.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Jika seri mendapatkan skor 0.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Permainan Jojo menang satu kali, seri 3 kali, dan kalah 2 kali.<\/li>\n<\/ul>\n<\/li>\n<li><span style=\"font-weight: 400;\">Pak Hasan memiliki 5 hektar kebun jeruk. Setiap 2&nbsp; hektar kebun membutuhkan pupuk 30 kg pupuk. Jika persediaan pupuk Pak Hasan 82,5 kg, berapakah sisa pupuk Pak Hasan?<\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400;\">Dari hasil operasi hitung ketiga pernyataan di atas:<\/span><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Pernyataan yang terdiri dari bilangan bulat adalah \u2026.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Hasil operasi hitung yang termasuk bilangan bulat negatif!<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Hasil operasi hitung yang bukan bilangan bulat!<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Hasil operasi hitung yang termasuk bilangan bulat!<\/span><\/li>\n<\/ol>\n<p><strong>Pembahasan:<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">1. Uang Andi = Rp20.000<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Harga 2,5 kg beras = Rp10.000 <\/span><span style=\"font-weight: 400;\">\u00d7<\/span><span style=\"font-weight: 400;\"> 2,5 = Rp25.000<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Hutang = harga beras \u2013 uang Andi<\/span><\/p>\n<p><span style=\"font-weight: 400;\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= Rp25.000 \u2013 Rp20.000<\/span><\/p>\n<p><span style=\"font-weight: 400;\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= Rp5.000 (hutang Andi) atau bisa ditulis -5.000<\/span><\/p>\n<p><span style=\"font-weight: 400;\">2. Selisih suhu ruang dan es batu = 20 \u2013 (-1)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 21 <\/span><sup><span style=\"font-weight: 400;\">o<\/span><\/sup><span style=\"font-weight: 400;\">C<\/span><\/p>\n<p><span style=\"font-weight: 400;\">3. Permainan Jojo, menang 1 kali, seri 3 kali, dan kalah 2 kali. Secara matematis, bisa dirumuskan sebagai berikut.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Skor Jojo = (5<\/span><span style=\"font-weight: 400;\">\u00d7<\/span><span style=\"font-weight: 400;\">1) + (3<\/span><span style=\"font-weight: 400;\">\u00d7<\/span><span style=\"font-weight: 400;\">0) + (-2<\/span><span style=\"font-weight: 400;\">\u00d7<\/span><span style=\"font-weight: 400;\">2)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 5 + 0 \u2013 4<\/span><\/p>\n<p><span style=\"font-weight: 400;\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 1<\/span><\/p>\n<p><span style=\"font-weight: 400;\">4. Kebun Pak Hasan = 5 hektar<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Setiap 2 kebun = 30 kg pupuk -&gt;<\/span><span style=\"font-weight: 400;\">&nbsp;setiap 1 hektar membutuhkan 15 kg pupuk<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Persediaan = 82,5 kg<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Kebutuhan 5 hektar = 15 <\/span><span style=\"font-weight: 400;\">\u00d7<\/span><span style=\"font-weight: 400;\"> 5 = 75 kg pupuk<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Sisa = 82,5 \u2013 75 = 7,5 kg pupuk<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Dari hasil operasi hitung ketiga pernyataan di atas:<\/span><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Pernyataan yang terdiri dari bilangan bulat adalah adalah pernyataan nomor 2 dan 3 karena semua nilai besarannya dalam bentuk bilangan bulat.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Hasil operasi hitung yang termasuk bilangan bulat negatif ditunjukkan oleh nomor 1, yaitu hutang Andi Rp5.000.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Hasil operasi hitung yang bukan bilangan bulat ditunjukkan oleh nomor 4, yaitu 7,5 kg pupuk.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Hasil operasi hitung yang termasuk bilangan bulat ditunjukkan oleh nomor 1, 2, dan 3.<\/span><\/li>\n<\/ol>\n<h2><strong>Contoh Soal 2<\/strong><\/h2>\n<p><span style=\"font-weight: 400;\">Seorang penjahit mengukur lingkar pinggang enam orang pelanggannya dan diperoleh hasil sebagai berikut.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Gina = 76<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Roni = 84<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Mega = 76,4<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Syahrial = 86<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Jeni = 73,4<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Diah = 80<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Dari data di atas, panjang lingkar pinggang yang termasuk bil. bulat dan yang tidak termasuk bil. bulat adalah\u2026.<\/span><\/p>\n<p><strong>Pembahasan:<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">Pelanggan yang panjang lingkar pinggangnya termasuk bil. bulat adalah Gina, Roni, Syahrial, dan Diah. Sementara itu, untuk Mega dan Jeni panjang lingkar pinggangnya berupa bilangan desimal (bukan bil. bulat).<\/span><\/p>\n<h2><strong>Contoh Soal 3<\/strong><\/h2>\n<p><span style=\"font-weight: 400;\">Tentukan bil. bulat yang terletak antara -7 dan 8 menggunakan garis bilangan!<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Pembahasan:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Berikut ini adalah bilangan bulat antara -7 dan 8.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-289936\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/bilangan-bulat-b.png\" alt=\"\" width=\"524\" height=\"96\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/bilangan-bulat-b.png 524w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/06\/bilangan-bulat-b-300x55.png 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Jadi, yang terletak antara -7 dan 8 adalah -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Itulah pembahasan Quipper Blog tentang bilangan bulat dan contohnya. Semoga bermanfaat buat Quipperian dan tentunya bikin makin semangat belajar, ya. Kalau kamu ingin dapat materi-materi lainnya, buruan <\/span><em><span style=\"font-weight: 400;\">kepoin<\/span><\/em> <a href=\"https:\/\/subscribe.quipper.com\/signup\"><strong>Quipper Video<\/strong><\/a><span style=\"font-weight: 400;\"> karena dijamin <\/span><em><span style=\"font-weight: 400;\">gak<\/span><\/em><span style=\"font-weight: 400;\"> bakal <\/span><em><span style=\"font-weight: 400;\">nyesel<\/span><\/em><span style=\"font-weight: 400;\">. Buruan daftar dan dapetin promo terbaiknya! Salam Quipper!<\/span><\/p>\n<p><strong>Penulis: Eka Viandari<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Halo Quipperian, apa kabar? Semoga tetap semangat belajar ya, meskipun pandemi Covid-19 belum juga berakhir. Selama belajar dari rumah, pelajaran apa sih yang paling&hellip;<\/p>\n","protected":false},"author":99400369,"featured_media":289938,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[679384888,679384865],"tags":[679386248],"ppma_author":[679386827,679386836],"class_list":["post-289934","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mapel","category-matematika","tag-matematika-kelas-7"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Materi Bilangan Bulat Lengkap dengan Contoh Soal - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Bilangan bulat adalah semua bilangan yang tidak dalam bentuk pecahan atau desimal. 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