{"id":9244,"date":"2025-08-13T10:00:00","date_gmt":"2025-08-13T03:00:00","guid":{"rendered":"https:\/\/example.com\/?p=9244"},"modified":"2025-08-19T05:35:18","modified_gmt":"2025-08-18T22:35:18","slug":"matematika-kelas-7-mengenal-bilangan-rasional-dan-irasional","status":"publish","type":"post","link":"https:\/\/staging-blog.sirogu.com\/blog\/matematika-kelas-7-mengenal-bilangan-rasional-dan-irasional","title":{"rendered":"Mengenal Bilangan Rasional &#038; Irasional\u00a0| Matematika Kelas 7"},"content":{"rendered":"<p style=\"text-align: justify;\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/8856a44a-d0e0-456c-a2a4-1b4ce7656eab.png\" alt=\"perbedaan bilangan rasional dan irasional\" width=\"820\" \/><\/p>\n<blockquote>\n<p style=\"text-align: center;\"><em>Pada <strong><a href=\"https:\/\/www.ruangguru.com\/blog\/c\/matematika\/matematika-smp-kelas-7\">artikel Matematika kelas 7<\/a><\/strong> kali ini, kamu akan mengetahui apa itu bilangan rasional dan irasional, disertai contohnya. Yuk, pelajari bersama!<\/em><\/p>\n<p style=\"text-align: center;\">&#8212;<\/p>\n<\/blockquote>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Tentunya kamu sudah belajar tentang jenis-jenis bilangan Matematika sewaktu duduk di bangku sekolah dasar bukan? Hayo, siapa di antara kamu yang masih ingat apa saja jenis-jenis bilangan Matematika itu?<\/p>\n<p style=\"text-align: justify;\">Yup, benar! Ada <strong><a href=\"https:\/\/www.ruangguru.com\/blog\/pengertian-dan-contoh-bilangan-bulat\">bilangan bulat<\/a><\/strong>, bilangan cacah, bilangan asli, dan <strong><a href=\"https:\/\/www.ruangguru.com\/blog\/jenis-jenis-bilangan-pecahan\">bilangan pecahan<\/a><\/strong>. Ternyata, bilangan Matematika itu banyak macamnya, lho! Tidak hanya yang kamu pelajari di sekolah dasar saja, tapi ada juga yang namanya bilangan rasional dan bilangan irasional.<\/p>\n<p style=\"text-align: justify;\">Hmm, kira-kira apa ya bilangan rasional dan bilangan irasional itu? Seperti apa sih contohnya? Penasaran, kan? Kalau begitu, langsung saja yuk kita simak penjelasannya pada artikel di bawah ini!<\/p>\n<p>&nbsp;<\/p>\n<h2><span style=\"font-size: 18pt;\">Apa itu Bilangan Rasional?<\/span><\/h2>\n<p style=\"text-align: justify;\">Bilangan rasional adalah <strong>bilangan yang dapat diubah menjadi pecahan biasa<\/strong> (a\/b)\u00a0dan apabila bilangan ini <strong>diubah ke pecahan desimal<\/strong>, maka angkanya <strong>akan berhenti di suatu bilangan tertentu<\/strong>. Apabila <strong>tidak berhenti<\/strong>, maka akan <strong>membentuk pola pengulangan<\/strong>.<\/p>\n<p style=\"text-align: justify;\">Contoh bilangan rasional:<\/p>\n<div style=\"text-align: justify;\">\n<ul>\n<li style=\"text-align: justify;\">Pecahan biasa: \u00bd, \u00be, \u20135\/8<\/li>\n<li style=\"text-align: justify;\">Bilangan bulat: \u20133, 0, 7\u00a0 \u00a0(karena bisa ditulis sebagai \u20133\/1, 0\/1, 7\/1)<\/li>\n<li style=\"text-align: justify;\">Desimal: 0,25\u00a0 \u00a0(karena 0,25 = 25\/100)<\/li>\n<li style=\"text-align: justify;\">Desimal dengan pola berulang: 0,333\u2026 = 1\/3; 2,121212\u2026 = 212\/99<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<\/div>\n<h2 style=\"text-align: justify;\"><span style=\"font-size: 18pt;\">Apa itu Bilangan Irasional?<\/span><\/h2>\n<p style=\"text-align: justify;\">Berbeda dengan bilangan rasional, kalau bilangan irasional adalah bilangan yang <strong>tidak dapat diubah ke pecahan biasa<\/strong> dan apabila bilangan ini <strong>diubah ke pecahan desimal<\/strong>, maka <strong>angkanya tidak akan berhenti dan tidak memiliki pola tertentu<\/strong>.<\/p>\n<p style=\"text-align: justify;\">Contoh bilangan irasional:<\/p>\n<div style=\"text-align: justify;\">\n<ul>\n<li style=\"text-align: justify;\">\u221a2 = 1,414213562\u2026\u00a0 \u00a0(tak pernah habis dan tak berulang)<\/li>\n<li style=\"text-align: justify;\">\u221a3, \u221a5, \u221a7\u00a0 \u00a0(akar dari bilangan bukan kuadrat sempurna)<\/li>\n<li style=\"text-align: justify;\">\u03c0 (pi) = 3,14159265\u2026\u00a0 \u00a0(tak berakhir dan tak berulang)<\/li>\n<li style=\"text-align: justify;\">e (bilangan Euler) = 2,7182818\u2026<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<p><strong>Baca Juga: <a href=\"https:\/\/www.ruangguru.com\/blog\/perkalian-dan-pembagian-bilangan-bulat\">Operasi Perkalian dan Pembagian pada Bilangan Bulat<\/a><\/strong><\/p>\n<p>&nbsp;<\/p>\n<h2><span style=\"font-size: 18pt;\">Letak Bilangan Rasional dan Irasional pada Garis Bilangan<\/span><\/h2>\n<p style=\"text-align: justify;\">Agar lebih jelas, coba bayangkan sebuah garis bilangan yang memuat angka-angka di sisi kiri (negatif) dan kanan (positif), dengan nol (0) di tengah.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-medium\" src=\"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/da1f874e-46c4-49d2-a395-d22bc9982d0c.png\" alt=\"garis bilangan\" width=\"600\" \/><\/p>\n<p style=\"text-align: center;\">Contoh garis bilangan. (Sumber: roboguru.com)<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><strong>Bilangan rasional mudah<\/strong> sekali <strong>ditempatkan pada garis bilangan<\/strong> karena bisa ditulis dalam bentuk pecahan atau desimal yang pasti. Misalnya:<\/p>\n<ul>\n<li style=\"text-align: justify;\">\u00bd terletak di tengah antara 0 dan 1.<\/li>\n<li style=\"text-align: justify;\">\u2013\u00be ada di antara \u20131 dan 0, lebih dekat ke \u20131.<\/li>\n<li style=\"text-align: justify;\">2 dan 0 sudah jelas posisinya di angka bulat.<\/li>\n<li style=\"text-align: justify;\">3,25 berada sedikit setelah angka 3.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Nah, <strong>bilangan irasional juga ada di garis bilangan<\/strong>, hanya saja <strong>posisinya tidak bisa ditentukan secara tepat<\/strong> dengan pecahan sederhana. Misalnya:<\/p>\n<ul>\n<li style=\"text-align: justify;\">\u221a2 \u2248 1,414, artinya posisinya ada di antara 1,4 dan 1,5.<\/li>\n<li style=\"text-align: justify;\">\u03c0 \u2248 3,14159\u2026, posisinya ada sedikit lewat angka 3, sebelum mencapai 3,2.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Jadi, meskipun bilangan irasional tidak bisa dituliskan sebagai pecahan sederhana, bilangan ini tetap bisa \u201cdidekati\u201d dan ditempatkan di garis bilangan.<\/p>\n<p>&nbsp;<\/p>\n<h2><span style=\"font-size: 18pt;\">Contoh Soal dan Pembahasan<\/span><\/h2>\n<p style=\"text-align: justify;\">Bagaimana, paham ya sampai di sini? Nah, setelah kamu tahu apa itu bilangan rasional dan bilangan irasional, selanjutnya ayo kita latihan soal, ya. Nanti, jawabannya kita selesaikan bersama-sama. Oke?<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Contoh%20soal%20bilangan%20rasional%20dan%20irasional.png\" alt=\"Contoh soal bilangan irasional dan pembahasan\" width=\"600\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><strong>Penyelesaian:<\/strong><\/p>\n<p style=\"text-align: justify;\">Dalam menyelesaikan soal di atas, kita dapat menyaring setiap pilihan jawabannya. Dapat dipastikan bahwa bilangan irasional merupakan bilangan yang tidak dapat diubah ke bentuk pecahan biasa. Sehingga, opsi b dan d bukan merupakan jawabannya.<\/p>\n<p style=\"text-align: justify;\">Kemudian, tersisa opsi a dan c. Ternyata, opsi a juga bukan merupakan jawaban yang tepat karena akar dari 25 merupakan bilangan bulat, yaitu 5. Jadi, sudah pasti jawabannya itu c ya, karena hasil dari \u221a2 adalah 1,4142135623\u2026 yang angkanya tidak berhenti di suatu bilangan tertentu dan tidak berpola.<\/p>\n<p><strong>Baca Juga: <a href=\"https:\/\/www.ruangguru.com\/blog\/nilai-tempat-bilangan-bulat-dan-desimal\">Cara Menentukan Nilai Tempat Bilangan Bulat &amp; Bilangan Desimal<\/a><\/strong><\/p>\n<p style=\"text-align: center;\">&#8212;<\/p>\n<p style=\"text-align: justify;\">Wah, ternyata mudah ya untuk menentukan bilangan-bilangan yang tergolong jenis bilangan rasional dan bilangan irasional. Biasanya, untuk menuliskan bilangan irasional diperlukan pembulatan angka. Misalnya, 2 atau 3 angka di belakang koma, seperti\u00a0\u03c0\u00a0yang dibulatkan menjadi 3,14.<\/p>\n<p style=\"text-align: justify;\">Nah, bagi kamu yang ingin tahu lebih lanjut tentang materi ini, y<em>uk<\/em>, cobain download dan belajar bareng\u00a0<em>Master Teacher<\/em>\u00a0di ruangbelajar! Ada fitur konsep kilat yang bisa membantu kamu mempelajari ringkasan, dan juga video Adapto yang bisa menyesuaikan kemampuanmu menerima materi! Ayo, gabung belajar di\u00a0<strong><a href=\"https:\/\/www.ruangguru.com\/promo\">ruangbelajar<\/a><\/strong>!<\/p>\n<p><a href=\"https:\/\/bayar.ruangguru.com\/\"><img decoding=\"async\" class=\"aligncenter size-medium\" src=\"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/ceb472c4-1feb-4a1d-afdf-4f92234a63d0.jpg\" alt=\"CTA Ruangguru\" \/><\/a><\/p>\n<p style=\"text-align: justify;\"><strong>Referensi:<\/strong><\/p>\n<p style=\"text-align: left;\">As&#8217;ari A.R, Tohir M, Valentino E, Imron Z, Taufiq I. (2017) Matematika SMP\/MTs Kelas VII Semester I. Pusat Kurikulum dan Perbukuan, Balitbang, Kemendikbud.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pada artikel Matematika kelas 7 kali ini, kamu akan mengetahui apa itu bilangan rasional dan irasional, disertai contohnya. Yuk, pelajari bersama! &#8212; &nbsp; Tentunya kamu sudah belajar tentang jenis-jenis bilangan Matematika sewaktu duduk di bangku sekolah dasar bukan? Hayo, siapa di antara kamu yang masih ingat apa saja jenis-jenis bilangan Matematika itu? Yup, benar! Ada [&hellip;]<\/p>\n","protected":false},"author":73,"featured_media":9244,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_knawatfibu_url":["https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/8856a44a-d0e0-456c-a2a4-1b4ce7656eab.png"],"_edit_last":["1"],"_edit_lock":["1755556377:1"],"_wp_old_date":["2018-09-04"],"_aioseo_title":[null],"_aioseo_description":["Pada artikel Matematika kelas 7 kali ini, kamu akan mengetahui apa itu bilangan rasional dan irasional, disertai contohnya. 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