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Bài tập 2 trang 51 Tài liệu dạy – học Toán 7 tập 1

Giải bài tập Viết các số sau dưới dạng số thập phân vô hạn tuần hoàn. Giải thích tại sao.
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Đề bài

Viết các số sau dưới dạng số thập phân vô hạn tuần hoàn. Giải thích tại sao. \({1 \over 7};\,\,{1 \over {11}};\,\,{3 \over {13}};\,\, - {5 \over {12}}\)

Phương pháp giải - Xem chi tiết

Các phân số tối giản với mẫu dương và mẫu có ước nguyên tố khác 2 và 5 nên các phân số ấy viết được dưới dạng số thập phân vô hạn tuần hoàn.

Lời giải chi tiết

\({1 \over 7} = 0,(142857);{1 \over {11}} = 0,(09);{3 \over {13}} = 0,(230769); - {5 \over {12}} =  - 0,41(6)\)Các phân số đã cho là các phân số tối giản với mẫu dương và mẫu có ước nguyên tố khác 2 và 5 nên các phân số ấy viết được dưới dạng số thập phân vô hạn tuần hoàn.

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