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Giải Bài 44 trang 24 sách bài tập toán 7 tập 1 - Cánh diều

Chữ số thập phân thứ 221 sau dấu “,” của số hữu tỉ

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Đề bài

Chữ số thập phân thứ 221 sau dấu “,” của số hữu tỉ \(\dfrac{1}{7}\) được viết dưới dạng số thập phân vô hạn tuần hoàn là chữ số nào?

Phương pháp giải - Xem chi tiết

Muốn xác định chữ số thập phân thứ 221 sau dấu “,” ta cần xác định được chu kì tuần hoàn của số hữu tỉ đã cho.

Lời giải chi tiết

Ta có: \(\dfrac{1}{7} = 1:7 = 0,142857142857... = 0,(142857)\).Số hữu tỉ \(\dfrac{1}{7}\) có chu kì tuần hoàn là (142857) gồm 6 chữ số.Mà \(221:6 = 36\) (dư 5) hay \(221 = 6.36 + 5\).Suy ra: chữ số thập phân thứ 221 là chữ số thứ 5 trong chu kì tuần hoàn của số hữu tỉ \(\dfrac{1}{7}\).Vậy chữ số thập phân thứ 221 sau dấu “,” của số hữu tỉ \(\dfrac{1}{7}\) được viết dưới dạng số thập phân vô hạn tuần hoàn là chữ số 5. 

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