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Giải bài 69 trang 47 sách bài tập Toán 6 – Cánh Diều Tập 2

Cho dãy số: 0,1;0,01;0,001;... a) Số hạng thứ 1 000 có bao nhiêu chữ số 0 ở phần thập phân? b) Để viết từ số hạng thứ nhất đến số hạng thứ 100 phải dùng bao nhiêu chữ số 1? Bao nhiêu chữ số 0?

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Đề bài

Cho dãy số: \(0,1;\;0,01;\;0,001;\;...\) a) Số hạng thứ 1 000 có bao nhiêu chữ số 0 ở phần thập phân? b) Để viết từ số hạng thứ nhất đến số hạng thứ 100 phải dùng bao nhiêu chữ số 1? Bao nhiêu chữ số 0?

Phương pháp giải - Xem chi tiết

a) Lập bảng liệt kê số chữ số 0 ở phần thập phân của các số trong dãy b) Mỗi số chứa 1 chữ số 1 nên số chữ số 1 là số các số Số hạng thứ n chứa n chữ số 0 nên tổng số chữ số 0 là tổng các số từ 1 đến 100

Lời giải chi tiết

a) Ta có bảng sau:

Số hạng thứ

Số thập phân

Số chữ số 0 ở hàng thập phân
1 0,1 0
2 0,01 1
3 0,001 2
… … …
1000 0,00…01 999
Vậy số hạng thứ 1000 có 999 chữ số 0 ở hàng thập phân.b) Từ số hạng thứ nhất đến số hạng thứ 100 cần dùng 100 chữ số 1 (mỗi số có một chữ số 1)Từ số hạng thứ nhất đến số hạng thứ 100 cần dùng 100 chữ số 0 là:\(1 + 2 +  \ldots  + 99 + 100 = (1 + 100).100:2 = 5050\)(chữ số 0)

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