Question

Viết các số thập phân vô hạn tuần hoàn sau dưới dạng phân số:

7,1(18)

0,01(6)

Answer 1

7,1(18)=\(\dfrac{1}{10}\).71,(18)

= \(\dfrac{1}{10}\).[71+0,(18)]

=\(\dfrac{1}{10}\).[71+\(\dfrac{1}{99}\).18]

= \(\dfrac{1}{10}\).[71+\(\dfrac{2}{11}\)]

= \(\dfrac{1}{10}\).\(\dfrac{783}{11}\)

= \(\dfrac{783}{110}\)

0,01(6)=\(\dfrac{1}{100}\).1,(6)

= \(\dfrac{1}{100}\).[1+0,(6)]

= \(\dfrac{1}{100}\).[1+\(\dfrac{1}{9}\).6]

= \(\dfrac{1}{100}\).[1+\(\dfrac{2}{3}\)]

= \(\dfrac{1}{100}\).\(\dfrac{5}{3}\)

= \(\dfrac{1}{60}\)

Answer 2

7,1(18)=7+0,1(18)=7+\(\dfrac{118-1}{990}\)

=7+\(\dfrac{13}{110}\)=\(\dfrac{783}{110}\)

0.01(6)=\(\dfrac{16-1}{900}=\dfrac{15}{900}=\dfrac{1}{60}\)

Answer 3

7,1(18)=

0,01(6)=6/9878