Question

Express the repeating decimal 2:1 as a fraction.

10
20
9
19
9
19
8
12

Answer 1

To express the repeating decimal 2:1 as a fraction, we can use the concept of infinite geometric series. The fraction that represents the repeating decimal 2:1 is 19/9.

Step-by-step explanation:

To express the repeating decimal 2:1 as a fraction, we can use the concept of infinite geometric series. Let's represent the repeating decimal as x:

x = 2.111111...

Multiplying x by 10, we can obtain:

10x = 21.111111...

Subtracting the equation x = 2.111111... from 10x = 21.111111..., we can eliminate the repeating part:

10x - x = 21.111111... - 2.111111...

Simplifying, we have:

9x = 19

So, the fraction that represents the repeating decimal 2:1 is 19/9.

Learn more about Repeating decimals