4.5.2 Repeating Decimals in Reverse

Instead of converting decimals to fractions, these problems give you a fraction and ask for the first few digits of the decimal.

Example: 23/90

The denominator 90 means the repeating fraction is in the form $.abbb\dots$

Find $a$ and $b$ such that $ab - a = 23$ (where $ab$ is a two-digit number)

Solution: $ab = 25$ , so the answer is 2555

Example: 17/45

The denominator has been reduced by 2, so multiply by 2/2:

\frac{17}{45} = \frac{34}{90} \Rightarrow ab - a = 34 \Rightarrow ab = 37

Answer: 3777

Practice these problems. Type your answer and press Enter to check:

First 4 digits of 16/90 = 0.

First 3 digits of 13/33 = 0.

First 4 digits of 17/45 = 0.

First 4 digits of 17/90 = 0.

First 4 digits of 43/90 = 0.

First 4 digits of 11/45 = 0.

First 4 digits of 31/90 = 0.

First 4 digits of 71/330 = 0.

First 3 digits of 42/99 = 0.

First 4 digits of 13/45 = 0.