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Converting multi-digit repeating decimals to fractions
Description
Exercise Name: Converting multi-digit repeating decimals to fractions
Math Missions: 8th grade (U.S.) Math Mission, Algebra I Math Mission, Mathematics II Math Mission
Types of Problems: 1

The Converting multi-digit repeating decimals to fractions exercise appears under the 8th grade (U.S.) Math Mission, Algebra I Math Mission and Mathematics II Math Mission. This exercise practices converting between repeating decimals and their corresponding fraction form.

## Types of Problems

There is one type of problem in this exercise:

1. Change into a fraction: This problem provides a repeating decimal. The user is asked to take the repeating decimal and change it into a fraction.

## Strategies

Knowing how to convert quickly from fractions into decimal can provide insight here for how to work backwards.

1. A decimal that repeats over n-spots will be an "over ${10^n-1}$" answer. For example, ${0.232323... = \frac{23}{99}}$.
2. The fraction answers need to be simplified, so ${\frac{1}{3}}$ is correct but ${\frac{3}{9}}$ is not.

## Real-life applications

1. Connections between fractions and decimals help in many scientific approximation applications.