# Fractions and Repeating Decimals

Home | Online Math Tutoring | 8th Grade Math Tutoring | **Fractions and Repeating Decimals**

__Arithemetic & Pre Algebra__

**The Number System**

1) Rational and Irrational Numbers

2) Compare Irrational Numbers

3) Fractions & Repeating Decimals

4) Approximating Square Roots

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__Algebra__

**Expressions and Equations**

1) Exponents and their properties

2) Square roots and Cube roots

3) Scientific Notation – addition, subtraction, division & multiplication

4) Equations with variables on both sides

5) Linear equations with one, zero, or infinite solutions

6) Age Word Problems

7) Solve systems of linear equations with elimination and substitution

8) Word Problems on System of Linear Equations

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__Geometry__

1) Parallel Lines

2) Congruent Angles

3) Finding Angle Measures

4) Pythagorean Theorem

5) Distance Formula

6) Word problems on Volume of Cones, Cylinders, and Spheres

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__Statistics and Probability__

## Fractions and Repeating Decimals

We have already discussed how to convert a given fraction into the decimal form with terminating decimals, https://www.etutorworld.com/fractions-to-decimals.html. Here, we will try to understand how to convert a given fraction to repeating decimal.

- Now, we consider each of the above cases separately and understand them with examples.

### Terminating and non-repeating decimal

* Example 1:* ===0.5 or by long division method

So, we observe that in this case the **remainder is zero** and hence the long division terminates and given fraction has a **terminating & non-repeating decimal representation**.

### Non-terminating and repeating decimal.

#### **Example 2:** Consider

**Example 2:**Consider

*Example 3:* Consider

*Example 3:*

**non-terminating & repeating decimal representation**.

So decimal representation of = 0.83333… and this repetition is denoted by putting a bar over the repeated number i.e. = 0.83333… =

From the above examples, we see that the decimal representation of a fraction is non-terminating and repeating if its long division does not terminate & we have the same remainder, which cannot be exactly divided by the divisor.

### CHECK POINT

Convert the following fractions to their decimal form and identify whether it is a repeating decimal or not.

##### Answer Key

__Arithemetic & Pre Algebra__

**The Number System**

1) Rational and Irrational Numbers

2) Compare Irrational Numbers

3) Fractions and Repeating Decimals

4) Approximating Square Roots

__Algebra__

**Expressions and Equations**

1) Exponents and their properties

2) Square roots and Cube roots

3) Scientific Notation – addition, subtraction, division and multiplication

4) Equations with variables on both sides

5) Linear equations with one, zero, or infinite solutions

6) Age Word Problems

7) Solve systems of linear equations with elimination and substitution

8) Word Problems on System of Linear Equations

__Geometry__

1) Parallel Lines

2) Congruent Angles

3) Finding Angle Measures

4) Pythagorean Theorem

5) Distance Formula

6) Word problems on Volume of Cones, Cylinders, and Spheres

__Statistics and Probability__

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