Fractions and Repeating Decimals
Fractions and Repeating Decimals
We have already discussed how to convert a given fraction into the decimal form with terminating decimals, https://staging.etutorworld.com/fractions-to-decimals.html. Here, we will try to understand how to convert a given fraction to repeating decimal.
![fractions and repeating decimals](https://staging.etutorworld.com/wp-content/uploads/2018/12/fractions-1.jpg)
- 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
![fractions and repeating decimals](https://staging.etutorworld.com/wp-content/uploads/2018/10/fractions2-1-300x174-300x174.jpg)
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.
![fractions and repeating decimals](https://staging.etutorworld.com/wp-content/uploads/2018/10/fractions4-288x300-288x300.jpg)
Example 2: Consider ![\frac{1}{3}](https://chart.apis.google.com/chart?cht=tx&chl=%5Cfrac%7B1%7D%7B3%7D)
![fractions and repeating decimals](https://staging.etutorworld.com/wp-content/uploads/2018/12/fractions10.jpg)
Example 3: Consider ![\frac{5}{6}](https://chart.apis.google.com/chart?cht=tx&chl=%5Cfrac%7B5%7D%7B6%7D)
![fractions and repeating decimals](https://staging.etutorworld.com/wp-content/uploads/2018/10/fractions5-300x293-300x293.jpg)
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
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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