1. Recurring Decimals
Recurring Decimals are those numbers that keep on repeating the same value after a decimal point. These numbers are also called Repeating Decimals.
For example, 1/3 = 0.3¯ = 0.3333…
Fractions in which the denominator has prime factors of only 2 or 5 will terminate (not repeat).
1.1 How to convert recurring decimals to fractions?
Converting recurring decimals to fractions is representing a recurring decimal as a fraction without changing its value.
For example,
0.24¯ = 0.24242424…
0.123¯ = 0.123123123… are all examples of recurring decimals.
Let's check the following steps involved in converting Repeating Decimals to fractions.
- Let 'x' be the Repeating Decimal number that we want to convert into a rational number.
- Observe the Repeating Decimal to identify the repeating digits.
- Carefully place the repeating digits to the left of the decimal point.
- Place the repeating digits to the right of the decimal point.
- Now deduct the left sides of the two equations. Then, apply the subtraction on the right side of the two equations. As we subtract, always ensure the differences between both sides should be positive.
Example: Convert 0.7 (one recurring digit) into a fraction.
Solution:
Example: Prove algebraically 3.47777… = 313/90
Solution:
Example: Prove algebraically that 0.73333… can be written as 11/15.
Solution:
