## Terminating Decimals and Non-Terminating Decimals

When we want to convert a fraction into a decimal form, we generally divide the numerator by the denominator till the remainder becomes zero. In some cases, we obtain zero as remainder but in other cases, the non-zero remainder is obtained.

Let us convert the following fractions into the decimal form.

1. 15/20 2. 1/8

We observe that on division, remainder zero is obtained. Such fractions which gives zero as a remainder on division are called

**terminating decimals**.Now, let us take some more examples and convert them into decimals.

1. 10/9 2. 13/6

Thus, we observe that on division, we get non-zero remainder infinitely. Such decimal are called

**non-terminating decimals**.If in a non-terminating decimal, a digit or a group of digits is repeating again and again, then the decimal is called the

**non-terminating repeating (recurring) decimal**.## Converting a Terminating Decimal to a Vulgar Fraction

To convert a terminating decimal into a vulgar fraction, we put 1 in the denominator and add as many zeroes as the number of digits after decimal.

**Example:**Convert the following decimals into fractions.

a. 0.7 b. 6.75

**Solution:**

a. 0.7 = 7/10 b. 6.75 = 675/100

## Converting a Non-terminating Repeating Decimal to a Vulgar Fraction

To convert a non-terminating repeating

**(**recurring) decimal into a vulgar fraction, look at the following example.**Example:**Convert the following decimals into vulgar fractions.

a. 0.777777….. b. 0.262626…...

**Solution:**

a. Let x = 0.777777….. (1)

Multiply equation (1) by 10, we get

10x = 7.777777…… (2)

Subtracting equation (1) from (2), we get

9x = 7

x = 7/9

b. Let x = 0.262626…... (1)

Multiply equation (1) by 100, we get

100x = 26.262626…… (2)

Subtracting equation (1) from (2), we get

99x = 26

x = 26/99

**Related Topics:**