Converting a Mixed Number to a Terminating Decimal - Basic

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Introduction

As we have already learnt, a mixed number has a whole number part and a proper fraction part.

Rules to convert a mixed number to a terminating decimal.

• We first take the whole number part of the mixed number and make it the whole number part of the decimal number.

• We next take the fractional part of mixed number and set it up as a long division and obtain its decimal value.

• The decimal value obtained above becomes the decimal part of the decimal number.

• For example, in $1 \frac{1}{4}, \: \frac{1}{4} = 0.25$, whole number part 1 of mixed number is retained in decimal number. So, $1 \frac{1}{4} = 1.25$

Example 1

Convert $2 \frac{2}{5}$ into a terminating decimal.

Solution

Step 1:

We retain the whole number part of the mixed number and do long division on the fractional part $\frac{2}{5}$, dividing 2 by 5.

Step 2:

We find that $\frac{2}{5} = 0.4$

Step 3:

So, the decimal has a whole number part 2 and a decimal part 0.4.

Step 4:

So, $2 \frac{2}{5} = 2.4$

Example 2

Convert $13 \frac{5}{8}$ into a terminating decimal.

Solution

Step 1:

We retain the whole number part of the mixed number 13 and do long division on the fractional part $\frac{5}{8}$, dividing 5 by 8

Step 2:

We find that $\frac{5}{8} = 0.625$

Step 3:

So, the decimal has a whole number part 13 and a decimal part 0.625

Step 4:

So, $13 \frac{5}{8} = 13.625$