**Decimal fractions** are the fractions whose denominator is 10 or higher powers of 10, like 100, 1000, 10000, etc. For example 1/10, 1/100, 1/1000, are fractions in decimal. If we simplify such fractions, we can write them in the decimal form such as 0.1, 0.01, 0.001, etc. It is easy to solve mathematical problems, such as dividing fractions, using this decimal form.

A fraction represents a part of the whole. For example, it tells how many slices of a pizza left or eaten with respect to the whole pizza-like, one-half, three-quarters. Generally, a fraction has two parts i.e. the numerator and the denominator. A decimal fraction is a fraction where its denominator is a power of 10 i.e. 101,102, 103 etc.

**For example:** 32/10,56/100,325/1000. It can be expressed as a decimal like 32/10=3.2,56/100=0.56.

We can perform all arithmetic operations on fractions by expressing them as a decimal. Letâ€™s practice some word problems on decimal fractions by using various arithmetical operations.

## Decimal Fractions Example Problems

**Example 1: ****A barrel has 56.32 litres capacity. If Supriya used 21.19 litres how much water is left in the barrel.**

**Solution: **Given,

Capacity of the barrel = 56.32 liters

Amount of water used= 21.19 liters

Amount of water left in the barrel = 56.32 â€“ 21.19 = 35.13 liters

**Example 2: ****Megha bought 12 bags of wheat flour each weighing 4563/100 Â kg. What will be the total weight?**

**Solution: Â **Total no. of bags = 12

Weight of each bag = Â 4563/100 kg = 45.63 kg

Total weight =45.63 x 12=547.56 kg

**Example 3: ****If circumference of a circle is 16.09 cm. What will be its diameter(Ï€=3.14)?**

**Solution: **Given, circumference = 16.09 cm

Circumference of a circle, C=2Ï€r

\(\Rightarrow 16.09 = 2 \pi r\)

\(\Rightarrow 16.09 = 2 \times 3.14 \times r\)

\(\Rightarrow r = \frac{16.09 \times 100}{6.28 \times 100}\)

\(\Rightarrow r = 2.56 \) cm

Therefore Diameter = 2r = 2 x 2.56 = 5.12 cm.

**Example 4:** **If the product of 38.46 and another number is 658.17, what is the other number?**

**Solution: **Given,

One number = 38.46

Product of two numbers = 658.17

The other number = 658.17Ã·38.46

= \(\frac{658.17}{100}\div \frac{38.46}{100}\)

= 17.11

**Example 5: ****Rakesh bought a new. Â He went on a road trip of 165.9 km on bike. After a week he went for another trip of 102.04 km. What will be the reading on meter reader of the bike?**

**Solution: **Given,

Distance travelled on first trip = 165.9 km

Distance travelled on second trip = 102.04km

Total distance travelled = 165.9 + 102.04 = 267.94 km

### Numerator and Denominator of Fractions

As we already know, the fractions are the parts of something whole. It is represented as a/b, where a and b are the integers. The integer above the bar is the numerator and below the bar is the denominator.

The numerator states the number that is equal parts and denominator states the number of parts of a given number. Let us see here some of the conditions for fractions:

- If numerator and denominator have equal values then the fraction is 1.
- If numerator is equal to 0, then the fraction is 0.
- If denominator is equal to 0, then the fraction goes to infinity.
- A decimal fraction is known as a recurring decimal when the digit after the decimal keeps on repeating.

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