In this article, you will learn about the Decimal and Fractional Expansion of a Decimal Number. Before Proceeding further know the definitions of Decimal, Fraction, and the Place Value Chart. A Decimal is any number in the base 10 number system and is used to separate units place from tenths place in decimal. The decimal point present in between separates the Whole Number Part and Decimal Part.

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### Decimal Expansion of a Number

Decimal Expansion of a Number is its representation in the base-10 system. In this System, each decimal place consists of digits 0-9 arranged such that each digit is multiplied by a power of 10 decreasing from left to right and a decimal place with 10^0 is the one’s place.

Decimal Expansion of Number 1423.25 is defined as

1423.25 = 1*10^{3}+4*10^{2}+2*10^{1}+3*10^{0}+2*10^{-1}+5*10^{-2}

= 1000+400+20+3+0.2+0.05

Decimal Expansion of a Number may terminate and in such case, the number is called a regular number or finite decimal. At times, the Decimal Expansion of a Number may become periodic and in such case, it is called a repeating decimal. However, the expansion may continue infinitely without repeating and it is called an irrational number.

### Fractional Expansion of Decimals

In the Expanded Form of Decimal Fractions, you will learn how to read and write the Decimal Numbers. Decimal Numbers can be written in expanded form using the Place Value Chart.

Let us understand the same by considering an example

384.264

384.264 = 3 × 100 + 8 × 10 + 4 × 1 + 2 × \(\frac { 1 }{10 } \) + 6 × \(\frac { 1 }{100 } \) + 4 × \(\frac { 1 }{1000 } \)

= 300+80+4+\(\frac { 2 }{10 } \)+\(\frac { 6 }{100 } \)+\(\frac { 4 }{1000 } \)

### Solved Examples on Decimal and Fractional Expansion

1. Write the decimal and fractional expansion of 334.252?

Solution:

In Decimal Expansion

334.252 = 3*100+3*10+4*1+2*\(\frac { 1 }{10 } \)+5*\(\frac { 1 }{100 } \)+2*\(\frac { 1 }{1000 } \)

= 300+30+4+\(\frac { 2 }{10 } \)+\(\frac { 5 }{100 } \) + \(\frac { 2 }{1000 } \)

= 300+30+4+0.2+0.05+0.002

In Fractional Expansion

= 3*100+3*10+4*1+2*\(\frac { 1 }{10 } \)+5*\(\frac { 1 }{100 } \)+2*\(\frac { 1 }{1000 } \)

= 300+30+4+\(\frac { 2 }{10 } \)+\(\frac { 5 }{100 } \) + \(\frac { 2 }{1000 } \)

2. Write the decimal and fractional expansion of 543.32?

Solution:

In Decimal Expansion

543.32 = 5*100+4*10+3*1+3*\(\frac { 1 }{10 } \)+2*\(\frac { 1 }{100 } \)

= 500+40+3+\(\frac { 3 }{10 } \)+\(\frac { 2 }{100 } \)

= 500+40+3+0.3+0.02

In Fractional Expansion

= 5*100+4*10+3*1+3*\(\frac { 1 }{10 } \)+2*\(\frac { 1 }{100 } \)

= 500+40+3+\(\frac { 3 }{10 } \)+\(\frac { 2 }{100 } \)

3. Write the Decimal and Fractional Expansion of 647.345?

Solution:

In Decimal Expansion

647.345 = 6*100+4*10+7*1+3*\(\frac { 1 }{10 } \)+4*\(\frac { 1 }{100 } \)+5*\(\frac { 1 }{1000 } \)

= 600+40+7+\(\frac { 3 }{10 } \)+\(\frac { 4 }{100 } \)+\(\frac { 5 }{1000 } \)

= 600+40+7+0.3+0.04+0.005

In Fractional Expansion

647.345 = 6*100+4*10+7*1+3*\(\frac { 1 }{10 } \)+4*\(\frac { 1 }{100 } \)+5*\(\frac { 1 }{1000 } \)

= 600+40+7+\(\frac { 3 }{10 } \)+\(\frac { 4 }{100 } \)+\(\frac { 5 }{1000 } \)

### FAQ’s on Decimal and Fractional Expansion

**1. What is Decimal in Expanded Form?**

Expanded form notation for the decimal numbers is the mathematical expression that shows the sum of the values of each digit in the number.

**2. What is the Decimal Expansion of Number 164.38?**

Decimal Number 164.38 can be written in expanded form by writing it as the sum of the place value of all the digits i.e. 1*100+6*10+4*1+3*\(\frac { 1 }{10 } \)+8*\(\frac { 1 }{100 } \) = 100+60+4+0.3+0.08

**3. What is the Fractional Expansion of Number 94.38?**

Fractional Expansion of Number 94.38 is 9*10+4*10+3*\(\frac { 1 }{10 } \)+8*\(\frac { 1 }{100 } \) which inturn results in 90+40+\(\frac { 3 }{10 } \)+\(\frac { 8 }{100 } \)