Decimal Fraction – Definition, Operations and Solved Examples

Introduction to Decimal Fraction

A decimal fraction is a number that is expressed as a fraction of 10. In other words, a decimal fraction is a number that is written as a number over 10 (with a decimal point in the middle). For example, the decimal fraction 0.5 can be written as 5/10.

The Right Way to Study about Decimals

To study decimals, it is important to understand what they are and how they work. Decimals are a part of mathematics that deal with fractions and percentages. They are used to represent numbers that are not whole numbers. In order to understand decimals, it is important to first understand fractions. Fractions are numbers that are divided into two parts. The top number is the numerator and the bottom number is the denominator. In a fraction, the numerator is always larger than the denominator. In a decimal, the numerator is always smaller than the denominator.

Decimals can be written in two ways. They can be written as a fraction with a decimal point in the numerator and denominator. For example, 0.5 can be written as 1/2. They can also be written as a decimal number. For example, 0.5 can be written as 0.5. In order to convert a fraction to a decimal, divide the numerator by the denominator. In order to convert a decimal to a fraction, divide the numerator by the denominator.

There are a few basic rules that apply to decimals. The first is that decimals always have a decimal point. The second is that the numbers to the right of the decimal point are always tenths, hundredths, thousandths, etc. The third is that when you are adding or subtracting decimals, the decimal point

What is Decimal Fraction?

A decimal fraction is a fraction in which the denominator is 10. For example, the fraction 3/10 is a decimal fraction. The number 3 is the numerator and 10 is the denominator.

Operations on Decimal Fractions:

Addition:

To add two decimal fractions, line the two fractions up vertically and add the numerators (top numbers) together. Then, add the denominators (bottom numbers) together. Finally, place the decimal point in the answer directly above the point in the problem that has the least number of digits.

For example, to add the fractions ¾ and 2/9, line them up vertically like this:

3/4 + 2/9 = 5/13

Then, add the numerators together: 3 + 2 = 5

Then, add the denominators together: 4 + 9 = 13

So, the answer is 5/13.

How to convert Decimal to Fraction

To convert a decimal to a fraction, divide the decimal number by 1 followed by the number of decimal places in the decimal number.

Operations on Decimal Fractions:

• Addition and Subtraction of Decimal Fractions:

The given Numbers are so placed under each other that the Decimal points lie in one column below one another. The Numbers are now added or subtracted in the regular way.

For example: add 0.007 and 3.002

0. 0 0 0 7

+ 3. 0 0 0 2

____________________

3. 0 0 0 9

• Multiplication of a Decimal Fraction:

When a Decimal Fraction is multiplied by the powers of 10, shift the Decimal point to the right by as many places as is the power of 10.

For example, 5.9632 x 1000 = 5963.2;

0.073 x 1000 = 730.

Multiply the given Numbers without a Decimal point. Now, in the product, the Decimal point is marked as many places of Decimal as is the sum of the Number of Decimal places in the given Numbers.

For example: we have to find the product 0.2 x 0.02 x 0.0002

Consider the Number without Decimal points

Now, 2 x 2 x 2 = 8.

Sum of Decimal places = (1 + 2 + 4) = 7.

Thus mark the Decimal point 7 places to the left that will be 0.0000008

.2 x .02 x .002 = .0000008

• Dividing a Decimal Fraction By a Counting Number:

Divide the given Number without the Decimal point, by the given Number. Now, in the quotient, mark the Decimal point as many places of Decimal as there are in the dividend.

For Example we have to find the quotient for 0.0204 ÷ 17

Now, 204 ÷ 17 = 12.

Dividend contains 4 places of Decimal.

So, 0.0204 ÷ 17 = 0.0012

• Dividing a Decimal Fraction By a Decimal Fraction:

Multiply both the dividend and the divisor by a suitable power of 10 to make the divisor a whole Number.

Now, proceed as above.