Decimals:

The value of a fraction with 10 or multiple of 10 as a denominator is called decimal.

Structuring a Decimal

Basics: The decimal always consists of two parts, the whole number and decimal part. These two parts are divided by a decimal point.

For example, 21.3456 is a decimal with 21 as a whole number and 3456 as a decimal part.

Fractions and Decimals

Any decimal can be converted into its equivalent fraction. Let us assume a decimal has number of digits in its decimal part. In order to convert it to its equivalent fraction, we simply multiply and divide the decimal by \(10^n\) .

For example, In order to convert 21.3456 into its equivalent fraction, we multiply and divide the decimal by \(10^4\). As it has 4 digits in its decimal part. Hence, its equivalent fraction is \(\frac{213456}{10000}\).

Keep in mind:

For simplicity, to convert a decimal to its equivalent fraction, we just remove the decimal point and put 1 followed by \(n\) number of zeros. Here, \(n\) is the number of digits in decimal part.

In the same way, any fraction can be converted to its equivalent decimal, by finding the fraction's value.

Keep in mind:

In order to convert a fraction with the denominator of the power of 10s, we simply add a decimal point after \(n\) number of digits, Counting from right. Here, \(n\) is the number of zeros in the denominator.

For example, In order to convert \(\frac{2154}{1000}\) to its equivalent decimal, we just add a decimal point after 3 digits, counting from right.

Recurring Decimal

A recurring decimal consists of a repeating decimal part. For example, decimal equivalent of the fraction \(\frac{1}{3}\) is 0.333... with \(3\) repeating forever. In the same way, the value of fraction \(\frac{1}{13}\) is, 0.076923076923... Here, the repeating part is a set of 6 digits 076293. These decimals are represented using bar on recurring on recurring digits and read as, zero point three bar.

Decimals and Exponents !!