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 !!