# Decimal

Decimal number is a number with a dot known as decimal point.

## Definition

A decimal number is a number having a whole number part and a fractional part separated by a decimal point.

We understand a decimal number elaborately by understanding each digit according to their place value.

Suppose we have a larger decimal number such as 724.365.

Thus joining the whole number and fractional part, we get the complete decimal number as shown below.

## Writing Decimals

### In Expanded Form

We read a decimal number by its expanded form based on the place value of each digit in it. The fractional part in a decimal number represents the values according to the decimal place value chart.

We read a decimal number by the place values of all the digits in it.

For example, in the decimal number 6234.7815, in the whole number part, 6 is at the 1000s. In the fractional part, 5 is at the 10,000ths place.

That means 6 represents 6000, and 5 represents 0.0005

### In Words

We can write the above number

For example, the number, 24.7 means ‘twenty-four and seven-tenths’.

If the number is 10 times smaller, the point shifts towards left. And, if the number is 10 times larger, the point shifts towards right.

Suppose 24.7 gets 10x smaller, it means it has to be divided by 10.

So, 24.7/10 = 2.47

The decimal point shifts to the left of 4 here.

If 2.47 gets 10x larger, means it has to be multiplied by 10.

So, 24.7 × 10 = 24.7

The decimal point shifts to the right of 4 here.

Write ‘fifty-five and three-tenths’ in decimal form.

Solution:

As we know,
Three-tenths is 3/10 = 0.3
And fifty-five is the whole number.
∴ 55 + 0.3 = 55.3
So, fifty-five and three-tenths = 55.3

Write ‘sixty-eight and thirty-seven-hundredths in decimal form.

Solution:

As we know,
Thirty-seven-hundredths is 37/100 = 0.37
And sixty-eight is the whole number.
∴ 68 + 0.37 = 68.37
So, sixty-eight and thirty-seven-hundredths = 68.37

## Types of Decimals

Decimals are categorized based on the types of digits occurring after the decimal point.

### 1. Terminating Decimals

The digits after the decimal point do not reoccur in such decimals. The number ends after a finite number of decimal places. Example: 737.534, 65.2, etc.

### 2. Non-terminating Decimals

The digits are infinite after the decimal point in such decimals.

Example, 737.537269541…, 34.123123123…… etc. We can be further divide non-terminating decimals into 2 parts:

• Recurring Decimal numbers: In such decimals, digits repeat after a fixed interval. Example: 5.232323…., 34.123123123… etc.
• Non-recurring Decimal numbers: In such decimals, digits never repeat after a fixed interval. Example: 737.537269541………, 1.41421356237309504……… and so on.
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