# Decimal Numbers

A decimal is one of the types of numbers, which has a whole number and the fractional part separated by a decimal point. The dot present between the whole number and fractions part is called the decimal point. For example, 34.5 is a decimal number. Here, 34 is a whole number part and 5 is the fractional part.

### Place Value of Decimals

The first digit after the decimal represents the tenths place. The next digit represents the hundredths place. The remaining digits continue to fill in the place values until there are no digits left.

In the number 627:

• the “7” is in the One’s position, meaning 7 ones (which is 7),
• the “2” is in the Tens position meaning 2 tens (which is twenty),
• and the “6” is in the Hundreds position, meaning 6 hundred.

#### Properties of Decimal Numbers

• Two decimal numbers are multiplied in any order, the product remains the same.
• If a whole number and a decimal number are multiplied in any order, the product remains the same.
• The decimal fraction is multiplied by 1, the product is the decimal fraction itself.
• If a decimal fraction is multiplied by 0, the product is zero (0).
• If a decimal number is divided by 1, the quotient is the decimal number.
• A decimal number is divided by the same number, the quotient is 1.
• If 0 is divided by any decimal, the quotient is 0.
• The division of a decimal number by 0 is not possible, as the reciprocal of 0 does not exist. What are Decimals?

In Algebra, decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point. The dot present between the whole number and fractions part is called the decimal point.

For example, 30.5 is a decimal number.

Here, 30 is a whole number part and 5 is the fractional part.

Let us discuss some other examples.

Here is the number “thirty-four and seven-tenths” written as a decimal number:

The decimal point goes between Ones and Tenths

34.7 has 3 Tens, 4 Ones, and 7 Tenths

#### Types of Decimal Numbers

Decimal Numbers may be of different kinds, namely

Recurring Decimal Numbers

Example:

3.125125 (Finite)

3.121212121212….. (Infinite)

Non-Recurring Decimal Numbers

Example:

3.2376 (Finite)

3.137654….(Infinite)

Decimal Fraction- It represents the fraction whose denominator in powers of ten.

Example:

81.75 = 8175/100

32.425 = 32425/1000

Converting the Decimal Number into Decimal Fraction:

For the decimal point place “1” in the denominator and remove the decimal point.

“1” is followed by several zeros equal to the number of digits following the decimal point.

For Example:

71 . 7 6

↓ ↓ ↓

1 0 0

81.75 = 8175/100

7 represents the power of 101 that is the tenths position.

1 represents the power of 10that is the unit’s position.

7 represents the power of 10-1 that is the one-tenth position.

6 represents the power of 10-2 that is the one-hundredths position.

So that is how each digit is represented by a particular power of 10 in the decimal number.