# Decimals

A decimal is a fraction with denominator 10, 100 or multiples of 10.

A point used or written before any number to represent its tenth or hundredth is called a decimal representation.

In decimals,

$$\begin{array}{l}\frac{1}{10} \end{array}$$
is written as 0.1.

Similarly,

$$\begin{array}{l}\frac{1}{100} \end{array}$$
= 0.01

$$\begin{array}{l}\frac{1}{100} \end{array}$$
= 0.001

## How to write fractions in the form of a decimal.

If the denominator of a fraction is 10, place the decimal before the numerator by leaving one place from right to left.

For example:

$$\begin{array}{l}\frac{1}{10} \end{array}$$
is written as 0.1

$$\begin{array}{l}\frac{2843}{10} \end{array}$$
is written as 284.3

If the denominator is 100, place a decimal point before the numerator by leaving two places from right to left.

For example:

$$\begin{array}{l}\frac{1}{100} \end{array}$$
is written has 0.01

$$\begin{array}{l}\frac{145}{100} \end{array}$$
is written has 1.45

If the denominator is 1000, place a decimal before the numerator by leaving three places from right to left.

### Place Value of Decimals

• The part of a decimal number on the right of the one’s place is called the decimal part.
• The place value of digits from the one’s place to the left becomes 10 times.
• The place value of digits to the right of one’s place decreases and becomes one-tenth of its value.
 Hundreds Tens Ones Decimal One tenth (1/10) One hundredth (1/100) One Thousandth (1/1000) 7 4 3 . 1 6 1 4 0 . 3 1 4 3 3 . 0 4 5 3 1 4 . 7 2 1 2 0 . 0 0 1

In words:

743.161 is written as seven hundred forty-three decimal one six one.

40.314 is written as forty decimal three one four.

33.045 is written as thirty-three decimal zero four five.

314.720 is written as three hundred fourteen decimal seven two zero.

120.001 is written as one hundred twenty decimal zero zero zero one.

### Convert Fractions Into Decimals And Decimals Into Fractions

For converting decimals into fractions:

• Put the number as a numerator of a fraction.
• Count the number of digits on the right side of the decimal and put as many ‘0’ in the denominator to the right side of 1.

For example:

0. 3 =

$$\begin{array}{l}\frac{3}{10} \end{array}$$

7.055 =

$$\begin{array}{l}\frac{7055}{1000} \end{array}$$

For converting fractions into decimals:

For example:

$$\begin{array}{l}\frac{145}{100} \end{array}$$
= 1.45

Convert a fraction into decimals by dividing the numerator by denominator:

For example:

$$\begin{array}{l}\frac{4}{5} \end{array}$$
= 0.8

• Divide the numerator 4 by 5
• 4 is not divisible by 5, hence the quotient is 0
• Put ‘0’ after decimal, in the dividend 4.
• Now divide by 5 to get 8 or 0.8.

### Addition, Subtraction, Multiplication and Division of a Decimal Number.

• While adding, decimal points should be in a lineup/down.
• When there is one digit after the decimal point in a number, then we can put ‘0’ after this, if need be, to make the number of places equal.

For example:

 1 Carryover 2 7 . 0 2 . 6 0 1 4 . 2 5 4 3 . 8 5

Subtraction of Decimal Numbers

While subtracting, we start subtraction from the rightmost digit with the least place value.

For example:

Subtract 54.275 and 25.25

 4 14 Borrowing 5 4 . 2 7 5 2 5 . 2 5 2 9 . 0 2 5

Multiplication of a Decimal Number

• Write the decimal number as per place value positions.
• Place a decimal between the whole and the decimal part.
• Start multiplying with the rightmost digit of the least place value.
• Place the decimal point in the product, as per the decimal number.

For example:

2015.75 * 5 = ____.

2015.75

* 5

_________

10078.35

_________

Division of a Decimal Number

• The same standard division procedure is followed for division in decimals.
• In the decimal, the tenth part is written after the decimal point. Hence, the quotient will be written after putting a decimal point.

For example:

158.44 ÷ 4 = ____.

4 ) 158.44 ( 39.61

– 12

__________

38

– 36

__________

24

– 24

__________

4

– 4

__________

0

__________

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