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.

Addition of Decimal Numbers

  • 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:

Add 27.0, 2.60 and 14.25

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

__________

Stay tuned to BYJU’S for more information on NIOS, syllabus, notes, along with its important questions and solutions.

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