Multiplication & Division of Decimals

Decimals

Multiplication of Decimals

1/10 of 1/10 = 1/10 × 1/10 = 1/100

⇒ 0.1 × 0.1 = 0.01

2/10 × 2/10 = 4/100

⇒ 0.2 × 0.2 = 0.04

2/10 × 3/10 = 6/100

⇒ 0.2 × 0.3 = 0.06

15/100 × 3/10 = \frac {15\times 3}{10\times 100}= 75/1000

⇒ 0.15 × 0.3 = 0.075

Rules for multiplying decimals

➤ Multiply the numbers normally as integers without decimal point.

➤ Add the number of digits after decimal points in decimals (let it be n).

➤ Put the decimal point in answer before n digits from right.

e.g., 2.5 × 3.75

→ 25 × 375 = 9375 ( without decimal point )

→ Number of digits after decimal points in decimals (n) = 1 + 2 =3

→ Put the decimal point before three digits from the right i.e. before 3 in 9375

→ 2.5 × 3.75 = 9.375

Multiplication of a Decimal Numbers by 10, 100 and 1000

When a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number but the decimal point in the product is shifted to the right by as many of places as there are zeros over one.

2.5 × 10 = 25.0

2.5 × 100 = 250.0

2.5 × 1000 = 2500.0

Division of Decimals

Change the decimals into fractions and then proceed,

→ 5.8 ÷ 2 = \frac{58}{10} \div 2 = \frac {58}{10} \times \frac {1}{2} (Multiplying with reciprocal)

= 58/20 = 29/10 = 2.9

→ 23.9 ÷ 10 = \frac {239}{10} \div 10 = \frac {239}{10} \times \frac{1}{10}

= 239/100 = 2.39

→ 19.9 ÷ 0.13 = \frac{199}{10} \div÷ \frac{13}{100}

= \frac{199}{10} \times \frac{100}{13}

= 19900/130 = 130

Division of a Decimal number by a Whole number

We first divide them as whole numbers. Then place the decimal point in the quotient as in the decimal number.

e.g., 9.6 ÷ 6 = 1.6

Division of a Decimal number by 10, 100 or 1000

Shift the digits in the decimal number to the left by as many places as there are zeros after 1, to get the quotient.

So, 63.9 ÷ 10 = 6.39,

63.9 ÷ 100 = 0 .639,

63.9 ÷ 1000 = 0.0639

Division of a Decimal by a Decimal

First shift the decimal point to the right by equal number of places in both, to convert the divisor to a whole number. No we can continue as dividing by the whole number.

e.g.,

2.4 ÷ 0.2

= 24 ÷ 2 (∵ 24/10 ÷ 02/10)

= 12,

0.242 ÷ 0.22

= 24.2 ÷ 22 (∵ 242/1000 ÷ 22/100)

= 1.1

Time to think

(1) Find: (i) 0.3 × 10

(ii) 1.2 × 100

(iii) 56.3 × 1000

(2) Find: (i) 235.4 ÷ 10

(ii) 235.4 ÷100

(iii) 235.4 ÷ 1000

(3) (i) 43.15 ÷ 5 = ?;

(ii) 82.44 ÷ 6 = ?

(4) Find: (i) 7.75/0.25

(ii) 42.8/0.02

(iii) 5.6/1.4

ANSWER

(1) (i) 0.3 ×10 =3, (one zero after 1, so the shift of decimal point to the first place to the right).

(ii) 1.2 ×100 =120, (two zero after 1, so the shift of decimal point to the second place to the right).

(iii) 56.3 × 1000 =56300

(2) (i) 235.4 ÷ 10 = 23.54, (one zero after 1, so the shift of decimal point to the first place to the left).

(ii) 235.4 ÷100 = 2.354, (two zero after 1, so the shift of decimal point to the second place to the left).

(iii) 235.4 ÷ 1000 = 0.2354

(3) (i) 43.15 ÷ 5 = 8.63,

(Divide ignoring the decimal point then put it in the result at the same place in the dividend).

(ii) 82.44 ÷ 6 = 13.76

(4) (i) 7.75/0.25 = 775/025 =31

(ii) 42.8/0.02 = 42.80/0.02 = 4280/2 = 2140

(iii) 5.6/1.4 = 56/14 = 4

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