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 = 15×3/10×100 = 75/1000
⇒ 0.15 × 0.3 = 0.075
The rules for multiplying decimals are as follow
➤ 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 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 = 58/10 ÷ 2 = 58/10 × 1/2 (Multiplying by reciprocal)
= 58/20 = 29/10
= 2.9
→ 23.9 ÷ 10 = 239/10 ÷ 10 = 239/10 × 1/10
= 239/100 = 2.39
→ 19.9 ÷ 0.13 = 199/10 ÷ 13/100
= 199/10 × 100/13
= 19900/130 = 130
To divide 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
To divide 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 thequotient.
So, 63.9 ÷ 10 = 6.39,
63.9 ÷ 100 = 0 .639,
63.9 ÷ 1000 = 0.0639
Dividing two decimal numbers,
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/
= 12,
0.242 ÷ 0.22
= 24.2 ÷ 22 (∵ 242/10
= 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 shift decimal point one place to the right.(ii) 1.2 ×100 =120 -two zero after 1, so shift decimal point two place to the right.
(iii) 56.3 × 1000 =56300
(2) (i) 235.4 ÷ 10 = 23.54 - one zero after 1, so shift decimal point one place to the left.
(ii) 235.4 ÷100 = 2.354 - two zero after 1, so shift decimal point two 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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