Basic Arithmetic operations - Decimal Fractions

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Basic Arithmetic operations - Decimal Fractions1. Addition and Subtraction of Decimal FractionsTo add/subtract decimals,
(i) Write down the numbers, one under the other, with the decimal points lie in one column.
(ii) Now the numbers can be added normally (remember to put the decimal point in the answer).

Examples

(a) 1.3 + 0.24 = ?		(b) 1.25 + 0.1024 + 3 = ?
1 . 3 0 . 2 4 -------- 1 . 5 4		1 . 2 5 0 . 1 0 2 4 3 ------------ 4 . 3 5 2 4

2. Multiplication of a Decimal Fraction by a Power of 10Shift the decimal point to the right by as many places as the power of 10

Examples

(a) 3.78 × 10 = 37.8
(b) 0.0043 × 100000 = 430

3. Multiplication of Decimal FractionsTo multiply decimals,
(i) Multiply the given numbers considering them without decimal point.
(ii) In the product obtained, place the decimal point by starting at the right and moving a number of places equal to the sum of the decimal places in the given numbers.

Examples

(a) 4 × .06 = ?		(b) 2 × .3 × 0.005= ?
4 × 6 = 24 Sum of the decimal places in the given numbers = 0 + 2 = 2 Hence, answer = .24		2 × 3 × 5 = 30 Sum of the decimal places in the given numbers = 0 + 1 + 3 = 4 Hence, answer = .0030 = .003

4. Division of Decimal Fraction by a Counting NumberTo divide a decimal by a counting number,
(i) Divide the given numbers considering them without decimal point.
(ii) In the quotient obtained, place the decimal point by starting at the right and moving a number of places equal to the sum of the decimal places in the given numbers.

Examples

(a) 0.04 ÷ 2 = ?		(b) 0.008 ÷ 4 = ?
4 ÷ 2 = 2 Sum of the decimal places in the given numbers = 2 + 0 = 2 Hence, answer = .02		8 ÷ 4 = 2 Sum of the decimal places in the given numbers = 3 + 0 = 3 Hence, answer = .002

5. Division of Decimal Fraction/Counting Number by a Decimal FractionTo divide a decimal/counting number by a decimal,
(i) Multiply both the dividend and the divisor by a suitable power of 10 to make divisor a whole number.
(ii) Now divide the numbers normally.

Examples

(a) $\frac{0.04}{0.2}=\frac{0.04\times 10}{0.2\times 10}$ $=\frac{0.4}{2}=0.2$

(b) $\frac{0.0009}{0.03}=\frac{0.0009\times {10}^2}{0.03\times {10}^2}$ $=\frac{0.09}{3}=0.03$

(c) $\frac{3}{0.03}=\frac{3\times {10}^2}{0.03\times {10}^2}$ $=\frac{300}{3}=100$

(d) $\frac{40}{0.002}=\frac{40\times {10}^3}{0.002\times {10}^3}$ $=\frac{40000}{2}=20000$