Chapter 2 - Powers (Ex-2.3) - Class 8 Math RD Sharma Solutions | RD Sharma Solutions for Class 8 Mathematics PDF Download

Question 1:

Express the following numbers in standard form:
(i) 6020000000000000
(ii) 0.00000000000943
(iii) 0.00000000085
(iv) 846 × 10⁷
(v) 3759 × 10⁻⁴
(vi) 0.00072984
(vii) 0.000437 × 10⁴
(viii) 4 ÷ 100000

Answer 1:

To express a number in the standard form, move the decimal point such that there is only one digit to the left of the decimal point.
(i) 6020000000000000 = 6.02 x 10¹⁵      (The decimal point is moved 15 places to the left.)
(ii) 0.0000000000943 = 9.43 x 10−12     (The decimal point is moved 12 places to the right.)
(iii) 0.00000000085 = 8.5 x 10⁻¹⁰     (The decimal point is moved 10 places to the right.)
(iv) 846 x 10⁷ = 8.46 x 10² x 10⁷ = 8.46 x 10⁹     (The decimal point is moved two places to the left.)
(v) 3759 x 10⁻⁴ = 3.759 x 10³ x 10⁻⁴ = 3.759 x 10⁻¹     (The decimal point is moved three places to the left.)
(vi) 0.00072984 = 7.984 x 10⁻⁴     (The decimal point is moved four places to the right.)
(vii) 0.000437 x 10⁴ = 4.37 x 10⁻⁴ x 10⁴ = 4.37 x 100 = 4.37     (The decimal point is moved four places to the right.)
(viii) 4/100000 = 4 x 100000⁻¹ = 4 x 10⁻⁵     (Just count the number of zeros in 1,00,000 to determine the exponent of 10.)

Question 2:

Write the following numbers in the usual form:
(i) 4.83 × 10⁷
(ii) 3.02 × 10⁻⁶
(iii) 4.5 × 10⁴
(iv) 3 × 10⁻⁸
(v) 1.0001 × 10⁹
(vi) 5.8 × 10²
(vii) 3.61492 × 10⁶
(viii) 3.25 × 10⁻⁷

Answer 2:

(i) 4.83 x 10⁷ = 4.83 x 1,00,00,000 = 4,83,00,000
(ii) 3.02 x 10⁻⁶ = 3.02/10⁶ = 3.02/10,00,000 = 0.00000302
(iii) 4.5 x 10⁴ = 4.5 x 10,000 = 45,000
(iv) 3 x 10⁻⁸ = 3/10⁸ = 3/10,00,00,000 = 0.00000003
(v) 1.0001 x 10⁹ = 1.0001 x 1,00,00,00,000 = 1,00,01,00,000
(vi) 5.8 x 10² = 5.8 x 100 = 580
(vii)  3.61492 x 10⁶ = 3.61492 x 10,00,000 = 3614920
(viii) 3.25 x 10⁻⁷ = 3.25/10⁷ = 3.25/1,00,00,000 = 0.000000325

Question 3:

Answer 3:
(d) 4/9
To square a number is to raise it to the power of 2. Hence, the square of (−2/3) is 

Question 4:

Answer 4:

(c) -1/8
The cube of a number is the number raised to the power of 3. Hence the cube of −1/2 is