Standard Form — Solutions

Full worked solutions, with method and final answer for every part.

Question 1

(a)Multiply the coefficients and add the powers of 10: (3.2×4)×10^(5−2).

= 12.8 × 10³ = 1.28 × 10⁴

Question 2

(a)Divide the coefficients and subtract the powers of 10: (6.4÷1.6)×10^(8−3).

= 4 × 10⁵

Question 3

(a)Divide the two values directly, keeping powers of 10 consistent.

(4.7×10⁷) ÷ (9.4×10⁵) = 0.5 × 10² = 50 times greater

Question 4

(a)Multiply coefficients, add powers: 2.5×4=10, powers −3+6=3.

10 × 10³ = 1 × 10⁴

Question 5

(a)Divide coefficients, subtract powers: 9÷3=3, powers 7−(−2)=9.

3 × 10⁹

Question 6

(a)Convert to the same power of 10 first: 3.2×10³ = 0.32×10⁴, then add.

5.6×10⁴ + 0.32×10⁴ = 5.92 × 10⁴

Question 7

(a)Count the places the decimal point moves to give a number between 1 and 10.

4.2 × 10⁻⁵

Question 8

(a)Move the decimal point 5 places to the right.

360 000

Question 9

(a)Divide the two diameters directly.

(2×10⁻⁶) ÷ (3×10⁻⁸) ≈ 66.7 times larger

Question 10

(a)Square the coefficient and double the power: 6²=36, power 3×2=6.

36 × 10⁶ = 3.6 × 10⁷

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