Standard form (a x 10^k) practice questions.

The speed of light is approximately 299 800 000 m s⁻¹. Written in the form a × 10^k, where 1 ≤ a < 10 and k is an integer, this speed is

• 2.998 × 10⁸
• 29.98 × 10⁷
• 2.998 × 10⁷
• 0.2998 × 10⁹

Answer: 2.998 × 10⁸

The decimal point moves 8 places to the left to give a coefficient between 1 and 10, so the number is 2.998 × 10⁸. The other forms do not satisfy 1 ≤ a < 10 or use the wrong exponent.

Calculate (3 × 10⁵) × (4 × 10⁻²), giving your answer in the form a × 10^k with 1 ≤ a < 10.

• 12 × 10³
• 1.2 × 10³
• 1.2 × 10⁴
• 7 × 10³

Answer: 1.2 × 10⁴

Multiply the coefficients (3 × 4 = 12) and add the exponents (5 + (−2) = 3) to get 12 × 10³, then rewrite as 1.2 × 10⁴ so that 1 ≤ a < 10.

Calculate (8 × 10⁶) ÷ (2 × 10⁻³), giving your answer in the form a × 10^k with 1 ≤ a < 10.

• 4 × 10³
• 4 × 10⁹
• 4 × 10¹⁸
• 1.6 × 10¹⁰

Answer: 4 × 10⁹

Divide the coefficients (8 ÷ 2 = 4) and subtract the exponents: 6 − (−3) = 9, giving 4 × 10⁹. Writing 6 − 3 = 3 is the classic sign error.

The width of a human hair is about 3.2 × 10⁻⁵ m. Written as an ordinary (decimal) number, this width in metres is

• 0.0000032
• 0.00032
• 320 000
• 0.000032

Answer: 0.000032

A power of 10⁻⁵ moves the decimal point 5 places to the left: 3.2 × 10⁻⁵ = 0.000032. Moving 6 or 4 places gives the common miscount distractors.

The sum 5.6 × 10⁴ + 8.1 × 10⁵ is written in the form a × 10^k with 1 ≤ a < 10. Determine the value of k.

• 4
• 9
• 5
• 6

Answer: 5

Convert to ordinary numbers first: 56 000 + 810 000 = 866 000 = 8.66 × 10⁵, so k = 5. You cannot simply add the exponents when adding numbers in standard form.

The Earth is approximately 1.5 × 10⁸ km from the Sun and Neptune is approximately 4.5 × 10⁹ km from the Sun. Neptune's distance from the Sun is how many times Earth's distance?

• 30
• 3
• 300
• 0.03

Answer: 30

(4.5 × 10⁹) ÷ (1.5 × 10⁸) = 3 × 10¹ = 30. Dividing only the coefficients and ignoring the powers of 10 gives the distractor 3.