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    Significant figures and standard form in GCSE Physics

    By Engr. Mehmood Kakar · Updated

    Quick answer

    Give your answer to the same number of significant figures as the least precise value in the question, usually 2 or 3, and only round at the very end. For very large or small numbers use standard form, A × 10ⁿ with A between 1 and 10, and type it with your calculator’s ×10ˣ or EXP button.

    What significant figures are

    Significant figures (s.f.) are the digits in a number that carry meaning about its size. You count from the first non-zero digit. 4.716 rounded to 2 s.f. is 4.7; to 3 s.f. it is 4.72.

    Which zeros count

    • Leading zeros never count. 0.0042 has 2 s.f. (the 4 and the 2).
    • Zeros between digits always count. 305 has 3 s.f.
    • Trailing zeros after a decimal point count. 2.50 m has 3 s.f. Writing the zero says you measured to the nearest centimetre.
    • Trailing zeros in a whole number are unclear. 4000 could have 1 to 4 s.f. Standard form removes the doubt: 4.0 × 10³ is clearly 2 s.f.

    How many to give

    Your answer can’t be more precise than your data. Use the least precise value in the question as your guide, and round only at the end.

    A cyclist travels 12.0 m in 7.0 s. Calculate her speed. (2 marks)

    1. v = s ÷ t = 12.0 ÷ 7.0 = 1.714… m/s
    2. 12.0 has 3 s.f. and 7.0 has 2 s.f., so give 2 s.f.
    3. v = 1.7 m/s

    If the question says "give your answer to 3 significant figures", do that even if the data suggest otherwise. In a multi-step question, keep the full value on your calculator between steps. Rounding halfway through can shift your final answer.

    Standard form

    A number in standard form is written A × 10ⁿ, where A is at least 1 and less than 10, and n is a whole number.

    • 3,400,000 = 3.4 × 10⁶ (the decimal point moved 6 places left)
    • 0.00045 = 4.5 × 10⁻⁴ (the point moved 4 places right, so the power is negative)
    • 600 = 6.0 × 10²

    Light has a speed of 3.0 × 10⁸ m/s and a frequency of 5.0 × 10¹⁴ Hz. Calculate its wavelength. (2 marks)

    1. λ = v ÷ f = 3.0 × 10⁸ ÷ 5.0 × 10¹⁴
    2. 3.0 ÷ 5.0 = 0.60, and 10⁸ ÷ 10¹⁴ = 10⁻⁶, giving 0.60 × 10⁻⁶
    3. Rewrite so the first number is between 1 and 10
    4. λ = 6.0 × 10⁻⁷ m

    Standard form on a calculator

    Use the ×10ˣ button (EXP on some models). To enter 5.0 × 10¹⁴, press 5.0, ×10ˣ, 14. The calculator treats it as one number, so dividing by it works properly.

    The common mistake is typing 3.0 × 10 ^ 8 ÷ 5.0 × 10 ^ 14. The calculator divides by 5.0 and then multiplies by 10¹⁴, giving a wildly wrong answer. If you do type it that way, put brackets around each number.

    Prefixes and standard form

    Every prefix is a power of ten, so converting is quick:

    • kilo (k) = × 10³: 4.5 kJ = 4.5 × 10³ J
    • mega (M) = × 10⁶: 2.0 MW = 2.0 × 10⁶ W
    • milli (m) = × 10⁻³: 250 mA = 250 × 10⁻³ A = 0.25 A
    • micro (µ) = × 10⁻⁶: 40 µs = 4.0 × 10⁻⁵ s
    • nano (n) = × 10⁻⁹: 500 nm = 5.0 × 10⁻⁷ m

    Our units and prefixes guide has the full list.

    Practice

    1. Round 0.004 862 to 2 significant figures.

    The first significant figure is 4. → 0.0049

    2. Write 0.000 072 m in standard form.

    Move the point 5 places right. → 7.2 × 10⁻⁵ m

    3. Calculate (3.0 × 10⁸) × (2.0 × 10⁻⁶) and give the answer in standard form.

    3.0 × 2.0 = 6.0 and 10⁸ × 10⁻⁶ = 10². → 6.0 × 10²

    4. A stone falls with g = 9.8 N/kg for 0.35 s from rest. Its speed is g × t. Give the answer to a sensible number of significant figures.

    9.8 × 0.35 = 3.43. Both values have 2 s.f. → 3.4 m/s

    Frequently asked questions

    How many significant figures should I give in GCSE Physics?

    Match the least precise value in the question. If the data are given to 2 significant figures, give your answer to 2. If the question asks for a number of significant figures, always do what it says.

    Do zeros count as significant figures?

    Zeros between other digits count (305 has 3). Zeros at the start of a decimal never count (0.0042 has 2). Trailing zeros after a decimal point count (2.50 has 3).

    How do I type standard form on a calculator?

    Use the ×10ˣ (or EXP) button. For 3.0 × 10⁸, type 3.0, then ×10ˣ, then 8. Don’t type × 10 ^ 8, which can go wrong when you divide.

    When should I use standard form?

    For numbers that are very large or very small, such as the speed of light (3.0 × 10⁸ m/s) or a wavelength of light (5.0 × 10⁻⁷ m). Ordinary numbers like 25 m/s don’t need it.

    Engr. Mehmood Kakar

    Written by Engr. Mehmood Kakar

    Physics educator and engineer (MSc Physics, B.Ed, M.Ed) with 8 years of hands-on teaching, from college students to teacher training. About the author · LinkedIn (opens in a new tab)

    Checked against the AQA GCSE Physics (8463) specification on 14 November 2026.