GCSE Maths · Number

Standard Form

Writing very large and very small numbers as a × 10ⁿ and calculating with them.

200 GCSE-style practice questions

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Standard Form, explained point by point

Everything the GCSE specification expects you to be able to do, and how to actually do it - the same lesson a signed-in student studies from.

  1. Write very large and very small numbers in standard form, and convert back to ordinary numbers

    Standard form writes every number as A × 10ⁿ where A is at least 1 but less than 10. So 3 400 000 = 3.4 × 10⁶, and 0.00052 = 5.2 × 10⁻⁴ - a negative power means a small number. To convert back, move the decimal point n places.

  2. Order and compare numbers written in standard form

    Compare the powers of 10 first - a bigger power means a bigger number, so 2 × 10⁷ beats 9 × 10⁶. Only when the powers are equal do you compare the front numbers: 7.1 × 10⁵ is more than 6.9 × 10⁵.

  3. Multiply and divide numbers in standard form, with and without a calculator

    Multiply the front numbers and ADD the powers: (3 × 10⁴) × (2 × 10⁵) = 6 × 10⁹. When dividing, divide the fronts and subtract the powers. If the front lands outside 1–10, adjust: 40 × 10⁶ must be rewritten as 4 × 10⁷.

  4. Add and subtract numbers in standard form

    Adding and subtracting needs matching powers of 10, so rewrite one number first: 3.2 × 10⁵ + 4 × 10⁴ becomes 3.2 × 10⁵ + 0.4 × 10⁵ = 3.6 × 10⁵. Alternatively, convert both to ordinary numbers, calculate, then convert back.

  5. Solve real-world problems with standard form - populations, distances in space, sizes of cells

    Exam questions dress standard form up in context: how many times further, how many cells fit, total mass of a population. Set up the calculation as usual (often a division), keep the numbers in standard form, and sense-check whether the answer should be huge or tiny.

Practice

Try a Standard Form question

A GCSE-style original question from this topic. Have a go before you open the working - deciding on an answer first is what makes the working stick.

Work out (4 × 10³) × (5 × 10⁴). Give your answer in standard form.

  1. 9 × 10⁷
  2. 2 × 10⁸
  3. 2 × 10⁷
  4. 2 × 10¹²
Show the answer and the working

Answer: 2 × 10⁸

4 × 5 = 20 and 10³ × 10⁴ = 10⁷, giving 20 × 10⁷, which must be adjusted to 2 × 10⁸ for standard form.

  1. Multiply the front numbers: 4 × 5 = 20.
  2. Add the indices: 10³ × 10⁴ = 10⁷.
  3. 20 × 10⁷ is not standard form because 20 ≥ 10.
  4. Rewrite 20 as 2 × 10¹: the answer is 2 × 10⁸.

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