Standard form

Revise Standard form for Mathematics A 4MA1 (O Level) — revision notes, 248 practice questions and instant AI marking.

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Pearson Edexcel International GCSE Mathematics A (4MA1)

Standard Form

The big idea: Standard form splits a number into “how big the digits are” (a, between 1 and 10) and “how many places” (the power of 10). Calculations work on each part separately, then tidy up so that a is back between 1 and 10.

Summary — What This Chapter Covers

Standard form: a × 10ⁿ where 1 ≤ a < 10 and n is an integer, e.g. 150 000 000 = 1.5 × 10⁸.
Large numbers have positive n; numbers between 0 and 1 have negative n.
Multiply or divide: deal with the numbers, then the powers of 10, then re-adjust.
Add or subtract: convert to ordinary numbers (or the same power of 10) first.
Higher: solve problems in context, and with algebraic powers.

1. Writing and Interpreting Standard Form

Foundation & Higher

a × 10ⁿ, with 1 ≤ a < 10

Move the decimal point until exactly one non-zero digit is in front of it. Count the places moved: that is n. For a number of 10 or more, n is positive; for a number less than 1, n is negative.

Examples 150 000 000 = 1.5 × 10⁸ 0.000 304 = 3.04 × 10⁻⁴ 4.7 × 10⁵ = 470 000

Worked Example

(a) Write 0.000 0582 in standard form. (b) 32 × 10⁴ is not in standard form. Write it in standard form. (c) Write these in order, smallest first: 3.1 × 10⁻², 2.9 × 10⁻³, 0.025

2. Calculating in Standard Form

Foundation & Higher

Numbers together, powers together

For multiplication and division, use the index laws on the powers of 10. If the number part is no longer between 1 and 10, adjust it. For addition and subtraction, the powers must match, so convert to ordinary numbers first. On a calculator, use the ×10^x (or EXP) key, not “× 10 ^”.

Worked Example

Work out, giving each answer in standard form: (a) (3 × 10⁴) × (5 × 10⁶) (b) (8.4 × 10⁷) ÷ (2.1 × 10⁻³) (c) 3.2 × 10⁵ + 4.1 × 10⁴

Practice Question 1

Work out (6.2 × 10⁵) × (3.1 × 10⁻²). Give your answer in standard form.

3. Problems Involving Standard Form

Higher tier

Context and algebra

Higher questions put standard form into context (astronomy, cells, populations) or use letters for the powers. Keep the answer in standard form and round the number part, not the power.

Worked Example

The mass of the Earth is 5.97 × 10²⁴ kg. The mass of the Moon is 7.35 × 10²² kg. How many times heavier than the Moon is the Earth? Give your answer correct to 3 significant figures.

Memorise

The rule

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Standard form

Standard Form

a × 10n, with 1 ≤ a < 10

Numbers together, powers together

Context and algebra

The rule

Past papers that test Standard form

More Mathematics A topics

a × 10ⁿ, with 1 ≤ a < 10