This mini-lesson covers the Number strand of Edexcel GCSE Maths (1MA1): place value & ordering, standard form, fractions, decimals & percentages, indices (including negative & fractional), surds, HCF & LCM by prime factorisation, and rounding, bounds & estimation.
Work through each screen, answer the questions as you go (most are calculations) and collect ⭐ stars. Press Start when you're ready.
Every digit's place value tells you its size. To order decimals, line them up by place value — compare the digits from the left, one column at a time, not by how many digits they have.
Put in ascending order: 0.7, 0.68, 0.709, 0.71
Tenths: 0.68 has 6, the rest have 7 → 0.68 is smallest.
Compare 0.7 (=0.700), 0.709, 0.71 (=0.710) by hundredths & thousandths.
0.68 < 0.7 < 0.709 < 0.71
Common slip: thinking 0.68 > 0.7 because "68 > 7". Line up the decimal points: 0.68 vs 0.70 — the 6 in the tenths column loses to the 7.
Every integer is a unique product of prime factors. Write it using a factor tree, then use index notation:
To find the HCF (highest common factor) and LCM (lowest common multiple) of two numbers, put their prime factors into a Venn diagram:
Remember which is which: HCF is the small answer (the shared middle only); LCM is the big answer (multiply all the factors in the diagram once).
These three are the same idea written three ways. You must move between them freely — the surest way to compare mixed forms is to turn everything into decimals:
Which is bigger, ⅗ or 58%?
⅗ = 3 ÷ 5 = 0.6 and 58% = 0.58
0.6 > 0.58, so ⅗ is bigger.
Watch out: a terminating decimal (like 0.75) always converts to an exact fraction. Turn every value into a decimal before you compare, so you're comparing like with like.
Standard form writes very large or very small numbers compactly:
Write 0.00056 in standard form.
Move the point until 1 ≤ a < 10: 0.00056 → 5.6, that's 4 places right.
Small number, so the power is negative: 5.6 × 10⁻⁴
Watch the rule 1 ≤ a < 10: writing 15 × 10⁷ is not standard form because 15 is bigger than 10. Correct it to 1.5 × 10⁸.
Tap an ordinary number on the left, then its matching standard form on the right.
The index laws let you simplify and evaluate powers, including negative and fractional ones:
Evaluate 27^(1/3).
A power of ⅓ means the cube root: ³√27
3 × 3 × 3 = 27, so 27^(1/3) = 3
Key facts to memorise: a⁰ = 1 for any non-zero a (not 0!), and a negative power means reciprocal: 2⁻³ = 1 ÷ 2³ = 1/8 = 0.125 — it does not make the answer negative.
A surd is a root that can't be simplified to a whole number, like √2. Simplify by pulling out the largest square factor, and rationalise a denominator by clearing the root from the bottom.
Rationalise 6 ÷ √3.
Multiply top and bottom by √3: (6 × √3) ÷ (√3 × √3)
= 6√3 ÷ 3 = 2√3
Use the largest square factor: √72 = √4 × √18 works but leaves more to do. Spotting 36 (= 6²) as the biggest square factor of 72 finishes it in one step: √72 = 6√2.
Round to a number of decimal places (d.p.) or significant figures (s.f.). To estimate, round each number to 1 s.f. first. A rounded value also hides a range of bounds.
Round 4.0871 to 2 decimal places.
Look at the 3rd decimal (7): 7 ≥ 5, so round the 8 up to 9.
= 4.09
Misconception: rounding 4.0871 to 2 d.p. is 4.09, not 4.08 — the 7 in the next place rounds the 8 up. Look one digit past where you're cutting.
A rational number can be written as a fraction; an irrational number (like most surds) cannot. Tap a number, then tap the box it belongs in.
Place value & ordering: line decimals up by place value; compare from the left.
HCF & LCM: prime factorise, then use a Venn — HCF is the overlap, LCM is everything.
Fractions, decimals & percentages: convert to decimals to compare mixed forms.
Standard form: a × 10ⁿ with 1 ≤ a < 10; small numbers use a negative power.
Indices: a⁰ = 1, a⁻ⁿ = 1 ÷ aⁿ, a^(1/n) = ⁿ√a — negative & fractional powers.
Surds: split off the largest square factor; rationalise denominators.
Rounding & bounds: d.p. & s.f., estimate to 1 s.f., upper & lower bounds.
Rational vs irrational: fractions & square roots that simplify are rational.
You've covered every sub-topic in the Edexcel 1MA1 Number strand — from place value to surds and index laws. Press Finish to see your score.
You've worked through the Number strand for Edexcel GCSE Maths (1MA1). 🎉
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Next: test yourself in the Evaluate stage Confidence Quiz, then lock it in with Verify.