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Edexcel GCSE Maths (1MA1) · Number
Mini-Lesson

Number

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.

-3 -2 -1 0 1 2 3 smaller larger
Everything starts on the number line: values ordered smallest to largest, left to right.

Work through each screen, answer the questions as you go (most are calculations) and collect ⭐ stars. Press Start when you're ready.

Place value & ordering

Place value & ordering numbers

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.

Worked example — order these

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.

Calculate

Your turn — fraction of an amount

1Work out ⅜ of 640.
Hint: 640 ÷ 8 = 80, then × 3.
HCF & LCM · prime factors

Prime factors, HCF & LCM

Every integer is a unique product of prime factors. Write it using a factor tree, then use index notation:

24 = 2³ × 3keep dividing by primes until only primes remain

To find the HCF (highest common factor) and LCM (lowest common multiple) of two numbers, put their prime factors into a Venn diagram:

24 = 2³ × 3 60 = 2² × 3 × 5 2 2 2 3 5 only in 24 shared only in 60
HCF = product of the overlap = 2 × 2 × 3 = 12.   LCM = product of everything = 2 × 2 × 2 × 3 × 5 = 120.

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).

Calculate

Your turn — HCF

224 = 2³ × 3 and 60 = 2² × 3 × 5. Find the highest common factor (HCF) of 24 and 60.
Hint: take the shared primes at their lowest power: 2² × 3 = 4 × 3.
Fractions · decimals · percentages

Fractions ⇄ decimals ⇄ percentages

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:

fraction decimal percentage ÷ ×100 ÷100
¾ = 0.75 = 75%. To get a percentage from a decimal, multiply by 100.
Worked example — compare

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.

Quick check

Ordering mixed forms

?Which of these is the largest?
Standard form

Standard form

Standard form writes very large or very small numbers compactly:

a × 10ⁿwhere 1 ≤ a < 10 and n is an integer
150 000 000 = 1.5 × 10⁸ move the point 8 places small numbers use 10⁻ⁿ,e.g. 0.00056 = 5.6 × 10⁻⁴
The power counts how far the decimal point moves.
Worked example — small number

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.

Calculate

Your turn — standard form

3Write 0.00056 in the form a × 10ⁿ. Type the power of 10 (the value of n).
Hint: move the point until 1 ≤ a < 10 (giving 5.6). It's a small number, so n is negative.
Match game

Ordinary ⇄ standard form

Tap an ordinary number on the left, then its matching standard form on the right.

Indices · negative & fractional

Laws of indices (negative & fractional)

The index laws let you simplify and evaluate powers, including negative and fractional ones:

aᵐ × aⁿ = aᵐ⁺ⁿ   ·   aᵐ ÷ aⁿ = aᵐ⁻ⁿ   ·   (aᵐ)ⁿ = aᵐⁿa⁰ = 1  ·  a⁻ⁿ = 1 ÷ aⁿ  ·  a^(1/n) = ⁿ√a  ·  a^(m/n) = (ⁿ√a)ᵐ
Worked example — fractional

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.

Calculate

Your turn — evaluate a power

4Work out the exact value of 2⁻³. Give your answer as a decimal.
Hint: 2⁻³ = 1 ÷ 2³ = 1 ÷ 8.
Surds

Surds

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.

√72 = √36 × √2 = 6√2√(ab) = √a × √b — split off the largest square factor
Worked example — rationalise

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.

Quick check

Simplify a surd

?Simplify √72 fully.
Rounding & bounds

Rounding, bounds & estimation

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.

Worked example — 2 d.p.

Round 4.0871 to 2 decimal places.

Look at the 3rd decimal (7): 7 ≥ 5, so round the 8 up to 9.

= 4.09

bounds = value ± ½ × (rounding unit)e.g. 12 cm to the nearest cm: 11.5 ≤ length < 12.5
11.5 12 12.5 lower bound upper bound
Anything in this range rounds to 12 cm.

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.

Calculate

Your turn — round to 2 d.p.

5Round 4.0871 to 2 decimal places.
Hint: the 3rd decimal is 7 (≥ 5), so round the 8 up.
Quick check

Spot the standard form

?Which of these numbers is written correctly in standard form?
Sort it

Rational or irrational?

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.

➗ Rational

√ Irrational

Recap

The whole Number strand

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.

🏆

Mini-lesson complete!

⭐⭐⭐

You've worked through the Number strand for Edexcel GCSE Maths (1MA1). 🎉

Your stars: 0 / 0

Next: test yourself in the Evaluate stage Confidence Quiz, then lock it in with Verify.

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Challenge a mate to beat your stars, or show a parent how you got on.

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