1.9Foundation tier4MA1 · Section 1: Numbers and the number system

Standard form

Key learnings

The form a × 10ⁿ
A number in standard form is $a \times 10^n$ where $1 \le a < 10$ and $n$ is an integer. A negative power means a small number (less than 1).
Multiply/divide: combine the fronts, add/subtract the powers
$(a \times 10^m)\times(b \times 10^n) = (a\times b)\times 10^{m+n}$ ; for division, divide the fronts and subtract the powers. Then re-normalise.

Common mistakes

Drawn from real examiner reports.

Final answer not in standard form

Leaving the front number $\ge 10$ , e.g. writing $52 \times 10^{145}$ instead of $5.2 \times 10^{146}$ — you must rewrite $52$ as $5.2 \times 10$ and add $1$ to the power.

Errors in the power of 10

Forgetting the carried power (e.g. $5.2 \times 10^{144}$ ) or getting the sign wrong ( $5.2 \times 10^{-146}$ ).

Putting the power on the front number

Writing $5.2^{146}$ instead of $5.2 \times 10^{146}$ — the power belongs to the $10$ , not to $a$ .

Exam tips

Check 1 ≤ a < 10 at the end
After combining, look at the front number; if it is $\ge 10$ (like $12$ or $52$ ) rewrite it and bump the power up by the right amount.

Revision notes

$a \times 10^{n}, \qquad 1 \le a < 10, \quad n \text{ an integer}.$

Big numbers → positive power: $4\,500\,000 = 4.5 \times 10^{6}$ .
Small numbers (less than 1) → negative power: $0.00032 = 3.2 \times 10^{-4}$ .
The power lives on the 10, never on the front number ( $5.2^{146}$ is wrong).

Flashcards

Foundation

What are the rules for a in standard form a × 10ⁿ?

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Standard form

Key learnings

Common mistakes

Exam tips

Revision notes

What standard form is

Multiplying and dividing

Adding and subtracting

Flashcards

Practice questions