The form a × 10ⁿ
A number in standard form is where and is an integer. A negative power means a small number (less than 1).
Multiply/divide: fronts, then powers
; for division, divide the fronts and subtract the powers. Then re-normalise.
Drawn from real examiner reports.
Errors in the power of 10
Forgetting the carried power (e.g. ) or getting the sign wrong ().
Both are commonly reported incorrect answers.
Final answer not in standard form
Leaving the front number , e.g. writing instead of — you must rewrite as and add to the power.
A commonly reported examiner note records that where $52 \times 10^{145}$ was a common partial answer.
Putting the power on the front number
Writing instead of — the power belongs to the , not to .
Reported as $5.2^{146}$ on a recent higher-tier paper.
Cannot subtract unequal powers directly
To add or subtract, the powers of must match first. . Subtracting the front numbers while the powers differ is wrong.
Front below 1 after normalising
A result like is not standard form: , so it becomes . Moving the point right one place drops the power by one.
Check 1 ≤ a < 10 at the end
After combining, look at the front number; if it is (like or ) rewrite it and bump the power up by the right amount.
Deal with fronts and powers separately
When multiplying or dividing, handle the number parts and the powers of apart: , then normalise to .
Convert to standard form for the final mark
If a worded answer comes out as an ordinary number like , the final mark needs it in standard form: . Finding the number is only half the marks.
What are the rules for a in standard form a × 10ⁿ?
Write as an ordinary number.
