Is standard form on the Foundation paper as well as Higher?

Yes. Standard form is spec reference N9 in Edexcel 1MA1 and it is common to both tiers, so the same skill is assessed at Foundation and at Higher. What changes is the packaging: Higher questions are more likely to hide it inside a rate, a density or a multi-step comparison, and to ask for the answer to a stated number of significant figures.

Do I need to do standard form without a calculator?

Yes. Paper 1 is the non-calculator paper and standard form turns up there regularly, normally as a conversion for 1 mark or a multiplication or division for 2. Practise adding and subtracting indices by hand, and practise the adjustment step that turns 40 10^5 into 4 10^6.

How many marks is standard form worth on Edexcel Higher?

Writing a number in standard form, or turning one back into an ordinary number, is normally 1 mark. A calculation in standard form is usually 2 marks, and a question set in a context, such as comparing two populations or two masses, can run to 3 or 4. Across a series of three 80-mark papers it is a handful of marks rather than a large block, but they are quick marks.

Does the number in front have to be between 1 and 10?

It has to satisfy 1 a < 10, so 1 itself is allowed and 10 is not. Answers such as 0.5 10^6 and 25 10^4 have the right value but the wrong form, and Edexcel mark schemes do not accept them for the final mark. Shift the decimal point one place right and reduce the index by 1 to turn 0.5 10^6 into 5 10^5.

Standard Form - Edexcel GCSE Higher Maths

Typically 2-4 marks per paper · Spec 1MA1

Standard form writes a number as $a \times 10^{n}$ , where $1 \le a < 10$ and $n$ is an integer. On Edexcel's 1MA1 specification it is reference N9, and it is not Higher-only content: the same requirement sits on Foundation, so on Higher it arrives as crossover material, usually wrapped in a context or buried inside a longer calculation rather than asked on its own.

Edexcel can set it on any of the three papers, and in practice it turns up often. Paper 1 has no calculator, so a conversion is worth about 1 mark and a multiplication or division in standard form is usually 2, with the second mark reserved for an answer that is genuinely in standard form. On Papers 2 and 3 you have a calculator, and the question then attaches a condition: give the answer in standard form, or to 2 or 3 significant figures, or both. That instruction is doing real work, and ignoring it costs the accuracy mark even when the value is right.

Most marks lost here are not lost through misunderstanding. Students reach $48 \times 10^{3}$ and stop, or copy a calculator display onto the answer line as 1.44 followed by a floating 10 with no power of ten between them, or subtract $6.0 \times 10^{7}$ from $9.9 \times 10^{8}$ by subtracting the indices and writing $3.9 \times 10^{1}$ . Three habits fix nearly all of it: adjust the front number the moment it drifts outside 1 to 10, rewrite both numbers with the same power of ten before you add or subtract, and after rounding check that the index still matches the size of the number.

Worked example

The mass of a hydrogen atom is

1.7 \times 10^{-27}

kg. The mass of a carbon atom is

2.0 \times 10^{-26}

kg. (a) Work out the total mass of one hydrogen atom and one carbon atom. Give your answer in standard form. (b) Work out how many times heavier the carbon atom is than the hydrogen atom. Give your answer to 2 significant figures.

[4 marks]

Rewrite the number with the smaller index so both share a power of ten: $1.7 \times 10^{-27} = 0.17 \times 10^{-26}$ .
M1: matching the powers of ten before adding (you cannot add the indices here)
Add the front numbers: $0.17 + 2.0 = 2.17$ , so the total mass is $2.17 \times 10^{-26}$ kg, which is already in standard form.
A1: correct total, front number checked against $1 \le a < 10$
For (b), divide: $\frac{2.0 \times 10^{-26}}{1.7 \times 10^{-27}} = \frac{2.0}{1.7} \times 10^{-26-(-27)} = 1.176\ldots \times 10^{1}$ .
M1: dividing the front numbers and subtracting the indices, $-26 - (-27) = 1$
$1.176\ldots \times 10 = 11.76\ldots$ , so the carbon atom is 12 times heavier, to 2 significant figures.
A1: 12, with the rounding done only at the final step

Practice questions

These are original questions in Edexcel 1MA1 Higher style. Do the pure standard form arithmetic without a calculator, the way Paper 1 asks it, and reach for a calculator only on the questions that name a number of significant figures. Where the answer is in standard form you type the two parts separately, so $4.8 \times 10^{4}$ is entered as $a = 4.8$ and $n = 4$ .

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

Question 1 Warm-up [1 mark]

Write $2.05 \times 10^{-4}$ as an ordinary number.

Your answer (fractions like 1/2 are fine)
Question 2 Exam pace [2 marks]

Work out $(7 \times 10^{-4}) + (5 \times 10^{-5})$ . Give your answer in standard form $a \times 10^{n}$ . State the values of $a$ and $n$ .

a = n =
Question 3 Exam pace [2 marks]

Work out $(9 \times 10^{5}) + (9 \times 10^{5})$ . Give your answer in standard form $a \times 10^{n}$ . State the values of $a$ and $n$ .

a = n =
Question 4 Exam pace [2 marks]

Write $630 \times 10^{-9}$ in standard form. Give the values of $a$ and $n$ in $a \times 10^{n}$ .

a = n =
Question 5 Stretch [3 marks]

The mass of the Earth is about $5.97 \times 10^{24}$ kg. The mass of the Moon is about $7.35 \times 10^{22}$ kg. Work out how many times heavier the Earth is than the Moon. Give your answer to 2 significant figures.

Your answer (fractions like 1/2 are fine)
Question 6 Stretch [3 marks]

Use a calculator to work out $(5.4 \times 10^{-7}) \div (8.1 \times 10^{4})$ . Give your answer in standard form $a \times 10^{n}$ , with $a$ to 3 significant figures. State the values of $a$ and $n$ .

a = n =

Common mistakes examiners see

Stopping at a front number outside 1 to 10, so $(6 \times 10^{4}) \times (8 \times 10^{1})$ is left as $48 \times 10^{5}$ instead of $4.8 \times 10^{6}$ .

Treat the adjustment as part of the method, not an optional tidy-up. If the front number is 10 or more, move the decimal point left and add 1 to the index for each place; if it is below 1, move right and subtract 1 for each place.
Getting the sign of the index wrong for numbers below 1, writing 0.00034 as $3.4 \times 10^{4}$ , or miscounting the places and writing $3.4 \times 10^{-3}$ .

Decide the sign first from the size: less than 1 means a negative index, 10 or more means a positive one. Then count the places the digits move, and check by saying the answer back as a decimal.
Reading the index as the number of zeros, so $3.5 \times 10^{5}$ is written as 3 500 000 rather than 350 000.

The index counts how many places the digits shift, not how many zeros you write. Move the decimal point five places to the right: 3.5, 35, 350, 3500, 35000, 350000.
Adding or subtracting by combining the indices, for example $9.9 \times 10^{8} - 6.0 \times 10^{7} = 3.9 \times 10^{1}$ .

Indices only combine for multiplication and division. To add or subtract, rewrite one number so both have the same power of ten ( $9.9 \times 10^{8} - 0.60 \times 10^{8}$ ), then subtract the front numbers and keep that power.
Copying the calculator display straight onto the answer line, so an answer of $1.44 \times 10^{10}$ is written as 1.44 10, or rounding to 2 significant figures and shifting the index to $1.4 \times 10^{11}$ .

Write out the times sign and the power in full on the answer line, then compare the rounded answer with the unrounded one: rounding 1.44 to 1.4 changes the front number only, so the index stays at 10.

Frequently asked questions

Is standard form on the Foundation paper as well as Higher?: Yes. Standard form is spec reference N9 in Edexcel 1MA1 and it is common to both tiers, so the same skill is assessed at Foundation and at Higher. What changes is the packaging: Higher questions are more likely to hide it inside a rate, a density or a multi-step comparison, and to ask for the answer to a stated number of significant figures.
Do I need to do standard form without a calculator?: Yes. Paper 1 is the non-calculator paper and standard form turns up there regularly, normally as a conversion for 1 mark or a multiplication or division for 2. Practise adding and subtracting indices by hand, and practise the adjustment step that turns $40 \times 10^{5}$ into $4 \times 10^{6}$ .
How many marks is standard form worth on Edexcel Higher?: Writing a number in standard form, or turning one back into an ordinary number, is normally 1 mark. A calculation in standard form is usually 2 marks, and a question set in a context, such as comparing two populations or two masses, can run to 3 or 4. Across a series of three 80-mark papers it is a handful of marks rather than a large block, but they are quick marks.
Does the number in front have to be between 1 and 10?: It has to satisfy $1 \le a < 10$ , so 1 itself is allowed and 10 is not. Answers such as $0.5 \times 10^{6}$ and $25 \times 10^{4}$ have the right value but the wrong form, and Edexcel mark schemes do not accept them for the final mark. Shift the decimal point one place right and reduce the index by 1 to turn $0.5 \times 10^{6}$ into $5 \times 10^{5}$ .

Standard Form - Edexcel GCSE Higher Maths

Worked example

Practice questions

Common mistakes examiners see

Frequently asked questions

Related topics