IGCSE Mathematics: Standard Form Practice Questions
A number in standard form is written as a multiplied by 10 to the power n, where a is at least 1 and less than 10, and n is an integer. A positive power means a large number and a negative power means a small one.
Topic 1.7 of Cambridge IGCSE Mathematics 0580 appears on both papers and is used constantly in Physics and Chemistry. The most frequent error is leaving an answer with a value of 10 or more in front, which is not standard form. The questions below make you check that every time.
What you need to know for Standard Form
- The forma x 10n, where 1 is less than or equal to a, and a is less than 10, and n is an integer. Exactly one non-zero digit sits before the decimal point.
- Large numbersMove the decimal point left until one digit remains before it, and count the moves. That count is the positive power of 10.
- Small numbersMove the decimal point right until one non-zero digit sits before it. The number of moves is the negative power of 10.
- MultiplyingMultiply the front numbers and add the powers. Then adjust so the front number lies between 1 and 10.
- DividingDivide the front numbers and subtract the powers, then adjust as needed.
- Adding and subtractingRewrite both numbers with the same power of 10 first, then add or subtract the front numbers, and finally convert back to correct standard form.
IGCSE Mathematics Standard Form questions and answers
4 exam-style questions written to the 0580 syllabus. Try each one on paper first, then open the worked answer to check your method against the marks.
Write 5 300 000 and 0.00042 in standard form.
Show the worked answer
- For 5 300 000, move the decimal point left until one digit remains before it: 5.3.
- The point moved 6 places, and the number is large, so the power is positive: 5.3 x 106.
- For 0.00042, move the decimal point right until one non-zero digit sits before it: 4.2.
- The point moved 4 places, and the number is small, so the power is negative: 4.2 x 10-4.
Work out (3 x 105) multiplied by (4 x 10-2), giving your answer in standard form.
Show the worked answer
- Multiply the front numbers: 3 x 4 = 12.
- Add the powers: 5 plus minus 2 = 3.
- This gives 12 x 103, which is not yet in standard form because 12 is greater than 10.
- Rewrite 12 as 1.2 x 101, so the answer becomes 1.2 x 104.
Work out (8 x 107) divided by (2 x 103), giving your answer in standard form.
Show the worked answer
- Divide the front numbers: 8 divided by 2 = 4.
- Subtract the powers: 7 minus 3 = 4.
- This gives 4 x 104.
- The front number 4 is already between 1 and 10, so no adjustment is needed.
Work out (3.2 x 105) plus (4 x 104), giving your answer in standard form.
Show the worked answer
- The powers are different, so they cannot simply be added. Rewrite both with the same power of 10.
- Convert the second number to the higher power: 4 x 104 = 0.4 x 105.
- Now add the front numbers: 3.2 + 0.4 = 3.6.
- The answer is 3.6 x 105. The front number lies between 1 and 10, so it is already in standard form.
Common mistakes in this topic
- Leaving a front number of 10 or more, or less than 1.
- Giving a positive power for a number smaller than 1.
- Adding the powers when adding two numbers in standard form.
- Dividing the powers instead of subtracting them.
- Miscounting the decimal point moves, particularly with several zeros.
Exam tips
- After every calculation, check that the front number is at least 1 and less than 10. That check catches the most common error in this topic.
- Sense check the sign: numbers above 1 have positive powers, numbers below 1 have negative powers.
- For addition and subtraction, always convert to the larger power. It keeps the front numbers tidy.
- Your calculator's EXP or times ten to the power x button avoids typing zeros. Learn where it is.
- Keep answers in standard form throughout Physics and Chemistry calculations too. It reduces zero counting errors.
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Standard Form FAQs
What is standard form?
Standard form writes a number as a multiplied by 10 to the power n, where a is at least 1 and less than 10, and n is an integer. Exactly one non-zero digit sits before the decimal point. Large numbers have positive powers and numbers smaller than 1 have negative powers.
How do I multiply numbers in standard form?
Multiply the front numbers and add the powers of 10. Then check the result: if the front number is 10 or more, rewrite it so it lies between 1 and 10 and increase the power accordingly. So 12 times 10 cubed becomes 1.2 times 10 to the fourth.
How do I add numbers in standard form?
Rewrite both numbers with the same power of 10 first, usually the larger one, then add the front numbers and keep that power. Never add the powers when adding numbers, since powers are only added when multiplying.
Why is 12 x 10 cubed not in standard form?
Standard form requires the front number to be at least 1 and less than 10, so 12 is too large. Rewrite it as 1.2 times 10, which turns the whole expression into 1.2 times 10 to the fourth. Forgetting this adjustment is the most common way to lose a mark here.
Continue through the IGCSE Mathematics syllabus
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Written to the published Cambridge IGCSE Mathematics (0580) syllabus. Check your school entry code and syllabus year, because Core and Extended candidates are assessed on different content. Last reviewed 2026-08-12.