Maths Library

Standard Form: Year 11 maths

This topic covers reading, writing, and calculating with numbers written in standard index form. The worksheet practises conversion to and from ordinary numbers alongside all four operations.

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What this covers

Standard Form is taught in Year 11 (age 15 to 16, KS4) as a topic to introduce. It sits in the Number strand.

Worked example

Calculate (3 × 10^4) × (6 × 10^3) giving your answer in standard form.

  1. Multiply the mantissas: 3 × 6 = 18
  2. Multiply the powers of ten: 10^4 × 10^3 = 10^7
  3. Adjust 18 × 10^7 into standard form (1 <= A < 10): 1.8 × 10^8

Answer: 1.8 × 10^8

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Convert large numbers between standard form and ordinary numbers with positive powers
  2. Convert small decimal numbers involving negative powers of ten
  3. Multiply and divide numbers in standard form without mantissa readjustment
  4. Multiply and divide requiring adjustment to ensure the coefficient is between 1 and 10
  5. Addition and subtraction of numbers with different powers of ten in standard form

Common mistakes

  • Leaving the leading number outside the range [1, 10), such as writing 42 * 10^5
  • Counting the number of zeros instead of counting decimal place shifts

Curriculum links

Indicative matches to National Curriculum for England. Check wording and codes against the official document.

  • Convert numbers between ordinary forms and standard index form to solve complex problems.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Standard Form

Year 11 maths

Qs
6
Marks
24
NameDateScore / 24
1.
Write 3.6 × 104 as an ordinary number.
[4]
2.
Write 4.9 × 10−5 as an ordinary number.
[4]
3.
Write 8.8 × 10−6 as an ordinary number.
[4]
4.
Write 0.032 in standard form.
[4]
5.
Write 9.9 × 10−5 as an ordinary number.
[4]
6.
Write 9.7 × 109 as an ordinary number.
[4]

Answer key

  1. 36 000Move the decimal point 4 places right
  2. 0.000049Move the decimal point 5 places left
  3. 0.0000088Move the decimal point 6 places left
  4. 3.2 × 10−2Move the decimal point to make a number between 1 and 10; It moves 2 places, so the power is −2
  5. 0.000099Move the decimal point 5 places left
  6. 9 700 000 000Move the decimal point 9 places right