Maths Library

Scientific Notation: Year 8 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

Scientific Notation is taught in Year 8 (age 13 to 14) 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 Australian Curriculum v9. Check wording and codes against the official document.

  • AC9M8N02 Express numbers in scientific notation and convert between standard form and decimal notation.

Sample sheet and answers

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

Scientific Notation

Year 8 maths

Qs
6
Marks
6
NameDateScore / 6
1.
Write 2000 in standard form.
[1]
2.
Write 7000 in standard form.
[1]
3.
Write 9 × 104 as an ordinary number.
[1]
4.
Write 600 in standard form.
[1]
5.
Write 6 × 103 as an ordinary number.
[1]
6.
Write 4 × 105 as an ordinary number.
[1]

Answer key

  1. 2 × 103Move the decimal point to make a number between 1 and 10; It moves 3 places, so the power is 3
  2. 7 × 103Move the decimal point to make a number between 1 and 10; It moves 3 places, so the power is 3
  3. 90 000Move the decimal point 4 places right
  4. 6 × 102Move the decimal point to make a number between 1 and 10; It moves 2 places, so the power is 2
  5. 6000Move the decimal point 3 places right
  6. 400 000Move the decimal point 5 places right