Maths Library

Scientific Notation: Grade 8 math

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 Grade 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 Common Core State Standards. Check wording and codes against the official document.

  • 8.EE.A.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities.

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

Grade 8 math

Qs
6
Marks
12
NameDateScore / 12
1.
Write 1600 in standard form.
[2]
2.
Write 76 000 in standard form.
[2]
3.
Write 9.6 × 105 as an ordinary number.
[2]
4.
Write 600 in standard form.
[2]
5.
Write 6.2 × 104 as an ordinary number.
[2]
6.
Write 3.8 × 107 as an ordinary number.
[2]

Answer key

  1. 1.6 × 103Move the decimal point to make a number between 1 and 10; It moves 3 places, so the power is 3
  2. 7.6 × 104Move the decimal point to make a number between 1 and 10; It moves 4 places, so the power is 4
  3. 960 000Move the decimal point 5 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. 62 000Move the decimal point 4 places right
  6. 38 000 000Move the decimal point 7 places right