Writing small numbers in standard form | Maths | Quizalize & Oak National Academy

Starter quiz

______ form follows this convention: $A \times 10^B$ and $1 ≤ A < 10$ and $B$ is an integer.
- 'Standard' ✓
Which of the following are written in standard form?
- ${3.76}\times10^{4}$ ✓
- ${26}\times10^{3}$
- ${0.98}\times10^{8}$
- ${9.04}\times10^{2}$ ✓
- ${597}\times10^{6}$
Write 480 000 in standard form.
- ${480}\times10^{3}$
- ${48}\times10^{4}$
- ${4.8}\times10^{4}$
- ${4.8}\times10^{5}$ ✓
- ${0.48}\times10^{6}$
Match each ordinary number to the equivalent number written in standard form.
- $60 300$
  
  ⇔
  
  ${6.03}\times10^{4}$ ✓
- $6 300 000$
  
  ⇔
  
  ${6.3}\times10^{6}$ ✓
- $603$
  
  ⇔
  
  ${6.03}\times10^{2}$ ✓
- $603 000$
  
  ⇔
  
  ${6.03}\times10^{5}$ ✓
- $6300$
  
  ⇔
  
  ${6.3}\times10^{3}$ ✓
- $63 000$
  
  ⇔
  
  ${6.3}\times10^{4}$ ✓
${2.45}\times10^{6}$ as an ordinary number is ______.
- '2 450 000' ✓
What should go in the box to make this statement correct? $240 000 000 000 000 = 2.4 \square$
- $\times10^{13}$
- $\times10^{15}$
- $\div10^{14}$
- $\times10^{14}$ ✓
- $\div10^{13}$

Exit quiz

Standard form follows this convention: $A \times 10^B$ and $1 ≤ A < 10$ and $B$ is an ______.
- 'integer' ✓
Which of the following are written in standard form?
- ${0.26}\times10^{-4}$
- ${3.04}\times10^{-5}$ ✓
- ${4.3}\div10^{3}$
- ${7.2}\times10^{-3}$ ✓
- ${5.23}\div10^{-2}$
Use a place value grid to write $0.00506$ in standard form.
- ${5}\div10^{-3}$
- ${5.06}\times10^{-2}$
- ${5.06}\times10^{-3}$ ✓
- ${5.06}\div10^{-3}$
- ${5}\times10^{-3}$
Write $0.00047$ in standard form.
- ${4.7}\times10^{-3}$
- ${4.7}\times10^{3}$
- ${4.7}\times10^{-4}$ ✓
- ${4.7}\div10^{-4}$
- ${4.7}\times10^{4}$
${4.08}\times10^{-4}$ as an ordinary number is ______.
- '0.000408' ✓
Match each ordinary number to the equivalent number written in standard form.
- $0.000402$
  
  ⇔
  
  ${4.02}\times10^{-4}$ ✓
- $42 000$
  
  ⇔
  
  ${4.2}\times10^{4}$ ✓
- $0.00042$
  
  ⇔
  
  ${4.2}\times10^{-4}$ ✓
- $4020$
  
  ⇔
  
  ${4.02}\times10^{3}$ ✓
- $0.00402$
  
  ⇔
  
  ${4.02}\times10^{-3}$ ✓
- $4200$
  
  ⇔
  
  ${4.2}\times10^{3}$ ✓

Worksheet

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Lesson Details

Key learning points

It is difficult to read very small numbers, due to the number of digits involved.
It can be more efficient to write these very small numbers in standard form.
There is a convention for standard form.

Common misconception

Pupils can incorrectly write a number in standard form or use a number in incorrect standard form whereby the number A does not satisfy 1 ≤ A < 10 or pupils use division of positive powers of 10.

Standard form represents a multiplicative relationship, so there should always be a multiplication. Embedding the understanding that negative exponents refer to 1/10^n is important. Using the place value chart with fractional and exponent form helps.

Keywords

Exponential form - When a number is multiplied by itself multiple times, it can be written more simply in exponential form.
Associative law - The associative law states that a repeated application of the operation produces the same result regardless of how pairs of values are grouped. We can group using brackets.
Standard form - Standard form is when a number is written in the form A × 10^n, (where 1 ≤ A < 10 and n is an integer).