Ordering numbers in standard form | Maths | Quizalize & Oak National Academy

Starter quiz

Numbers written in standard form are written in the form $A \times 10^B$ where $A$ is ___________.
- greater than 1 and less than 10
- greater than or equal to 1 and less than 10 ✓
- greater than or equal to 1 and less than or equal to 10
- greater than 1 and less than or equal to 10
- an integer
Which of the following are written in standard form?
- ${2.3}\div10^{2}$
- ${2.08}\times10^{-5}$ ✓
- ${0.258}\times10^{-4}$
- ${1.07}\div10^{-2}$
- ${1.0045}\times10^{-3}$ ✓
Use a place value grid to write $0.00026$ in standard form.
- ${2.6}\times10^{-3}$
- ${2}\div10^{-4}$
- ${2.6}\div10^{-3}$
- ${2.6}\times10^{-4}$ ✓
- ${2}\times10^{-4}$
Write $0.000026$ in standard form.
- ${2.6}\times10^{-4}$
- ${2.6}\times10^{-5}$ ✓
- ${2.6}\div10^{-5}$
- ${2.6}\times10^{5}$
- ${26}\times10^{-6}$
${5.23}\times10^{-2}$ as an ordinary number is ______.
- '0.0523' ✓
Match each ordinary number to the equivalent number written in standard form.
- $0.0033$
  
  ⇔
  
  ${3.3}\times10^{-3}$ ✓
- $30 300$
  
  ⇔
  
  ${3.03}\times10^{4}$ ✓
- $0.00303$
  
  ⇔
  
  ${3.03}\times10^{-3}$ ✓
- $33 000$
  
  ⇔
  
  ${3.3}\times10^{4}$ ✓
- $0.0303$
  
  ⇔
  
  ${3.03}\times10^{-2}$ ✓
- $330 000$
  
  ⇔
  
  ${3.3}\times10^{5}$ ✓

Exit quiz

These are all examples of numbers written in ______ form: ${9.04}\times10^{2}$ , ${2.98}\times10^{-2}$ and ${1.39}\times10^{8}$
- 'standard' ✓
Which of the following inequalities is incorrect?
- ${9.88}\times10^{2} <{2.5}\times10^{3}$
- ${1.8}\times10^{8} < {2.5}\times10^{8}$
- ${3.02}\times10^{3}<{2.5}\times10^{5}$
- ${5.4}\times10^{3}<{5.04}\times10^{3}$ ✓
- ${1.45}\times10^{6}<{1.456}\times10^{6}$
Starting with the smallest, put these numbers written in standard form in order of size.
- 1
  
  ⇔
  
  ${8}\times10^{2}$
- 2
  
  ⇔
  
  ${1.31}\times10^{3}$
- 3
  
  ⇔
  
  ${2.1}\times10^{4}$
- 4
  
  ⇔
  
  ${2.2}\times10^{4}$
- 5
  
  ⇔
  
  ${2.8}\times10^{5}$
Which of the following inequalities is incorrect?
- ${6.7}\times10^{-4}<{1.4}\times10^{-3}$
- ${2.72}\times10^{-1}<{2.8}\times10^{-2}$ ✓
- ${8.2}\times10^{-3}<{2.8}\times10^{-2}$
- ${2.72}\times10^{-1}<{2.8}\times10^{-1}$
- ${1.04}\times10^{-6}<{1.045}\times10^{-6}$
Starting with the smallest, put these numbers written in standard form in order of size.
- 1
  
  ⇔
  
  ${7.4}\times10^{-6}$
- 2
  
  ⇔
  
  ${9.4}\times10^{-5}$
- 3
  
  ⇔
  
  ${2.308}\times10^{-4}$
- 4
  
  ⇔
  
  ${2.318}\times10^{-4}$
- 5
  
  ⇔
  
  ${3.23}\times10^{-2}$
Starting with the smallest, put these numbers in order of size.
- 1
  
  ⇔
  
  ${4.6}\times{10}^{-4}$
- 2
  
  ⇔
  
  ${4.6}\times0.01$
- 3
  
  ⇔
  
  ${4.6}\times{10}^{-1}$
- 4
  
  ⇔
  
  ${4.6}\times{10}^2$
- 5
  
  ⇔
  
  ${4600}\times{{1}\over{10}^{-1}}$

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Lesson Details

Key learning points

It can be easier to compare numbers if they are all in standard form.
If all numbers are in standard form, you can compare the powers of 10
When powers of 10 are the same, you can compare the digits of what remains.

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

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).