It can be useful to have very large or very small numbers written in standard form.
Being able to perform arithmetic operations on numbers written in standard form reduces error during conversion.
Standard form calculations can be done quickly with the use of a calculator.

Keywords

Standard form - Standard form is when a number is written in the form A × 10n, (where 1 ≤ A < 10 and n is an integer).
Exponential form - When a number is multiplied by itself multiple times, it can be written more simply in exponential form.
Commutative - The commutative law states you can write the values of a calculation in a different order without changing the calculation; the result is still the same. It applies for addition and multiplication.
Associative - The associative law states that it doesn't matter how you group or pair values (i.e. which we calculate first), the result is still the same. It applies for addition and multiplication.

Common misconception

Incorrect use of the calculator when finding the mean of numbers. Omitting the brackets when summing the values.

Encourage pupils to calculate the sum of the values and record this before dividing by the number of values. This also encourages a record of a method.

To help with the second learning cycle you could have 'chocolate spheres' and toilet roll tubes to help pupils visualise the problem. They could also test out the theory of 64% of the volume of the cylinder being consumed.

Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.

Standard form is when a number is written in the form $$A × 10^n$$. When numbers are written in standard form the value of $$A$$ must be greater than or equal to and less than 10.

Correct Answer: 1, one

Q2.

Calculate $$(4.6\times10^6)\div(2\times10^2)$$.

$$2.3\div10^3$$

$$2.3\div10^4$$

$$2.3\times10^3$$

Correct answer: $$2.3\times10^4$$

$$2.6\times10^4$$

Q3.

Calculate $$(5.4\times10^{5})\div(3\times10^{-2})$$.

$$1.8\times10^3$$

Correct answer: $$1.8\times10^7$$

$$1.8\div10^7$$

$$1.8\div10^3$$

$$2.4\times10^7$$

Q4.

Calculate $$480\text{ } 000\div(4\times10^{-2})$$.

$$1.2\times10^{-1}$$

$$1.2\times10^{-2}$$

$$1.2\times10^{2}$$

$$1.2\times10^{3}$$

Correct answer: $$1.2\times10^{7}$$

Q5.

Calculate $${(1.6\times10^4)\times(2\times10^{-5})}\over(6.4\times10^2)$$. Give your answer in standard form.

$$0.5\times10^{-3}$$

$$5\times10^{-3}$$

Correct answer: $$5\times10^{-4}$$

$$0.5\times10^{-4}$$

Q6.

A grain of sand has a mass of $$1.6\times10^{-5}$$ g. How many grains of sand are there in $$5$$ kg? Give you answer as an ordinary number.

Correct Answer: 312 500 000, 312500000, 312,500,000

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6 Questions

Q1.

Which of the following is described here: The middle (or average middle) value in an ordered data set.

Mean

Correct answer: Median

Mode

Range

Q2.

What is the mode of the following? $$4.5\times10^3$$, $$4.5\times10^{-2}$$, $$4.5\times10^2$$, $$4.5\times10^3$$, $$4.2\times10^4$$.

$$4.5\times10^{-2}$$

$$4.5\times10^2$$

Correct answer: $$4.5\times10^3$$

$$4.2\times10^4$$

Q3.

Starting with the smallest number, put these numbers in ascending order.

1 - $$4.5\times10^3$$

2 - $$5.4\times10^3$$

3 - $$4.5\times10^4$$

4 - $$4.2\times10^5$$

5 - $$4.5\times10^5$$

6 - $$4.8\times10^6$$

Q4.

Find the median of: $$4.5\times10^5$$, $$4.5\times10^3$$. $$4.2\times10^5$$, $$5.4\times10^3$$ and $$4.5\times10^4$$.

$$4.5\times10^3$$

Correct answer: $$4.5\times10^4$$

$$4.2\times10^5$$

$$4.5\times10^5$$

$$5.4\times10^3$$

Q5.

Convert $$4\times10^6 $$ m$$^3$$ into cm$$^3$$.

$$4\times10^8 $$ cm$$^3$$

$$4\times10^9 $$ cm$$^3$$

$$4\times10^{10} $$ cm$$^3$$

$$4\times10^{11} $$ cm$$^3$$

Correct answer: $$4\times10^{12} $$ cm$$^3$$

Q6.

The volume of a football is $$4200$$ cm$$^3$$. The volume of Wembley is $$4\times10^6 $$ m$$^3$$. Assuming no gaps, approximately how many footballs will fit into Wembley stadium?

100 billion

10 billion

Correct answer: 1 billion

100 million

10 million