Problem solving with standard form calculations | Maths

Starter quiz

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.

'1' ✓
Calculate $(4.6\times10^6)\div(2\times10^2)$ .

$2.3\div10^3$

$2.3\div10^4$

$2.3\times10^3$

$2.3\times10^4$ ✓

$2.6\times10^4$
Calculate $(5.4\times10^{5})\div(3\times10^{-2})$ .

$1.8\times10^3$

$1.8\times10^7$ ✓

$1.8\div10^7$

$1.8\div10^3$

$2.4\times10^7$
Calculate $480\text{ } 000\div(4\times10^{-2})$ .

$1.2\times10^{-1}$

$1.2\times10^{-2}$

$1.2\times10^{2}$

$1.2\times10^{3}$

$1.2\times10^{7}$ ✓
Calculate ${(1.6\times10^4)\times(2\times10^{-5})}\over(6.4\times10^2)$ . Give your answer in standard form.

$0.5\times10^{-3}$

$5\times10^{-3}$

$5\times10^{-4}$ ✓

$0.5\times10^{-4}$
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.

'312 500 000' ✓

Exit quiz

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

Mean

Median ✓

Mode

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

$4.5\times10^{-2}$

$4.5\times10^2$

$4.5\times10^3$ ✓

$4.2\times10^4$
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

⇔

$4.8\times10^6$
Find the median of: $4.5\times10^5$ , $4.5\times10^3$ . $4.2\times10^5$ , $5.4\times10^3$ and $4.5\times10^4$ .

$4.5\times10^3$

$4.5\times10^4$ ✓

$4.2\times10^5$

$4.5\times10^5$

$5.4\times10^3$
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 $^3$

$4\times10^{12}$ cm $^3$ ✓
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

1 billion ✓

100 million

10 million

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Lesson Details

Key learning points

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.

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.

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.