Checking and securing understanding of writing large numbers in standard form | Maths

Starter quiz

Standard form is when a number is written in the form $A \times 10^n$ , (where ___________ and $n$ is an integer).

$A < 10$

$1 ≤ A ≤ 10$

$1 ≤ A < 10$ ✓

$1 < A < 10$
Which of the following numbers are written in standard form?

$287546\times10^{12}$

$9.8\times10^{-5}$ ✓

$9.4\times10^5$ ✓

$1\times10^9$ ✓

$9.4\div10^5$
Match each number written in exponent form with its place value.

$10^5$

⇔

Hundred thousands ✓

$10^4$

⇔

Ten thousands ✓

$10^3$

⇔

Thousands ✓

$10^2$

⇔

Hundreds ✓

$10^0$

⇔

Ones ✓
Match each measurement to an equivalent measurement.

4 km

⇔

4000 m ✓

4 cm

⇔

40 mm ✓

4 mm

⇔

0.4 cm ✓

4 m

⇔

400 cm ✓
Starting with the smallest, put these measurements in order of size.

1

⇔

3 cm

2

⇔

3000 mm

3

⇔

30 m

4

⇔

3 km
0.03 km + 4.9 m + 560 mm is equal to ______ centimetres.

'3546' ✓

Exit quiz

Match each number to its standard form equivalent.

340 000

⇔

$3.4\times10^5$ ✓

3400

⇔

$3.4\times10^3$ ✓

430 000

⇔

$4.3\times10^5$ ✓

4 300 000

⇔

$4.3\times10^6$ ✓
Which of the following numbers have not been written in standard form?

$44.4\times10^5$ ✓

$4.4\times10^5$

$0.34\times10^5$ ✓

$340\times10^5$ ✓

$34\times10^5$ ✓
Match each number to its correct standard form equivalent.

$44\times10^5$

⇔

$4.4\times10^6$ ✓

$0.4\times10^5$

⇔

$4\times10^4$ ✓

$0.34\times10^5$

⇔

$3.4\times10^4$ ✓

$340\times10^5$

⇔

$3.4\times10^7$ ✓

$34\times10^5$

⇔

$3.4\times10^6$ ✓
Starting with the smallest, put these numbers into ascending order.

1

⇔

$13 \text{ }400$

2

⇔

$49\text{ } 000$

3

⇔

$3.9\times10^{5}$

4

⇔

$78.2\times10^{4}$

5

⇔

$9.9\times10^{5}$
Starting with the place with the smallest population, put these towns and cities in ascending order of population size.

1

⇔

Bath: $0.95\times10^5$

2

⇔

Preston: $313\times10^3$

3

⇔

Leeds: $4600\times10^2$

4

⇔

Nottingham: $7.3\times10^5$
Saturn is $1.43\times10^9$ km from the Sun. Neptune is further from the Sun than Saturn. Which of these lengths could show the distance from the Sun to Neptune?

$4\text{ } 500\text{ }000\text{ }000$ km ✓

$22\text{ }800\text{ }000\text{ }000\text{ }000$ cm

$1.43\times10^{12}$ m

$150\text{ } 000 \text{ }000\text{ }000$ m

Worksheet

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Lesson Details

Key learning points

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

Common misconception

When a number is not quite written in standard form, pupils can incorrectly convert the number.

When the A number is greater than 10, add the necessary multiplications of 10 to the index of 10. When the A number is less than 10, subtract the necessary multiplications of 10 from the index of 10.

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).
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.