What is 7 200 000 in standard form?

7.2 × 10⁶. The decimal point moves 6 places.

What is 0.0005 in standard form?

5 × 10⁻⁴. The decimal point moves 4 places to the right.

What is 3.1 × 10³ as an ordinary number?

3100. Move the decimal point 3 places to the right.

What is (2 × 10³) × (4 × 10⁵)?

8 × 10⁸. Multiply 2 × 4 and add the powers.

Which number is written in standard form?

4.5 × 10⁻². The front number must be between 1 and 10, times a power of 10.

Standard form · Cambridge IGCSE Mathematics 0580 revision

In plain words

The Sun is 150 000 000 km away; a virus is 0.0000001 m across. Counting zeros is asking for mistakes. Standard form writes any number as a number between 1 and 10, times a power of ten that says where the decimal point really belongs.

Three things to know

Standard form is A × 10ⁿ, where A is at least 1 and less than 10.
Big numbers have a positive power: 45 000 = 4.5 × 10⁴. Small numbers have a negative power: 0.00042 = 4.2 × 10⁻⁴.
To multiply, multiply the front numbers and add the powers. To divide, divide and subtract. Then check the front number is still between 1 and 10.

Worked example

Work out (3 × 10⁴) × (5 × 10³), giving the answer in standard form.

Multiply the front numbers: 3 × 5 = 15. Add the powers: 4 + 3 = 7. That gives 15 × 10⁷.
15 is not between 1 and 10. Write it as 1.5 × 10.
1.5 × 10⁸.

Tips and tricks

The power counts how many places the decimal point moves, not the number of zeros.
To add or subtract, turn the numbers into ordinary numbers first.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Standard form: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

What is 7 200 000 in standard form?
- 72 × 10⁵
- 7.2 × 10⁶ (the answer)
- 7.2 × 10⁵
- 0.72 × 10⁷
The decimal point moves 6 places.
What is 0.0005 in standard form?
- 5 × 10⁴
- 5 × 10⁻³
- 5 × 10⁻⁴ (the answer)
- 0.5 × 10⁻³
The decimal point moves 4 places to the right.
What is 3.1 × 10³ as an ordinary number?
- 310
- 3100 (the answer)
- 31 000
- 0.0031
Move the decimal point 3 places to the right.
What is (2 × 10³) × (4 × 10⁵)?
- 6 × 10⁸
- 8 × 10¹⁵
- 8 × 10⁸ (the answer)
- 8 × 10²
Multiply 2 × 4 and add the powers.
Which number is written in standard form?
- 45 × 10³
- 0.45 × 10⁴
- 4.5 × 10⁻² (the answer)
- 4.5 × 100
The front number must be between 1 and 10, times a power of 10.

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

3 questions, 6 marks. Write your answers on paper, then check them.

Standard form

Cambridge IGCSE Mathematics 0580 · 6 marks · papermunch.org

Name ______________________________ Date ______________

Write 45 000 and 0.0036 in standard form.[2]
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4.5 × 10⁴ and 3.6 × 10⁻³.
I got this one
Work out (6 × 10⁵) ÷ (2 × 10²), giving the answer in standard form.[2]
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3 × 10³.
I got this one
Work out 2.5 × 10³ + 4 × 10², giving the answer in standard form.[2]
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2.9 × 10³. 2500 + 400 = 2900.
I got this one

Answers: Standard form

1. 4.5 × 10⁴ and 3.6 × 10⁻³.
2. 3 × 10³.
3. 2.9 × 10³. 2500 + 400 = 2900.