Year 9

Standard form

Convert numbers between ordinary form and standard form, and use standard form to multiply and divide very large or very small numbers.

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Lesson overview

Number - notation and calculation

Standard form (also called scientific notation) is a way of writing very large or very small numbers using powers of 10. A number in standard form looks like: A × 10ⁿ, where A is a number between 1 and 10 (including 1 but not including 10), and n is any integer (positive, negative or zero). Standard form makes it much easier to work with numbers like the mass of the Earth (5.97 × ${10}^{24}$ kg) or the size of a virus (2.5 × ${10}^{-8}$ m).

Converting a large number to standard form

Write 4,700,000 in standard form.

Count how many places you move the decimal point to get a number between 1 and 10. Moving left gives a positive power.

Converting a small number to standard form

Write 0.000035 in standard form.

Moving the decimal point right gives a negative power. The power tells you how many places you moved.

Converting back from standard form

Write 6.2 × ${10}^{3}$ as an ordinary number.

Positive power → move decimal right. Negative power → move decimal left.

Multiplying numbers in standard form

Calculate (3 × ${10}^{4}$ ) × (2 × ${10}^{3}$ ). Give your answer in standard form.

Multiply the A values together. Add the powers. Check A is still between 1 and 10.

Dividing numbers in standard form

Calculate (8 × ${10}^{6}$ ) ÷ (4 × ${10}^{2}$ ). Give your answer in standard form.

Divide the A values. Subtract the powers. Check A is between 1 and 10.

Worked example

The speed of light is approximately 3 × ${10}^{8}$ m/s. Light takes about 5 × ${10}^{2}$ seconds to travel from the Sun to the Earth. Calculate the distance from the Sun to the Earth in standard form.

Use distance = speed × time.
Multiply the A values: 3 × 5 = 15.
Add the powers: ${10}^{8}$ × ${10}^{2}$ = ${10}^{10}$ .
Result so far: 15 × ${10}^{10}$ .
15 is not between 1 and 10 — adjust: 15 = 1.5 × ${10}^{1}$ .
So the answer is 1.5 × ${10}^{10}$ × ${10}^{1}$ = 1.5 × ${10}^{11}$ metres.

Try it

Use the examples carefully, then choose the answer.

Question 1

Write 52,000 in standard form.

💡 Move the decimal point to get a number between 1 and 10.

Question 2

Write 0.0007 in standard form.

💡 Count how many places the decimal moves to the right.

Question 3

Write 3.6 × ${10}^{5}$ as an ordinary number.

💡 Move the decimal point 5 places to the right.

Question 4

Calculate (4 × ${10}^{3}$ ) × (5 × ${10}^{2}$ ). Give your answer in standard form.

💡 Multiply 4 × 5. Add the powers: 3 + 2. Adjust if A is not between 1 and 10.

Question 5

Calculate (9 × ${10}^{7}$ ) ÷ (3 × ${10}^{4}$ ). Give your answer in standard form.

💡 Divide 9 ÷ 3. Subtract the powers: 7 − 4.

Standard form

Lesson overview

Worked example

Try it

Independent practice will plug in here