Maths · Number & Negatives
Powers of 10 & large numbers
Read, write, and manipulate powers of 10 up to millions.
What are powers of 10?
Powers of 10 show how many times we multiply 10 by itself. We write 10 × 10 as 10² (ten squared). The small raised number is called the exponent or power. It tells us how many tens to multiply together.
Building larger numbers
Each time the power increases by 1, the number gets 10 times bigger. So 10³ = 1000 (three zeros), 10⁴ = 10 000 (four zeros), and 10⁵ = 100 000 (five zeros). The power matches the number of zeros after the 1.
Why powers of 10 matter
Powers of 10 help us write very large numbers neatly. Instead of writing 1 000 000, we can write 10⁶. This shorthand is especially useful in science and when working with big measurements like populations or distances.
Multiplying by powers of 10
When we multiply a number by a power of 10, we move the digits left. Multiplying 34 by 10² gives 3400. We can think of it as adding two zeros, or shifting each digit two places to the left.
Working backwards
If we know that 10⁴ = 10 000, we can use this to solve problems. For example, 5 × 10⁴ means 5 × 10 000 = 50 000. We multiply the number by 1 followed by the right number of zeros.
Worked examples
1. Write 10⁵ as an ordinary number.
- The power 5 tells us how many zeros follow the 1.
- So 10⁵ = 1 followed by 5 zeros.
- 10⁵ = 100 000
2. Calculate 7 × 10³
- First work out 10³ = 1000 (three zeros after the 1).
- Now multiply: 7 × 1000.
- 7 × 10³ = 7000
3. Write 1 000 000 as a power of 10.
- Count the zeros after the 1: there are 6 zeros.
- The number of zeros equals the power.
- 1 000 000 = 10⁶
Try it yourself
What is 4 × 10⁴ written as an ordinary number?
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