Powers of Ten
Multiplying by 10ⁿ shifts the decimal point n places.
Key idea
Multiplying by 10ⁿ shifts the decimal point n places.
In depth
Each power of ten shifts the decimal point: 10³ = 1000, 10⁻² = 0.01. Multiplying by 10ⁿ shifts the point n places right; dividing shifts it left. They make very large or small numbers manageable.
Worked example
4.7 × 10³ = 4700; 4.7 ÷ 10² = 0.047.
Formula
Real-world uses
- Converting between kilometres and metres
- Understanding prefixes such as kilo, mega and giga in technology
Common mistake
Moving the decimal point in the wrong direction.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Powers of Ten?
Multiplying by 10ⁿ shifts the decimal point n places. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Powers of Ten?
The key formula is 10³ = 1000.
Where is Powers of Ten used in real life?
Real-world examples: Converting between kilometres and metres; Understanding prefixes such as kilo, mega and giga in technology.
What should I learn before Powers of Ten?
Make sure you are comfortable with Averages: Median and Mode, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Powers of Ten?
Moving the decimal point in the wrong direction.
How can I practise Powers of Ten?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Powers of Ten?
Move on to Scientific Notation next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.