Scientific Notation
Write numbers as a×10ⁿ with 1 ≤ a < 10.
Key idea
Write numbers as a×10ⁿ with 1 ≤ a < 10.
In depth
Scientific notation writes a number as a × 10ⁿ with 1 ≤ a < 10. The exponent n tells the order of magnitude. It makes huge and tiny numbers easy to read and compare.
Worked example
93,000,000 = 9.3 × 10⁷; 0.00042 = 4.2 × 10⁻⁴.
Formula
Real-world uses
- Writing the distance to the Sun or the mass of an electron compactly
- Reading calculator displays
Common mistake
Leaving a ≥ 10, such as 12 × 10⁵, or using a positive exponent for numbers below 1.
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 Scientific Notation?
Write numbers as a×10ⁿ with 1 ≤ a < 10. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Scientific Notation?
The key formula is 6.02×10²³.
Where is Scientific Notation used in real life?
Real-world examples: Writing the distance to the Sun or the mass of an electron compactly; Reading calculator displays.
What should I learn before Scientific Notation?
Make sure you are comfortable with Powers of Ten, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Scientific Notation?
Leaving a ≥ 10, such as 12 × 10⁵, or using a positive exponent for numbers below 1.
How can I practise Scientific Notation?
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 Scientific Notation?
Move on to Significant Figures 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.