Study Notes
Standard form is a shorthand way of expressing very large or very small numbers using powers of ten.
- Standard Form — a way to write numbers as A×10^n, where A is between 1 and 10 and n is a whole number. Example: 3.2×10^6
- Converting Standard Form to Ordinary Numbers — involves moving the decimal point based on the power of ten. Example: 4.2×10^5 = 420000
- Writing Ordinary Numbers in Standard Form — involves adjusting the decimal point to create a number between 1 and 10, then using the number of moves as the power of ten. Example: 56,700,000 = 5.6×10^7
Exam Tips
Key Definitions to Remember
- Standard form is A×10^n, where 1 ≤ A < 10 and n is a whole number.
- Converting involves moving the decimal point based on the power of ten.
Common Confusions
- Forgetting that A must be between 1 and 10.
- Confusing the direction of the decimal point movement for positive and negative powers.
Typical Exam Questions
- How do you express 4.2×10^5 as an ordinary number? 420000
- How do you write 56,700,000 in standard form? 5.6×10^7
- How do you express 0.0000099 in standard form? 9.9×10^-6
What Examiners Usually Test
- Understanding of how to convert between standard form and ordinary numbers.
- Ability to correctly apply the rules for writing numbers in standard form.