Study Notes
Standard form is a shorthand way of expressing large numbers using powers of ten.
- Standard Form — a way to write numbers as a product of a number and a power of ten. Example: 3.2 × 10^5
- Converting to Ordinary Numbers — changing a number from standard form to its full numerical value. Example: 4.2 × 10^5 = 420,000
- Writing Large Numbers in Standard Form — expressing a large number in standard form by moving the decimal point. Example: 56,700,000 becomes 5.67 × 10^7
Exam Tips
Key Definitions to Remember
- Standard form is written as A × 10^n where 1 ≤ A < 10
- To convert to ordinary numbers, multiply A by 10 raised to the power of n
Common Confusions
- Forgetting that A must be between 1 and 10
- Miscounting the number of decimal places moved when converting
Typical Exam Questions
- What is 3.2 × 10^5 as an ordinary number? Answer: 320,000
- Convert 420,000 to standard form. Answer: 4.2 × 10^5
- Write 56,700,000 in standard form. Answer: 5.67 × 10^7
What Examiners Usually Test
- Ability to convert between standard form and ordinary numbers
- Understanding of how to express large numbers in standard form