Study Notes
Standard form is a way of writing numbers that are too large or too small to be conveniently written in decimal form. It is expressed as A × 10^n, where A is a number between 1 and 10, and n is a whole number.
- Standard Form — a way to write numbers using powers of ten. Example: 3.2 × 10^6
- Converting Large Numbers — moving the decimal point to the left and counting the moves as the power of ten. Example: 56,700,000 = 5.67 × 10^7
- Converting Small Numbers — moving the decimal point to the right and counting the moves as the negative power of ten. Example: 0.0000099 = 9.9 × 10^-6
Exam Tips
Key Definitions to Remember
- Standard form is written as A × 10^n, where 1 ≤ A < 10 and n is an integer.
- Large numbers in standard form have positive powers of ten.
- Small numbers in standard form have negative powers of ten.
Common Confusions
- Forgetting to adjust the power of ten when moving the decimal point.
- Confusing positive and negative powers when converting numbers.
Typical Exam Questions
- Express 4.2 × 10^5 as a number? Answer: 420,000
- Write 0.0000043 in standard form? Answer: 4.3 × 10^-6
- Convert 670 to standard form? Answer: 6.7 × 10^2
What Examiners Usually Test
- Ability to convert between standard form and decimal form.
- Understanding of positive and negative powers in standard form.
- Correct placement of the decimal point when converting numbers.