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 indicating the number of places the decimal point moves.
- Standard Form — A way to write numbers using powers of ten. Example: 3.2 × 10^6
- Converting to Large Numbers — Moving the decimal point to the right. Example: 4.2 × 10^5 = 420000
- Converting to Small Numbers — Moving the decimal point to the left. Example: 2.8 × 10^-4 = 0.00028
- Writing Large Numbers in Standard Form — Moving the decimal point to the left and counting the moves. Example: 56,700,000 = 5.67 × 10^7
- Writing Small Numbers in Standard Form — Moving the decimal point to the right and counting the moves. Example: 0.0000099 = 9.9 × 10^-6
Exam Tips
Key Definitions to Remember
- Standard form is A × 10^n, where 1 ≤ A < 10 and n is a whole number.
Common Confusions
- Confusing the direction of the decimal point movement when converting.
- Forgetting to adjust the sign of n based on the direction of movement.
Typical Exam Questions
- Convert 4.2 × 10^5 to a normal number? 420000
- Write 0.0000043 in standard form? 4.3 × 10^-6
- Express 670 in standard form? 6.7 × 10^2
What Examiners Usually Test
- Ability to convert between standard form and normal numbers.
- Understanding of how to determine the power of ten based on decimal movement.