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 expresses numbers as a decimal between 1.0 and 10.0 multiplied by a power of 10.
- Standard Form — a number written as a decimal between 1.0 and 10.0 multiplied by a power of 10. Example: 4.2 x 10^5 = 420,000
- Negative Exponents — used in standard form to represent very small numbers. Example: 3.5 x 10^-3 = 0.0035
- Ordinary Numbers — numbers not in standard form, often converted from or to standard form. Example: 5.17 x 10^4 = 51,700
Exam Tips
Key Definitions to Remember
- Standard form is a number written as a decimal between 1.0 and 10.0 multiplied by a power of 10.
- Negative exponents are used to represent very small numbers in standard form.
Common Confusions
- Forgetting to adjust the power of 10 when converting between standard form and ordinary numbers.
- Mixing up the rules for adding/subtracting and multiplying/dividing numbers in standard form.
Typical Exam Questions
- Work out (3.2 × 10^4) + (2.3 × 10^3), giving your answer in standard form? Answer: 3.43 x 10^4
- Write 346 in standard form? Answer: 3.46 x 10^2
- Write 0.00216 in standard form? Answer: 2.16 x 10^-3
What Examiners Usually Test
- Ability to convert between standard form and ordinary numbers.
- Performing calculations using numbers in standard form.
- Understanding and applying index laws in standard form calculations.