Rounding Numbers, Significant Figures, and Scientific Notation (Advanced)
1. Rounding Numbers (Advanced)
- Rounding to a specific decimal place (e.g., 3 decimal places, 5 decimal places, etc.):
Example:
- Round 8.42356 to the third decimal place: 8.424
- Round 4535654 to the nearest ten thousand: 4550000
- Round 7.12987 to the nearest hundredth: 7.13
- Round 123456789 to the nearest million: 123000000
- **With Negative Numbers:**
- Round -5.23567 to the second decimal: -5.24
- Round -3125.487 to the nearest hundred: -3200
2. Significant Figures (Advanced)
- **Counting Significant Figures (SF):**
- Non-zero digits are always significant.
- Zeros between non-zero digits are significant.
- Leading zeros are NOT significant.
- Trailing zeros in decimal numbers are significant.
- Examples:
- 0.000905 -> 3 significant figures
- 5300000 (without a decimal) -> 2 significant figures
- 4.600 × 10^4 -> 4 significant figures
- Round 0.00987634 to 3 significant figures: 0.00988
- Round 2030000 to 2 significant figures: 2000000
- **Operations with Significant Figures:**
- Multiply 0.00456 × 1000 -> 0.005 (rounded to 1 SF)
- Divide 153000 by 230.4 -> 664.0 (rounded to 3 SF)
3. Scientific Notation (Advanced)
- **Scientific Notation for Large and Small Numbers:**
- 5670000000000 -> 5.67 × 10^12
- 0.00000642 -> 6.42 × 10^-6
- Convert 0.000000321 to scientific notation: 3.21 × 10^-7
- **Operations with Scientific Notation:**
- Add 3.2 × 10^4 and 5.6 × 10^3:
Convert both to the same exponent: 32 × 10^3 + 5.6 × 10^3 = 37.6 × 10^3
Final answer: 3.76 × 10^4
4. Practice Questions (Advanced)
- **Rounding Numbers:**
1. Round 15869.7843 to the nearest thousand.
2. Round 0.00543678 to the third decimal place.
3. Round 245.98765 to the nearest tenth.
4. Round -642.5678 to the nearest hundred.
- **Significant Figures:**
1. Identify the significant figures in 0.00000452.
2. Round 9120000 to 3 significant figures.
3. How many significant figures are in 0.0098005?
4. Round 1357892 to 4 significant figures.
5. Multiply 0.00245 × 1050 and give the result with the correct number of significant figures.
- **Scientific Notation:**
1. Convert 9030000000000 to scientific notation.
2. Convert 0.0000573 to scientific notation.
3. Add 4.8 × 10^6 and 3.2 × 10^7 in scientific notation.
4. Subtract 2.5 × 10^5 from 4.5 × 10^6.