Chemistry / Unit 1: Matter and Measurement
1.6 Scientific Notation
Notes
Scientific notation writes a number as $a \times 10^n$ where $1 \le a < 10$.
- Large numbers have positive exponents: $45{,}000 = 4.5 \times 10^4$.
- Small numbers have negative exponents: $0.00032 = 3.2 \times 10^{-4}$.
- Multiply: multiply the numbers and add the exponents. Divide: divide the numbers and subtract the exponents.
- Example: $(3.0 \times 10^4)(2.0 \times 10^3) = 6.0 \times 10^7$.
Practice
Write 0.000560 in scientific notation.
Move the decimal 4 places right to get 5.60, so the exponent is $-4$. Keep all 3 sig figs.
Calculate $\displaystyle \frac{8.0 \times 10^6}{2.0 \times 10^{-2}}$.
$8.0 \div 2.0 = 4.0$ and $6 - (-2) = 8$.
Calculate $(6.0 \times 10^{5})(5.0 \times 10^{3})$.
$6.0 \times 5.0 = 30 = 3.0 \times 10^1$, and $10^1 \times 10^5 \times 10^3 = 10^9$.
Ready for more? Take the Unit 1 test.