Scientific Notation and Significant Figures in Engineering & Science
How scientists write astronomical distances and atomic scales, plus rules for rounding measured precision.
Why Scientific Notation Exists
In physics and chemistry, numbers range from the mass of the Sun (1,989,000,000,000,000,000,000,000,000,000 kg) to the charge of an electron (0.0000000000000000001602 Coulombs). Writing these with standard zeroes is error-prone. Scientific notation writes numbers in standard exponential form.
Where 1 ≤ |a| < 10 (called the mantissa or significand) and b is an integer exponent.
The 4 Rules of Significant Figures (“Sig Figs”)
Significant figures convey the precision of a measurement:
1. All non-zero digits are significant: 148 has 3 sig figs.
2. Zeros between non-zero digits are significant: 4005 has 4 sig figs.
3. Leading zeros are NOT significant: 0.0032 has only 2 sig figs (the leading zeros are placeholders).
4. Trailing zeros AFTER a decimal point ARE significant: 45.00 has 4 sig figs (it shows precision to the hundredth).
Calculate (4.5 × 10³) × (2.00 × 10−²) with correct significant figures:
1. Multiply coefficients: 4.5 × 2.00 = 9.0.
2. Add exponents: 10³ × 10−² = 10^(3 − 2) = 10¹.
3. Check sig figs: 4.5 has 2 sig figs; 2.00 has 3 sig figs. The result must have 2 sig figs.
4. Final answer: 9.0 × 10¹ (or 90. with 2 sig figs).