Question

How many significant digits are in each of the following?

(a) 83200±200 m
(b) 6.121×10⁻⁴ ±0.005×10⁻⁴
(c) 87.005±0.003

Answer 1

The number of significant digits in a measurement represents the precision or accuracy of the measurement. Non-zero digits are always significant, while leading zeros are not significant. Trailing zeros are significant if they appear after the decimal point.

Step-by-step explanation:

The number of significant digits in a measurement represents the precision or accuracy of the measurement. In order to determine the number of significant digits, we follow these rules:

1. Non-zero digits are always significant. For example, 83200 has 5 significant digits.
2. Leading zeros, which are zeros that come before any non-zero digit, are not significant. For example, 0.005 has 1 significant digit.
3. Trailing zeros, which are zeros that come after any non-zero digit, are significant if they are after the decimal point. For example, 87.005 has 5 significant digits.
4. Trailing zeros are not significant if they are before the decimal point. For example, 83200 has 5 significant digits, not 6.
5. If a number is expressed in scientific notation, all digits in the coefficient are significant. For example, 6.121×10⁻⁴ has 4 significant digits.
6. Uncertainty values, such as ±200 in 83200±200, do not affect the significant digits of the number.