Answer: Significant figures in a measured value are all the reliably known digits plus the first uncertain digit. The order of magnitude of a quantity is the power of 10 (n) when the quantity is written as \( A \times 10^{n} \) with \( 0.5 \le A < 5 \).
Significant figures:
- The significant figures in the measured value of a physical quantity are the reliable digits plus the first uncertain digit.
- Larger the number of significant figures in a measurement, greater is its accuracy, and vice versa.
- An instrument with a smaller least count gives a measurement with more significant figures.
Rules for counting significant figures:
- All non-zero digits are significant. E.g. 178.43 cm3 has 5 significant figures (1, 7, 8, 4, 3).
- All zeros between two non-zero digits are significant. E.g. 165.02 g has 5 significant figures.
- If the number is less than 1, the zeros to the right of the decimal point but to the left of the first non-zero digit are not significant. E.g. in 0.001405 the three zeros before 1 are not significant (the zero between 4 and 5 is); so it has 4 significant figures (1, 4, 0, 5).
- Zeros to the right of the last non-zero digit are significant if the number has a decimal point. E.g. 1.500 and 0.01500 each have 4 significant figures.
But a change of units does not change the number of significant figures: L = 125 m = 12500 cm = 125000 mm has only 3 significant figures (better written as \( 1.25 \times 10^{4} \) cm).
Order of magnitude:
Any physical quantity can be expressed as \( A \times 10^{n} \), where A is a number such that \( 0.5 \le A < 5 \). The integer n is called the order of magnitude of the quantity.
Examples:
- Speed of light in air = \( 3 \times 10^{8} \) m/s; here A = 3, so the order of magnitude = 8.
- Mass of an electron = \( 9.1 \times 10^{-31} \) kg = \( 0.91 \times 10^{-30} \) kg; here A = 0.91, so the order of magnitude = –30.