Final answer:
Significant digits represent the precision of a measurement and include all known digits plus one estimated digit. Each given measurement has a specific number of significant digits based on rules such as non-zero digits being significant, zeros between non-zero digits being significant, and trailing zeros after a decimal point also being significant.
Step-by-step explanation:
Understanding significant digits is essential in expressing the precision of a measurement. Significant digits include all the numbers that are known with certainty plus one final digit, which is somewhat uncertain or estimated.
- (a) 2688 cm has four significant digits. All non-zero digits are considered significant.
- (b) 3.507 g has four significant digits. Here, zeros between non-zero digits are significant.
- (c) 5.700 km has four significant digits, including the trailing zeros because they come after a decimal point.
- (d) 0.00400 kg has three significant digits. Leading zeros are not significant, but the trailing zeros after a decimal point are.
- (e) 24.00300 m has seven significant digits. Here, both the zeros between non-zero digits and the trailing zeros after a decimal point count as significant.
- (f) 2400 m has two or more significant digits depending on whether it is rounded or an exact count. Without additional context, we typically assume it has two significant digits.
- (g) 9.5000 × 10³ m has five significant digits. This includes all four digits and the implied multiplicative factor of 10 raised to the power of 3.
- (h) 0.0020056 g has five significant digits, not including the leading zeros, but counting all other numbers.