Question

Of the given numbers,
(1) 25300
(2) 5.600
(3) 0.07200
the number of significant figures for

• (1) is five
• (2) is two
• (3) is three
• (1) and (2) are four
• (2) and (3) are four

Hint:

Logic Tip: The presence of a decimal point is the absolute key for trailing zeros. "25300" has 3 sig figs, but "25300." (with a decimal) has 5 sig figs. Always scan for the decimal point first!

Answer 1

Answer: (E)

Concept:
The rules for determining significant figures are: 1. All non-zero digits are significant. 2. Leading zeros (zeros to the left of the first non-zero digit) are NEVER significant. 3. Trailing zeros in a number without a decimal point are generally NOT significant. 4. Trailing zeros in a number containing a decimal point are ALWAYS significant.
Step 1: Evaluate the first number.
Number: $25300$ This is a whole number without a decimal point. The trailing zeros are placeholders and are not considered significant. Significant digits: 2, 5, 3 Total significant figures = 3
Step 2: Evaluate the second number.
Number: $5.600$ This number contains a decimal point. Therefore, the trailing zeros are significant because they indicate the precision of the measurement. Significant digits: 5, 6, 0, 0 Total significant figures = 4
Step 3: Evaluate the third number.
Number: $0.07200$ The leading zeros ($0.0$) merely position the decimal point and are not significant. The trailing zeros are significant because of the presence of the decimal point. Significant digits: 7, 2, 0, 0 Total significant figures = 4
Step 4: Compare with the given options.
Based on our analysis, numbers (2) and (3) both have exactly four significant figures. This matches Option E.