Question

2.14 indicate if the zeros are significant in each of the following measurements: a. 20.05 °c b. 5.00 m c. 0.000 02 g d. 120 000 yr e. 8.05 × 10² l

Explanation:

Step1: Recall significant - figure rules

Non - zero digits are always significant. Zeros between non - zero digits are significant. Leading zeros (zeros before the first non - zero digit) are not significant. Trailing zeros in a number with a decimal point are significant. Trailing zeros in a whole number without a decimal point may or may not be significant.

Step2: Analyze 20.05 °C

The zero between 2 and 5 is between non - zero digits, so it is significant. The zero after the decimal point is also significant.

Step3: Analyze 5.00 m

The two zeros after the decimal point are trailing zeros in a number with a decimal point, so they are significant.

Step4: Analyze 0.00002 g

The zeros before the 2 are leading zeros, so they are not significant.

Step5: Analyze 120000 yr

The zeros are trailing zeros in a whole number without a decimal point. Without additional information, we assume they are not significant.

Step6: Analyze 8.05×10² L

The zero between 8 and 5 is between non - zero digits, so it is significant.

Answer:

a. Both zeros are significant.
b. Both zeros are significant.
c. None of the zeros are significant.
d. None of the zeros are significant.
e. The zero is significant.