Question

1. in the measurements below, the significant digits are underlined. determine the rule(s) that were used to decide which digits were significant, and which were not significant.

a. 0.420 g
b. 2100 g
c. 51.0 m
d. 590 students
e. 5,200.0 g
f. 6020 mg

Explanation:

Step1: Recall significant - digit rules

Non - zero digits are always significant. Zeros between non - zero digits are 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 0.420 g

The non - zero digits 4 and 2 are significant. The trailing zero after the decimal point is also significant.

Step3: Analyze 2100 g

The non - zero digits 2 and 1 are significant. The trailing zeros may be just placeholders, so they are not considered significant in this case.

Step4: Analyze 51.0 m

The non - zero digits 5 and 1 are significant. The trailing zero after the decimal point is significant.

Step5: Analyze 590 students

The non - zero digits 5 and 9 are significant. The trailing zero may be just a placeholder, so it is not considered significant.

Step6: Analyze 5,200.0 g

The non - zero digits 5 and 2 are significant. The zeros between non - zero digits and the trailing zero after the decimal point are significant.

Step7: Analyze 6020 mg

The non - zero digits 6 and 2 are significant. The zero between non - zero digits is significant. The trailing zero may be a placeholder, so it is not considered significant.

Answer:

a. Non - zero digits (4, 2) and trailing zero after decimal are significant.
b. Non - zero digits (2, 1) are significant, trailing zeros are not.
c. Non - zero digits (5, 1) and trailing zero after decimal are significant.
d. Non - zero digits (5, 9) are significant, trailing zero is not.
e. Non - zero digits (5, 2), zero between non - zero digits and trailing zero after decimal are significant.
f. Non - zero digits (6, 2) and zero between non - zero digits are significant, trailing zero is not.