Question

1. how many significant figures are in each of the following? a) 3.405 b) 0.00289 c) 1030 d) 7.0040 x 10^(-3) e) 102.00 f) 0.000980 g) 9.80

Explanation:

Step1: Identify 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, but here we assume they are not significant for standard cases.

Step2: Analyze 3.405

All digits (3, 4, 0, 5) are significant. So there are 4 significant figures.

Step3: Analyze 0.00289

The leading zeros are not significant. The non - zero digits 2, 8, 9 are significant. So there are 3 significant figures.

Step4: Analyze 1030

The zero between 1 and 3 is significant, but the trailing zero is not significant. So there are 3 significant figures.

Step5: Analyze 7.0040×10⁻³

All digits (7, 0, 0, 4, 0) are significant. So there are 5 significant figures.

Step6: Analyze 102.00

All digits (1, 0, 2, 0, 0) are significant. So there are 5 significant figures.

Step7: Analyze 0.000980

The leading zeros are not significant. The non - zero digits 9, 8 and the trailing zero are significant. So there are 3 significant figures.

Step8: Analyze 9.80

All digits (9, 8, 0) are significant. So there are 3 significant figures.

Answer:

a) 4
b) 3
c) 3
d) 5
e) 5
f) 3
g) 3