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: Recall significant - figure rules

Non - zero digits are always significant. Zeros between non - zero digits are significant. Leading zeros (zeros before non - zero digits) are not significant. Trailing zeros in a number with a decimal point are significant.

Step2: Analyze 3.405

Non - zero digits 3, 4, 5 and zero between 4 and 5 are significant. So, there are 4 significant figures.

Step3: Analyze 0.00289

Leading zeros are not significant. Non - zero digits 2, 8, 9 are significant. So, there are 3 significant figures.

Step4: Analyze 1030

Non - zero digits 1, 3 and zero between 1 and 3 are significant. Trailing zero without a decimal point may or may not be significant. Assuming it is not a measured value with known precision, we consider it non - significant for counting significant figures here. So, there are 3 significant figures.

Step5: Analyze 7.0040×10⁻³

In scientific notation, we consider the digits in the coefficient. Non - zero digits 7, 4 and zeros between and after non - zero digits are significant. So, there are 5 significant figures.

Step6: Analyze 102.00

Non - zero digits 1, 2 and zeros between non - zero digits and trailing zeros after decimal point are significant. So, there are 5 significant figures.

Step7: Analyze 0.000980

Leading zeros are not significant. Non - zero digits 9, 8 and trailing zero after non - zero digits is significant. So, there are 3 significant figures.

Step8: Analyze 9.80

Non - zero digits 9, 8 and trailing zero after decimal point are significant. So, there are 3 significant figures.

Answer:

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