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Units, Scientific Notation, and Significant Figures

Problems

Significant Figures

Accuracy vs. Precision

Problem : Silver has a density of 10.5 g/mL at 25 C. What is the mass of 16 mL of silver?

However if 16 mL was a measured value, it has only 2 significant figures. Therefore the final answer must be 170 g. Since there is ambiguity as to whether the final zero here is significant or not, the answer is best expressed: 1.7 x 102 g.

Problem : How many significant figures are there in the following numbers:

a. 209.4
B. 1.74x10-23
c. 0.00220
d. 0.087686

Answers: a: 4, because the number neither begins nor ends with zeros.
B: 3, All are non-zero digits
c: 3, The first three zeros just mark the decimal place, but the zero after the 2 is significant since it indicates certainty
d. 5, the zeros serve only to mark the place

Problem : Please perform the necessary math and give the number with the correct number of significant figures. Use scientific notation where appropriate. A. 4.632 x 2.5
B. 12.443 +1.94672
C. 0.0000042 x 24365
D. 5.4 x 104 x 2.3 x 102
E. (41 x 3890)/36

A. 12
B. 14.390
C. 1.0x10-1
D. 1.2x107
E. 4.4x103

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