1. Each part of this problem relates to significant figures, scientific notation

Question

1. Each part of this problem relates to significant figures, scientific notation, and/or unit conversion. Together, these four parts all count as a single problem for the purposes of omitting the problem you do not want me to grade. (a) (1 point) How many significant figures does mumber 0.0030670 have? (b) (1 point) Complete this calculation to the correct number of significant figures: 1 101.14 = 05.4- (c) (1 point) Express (1.7 x 106)-5 in scientific notation. (d) (1 point) Given that there are 12 inches in a foot and that 1 in. 2.54 cm, convert 1.17f to MKS units.

Explanation / Answer

1. a. given number

0.0030670

so significant digits = 5

because zeroes after decimal are not counted where as zeroes after the non zero digits after the decimal are counted

b. 105.4 - 101.14 = 4.26

now the first number has 4 significant digits and the other one has 5

so the answer can have only 4 significant digits

hence answer is 4.26

c. (1.7*10^6)^(-0.5) = 7.7*10^-4

after rounding off the answer should have the same number of significant figures as the problem which in this case is 2

d. 12 inches in a foot

1 in = 2.54 cm

1.17ft^2 = 1.17*(12^2) in^2 = 168.48 in^2

168.48 in^2 = 168.48*(2.54^2) cm^2 = 1086.965568 cm^2

1086.965568 cm^2 = 0.1086965568 m^2

hence in MKS system the answer is 0.109 cm^2 ( correct upto 3 significant firgures as the original problem had 3 significant digits)

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