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Working with significant figures

Please give rules for significant figures and explain as go along.

1) Put in decimal form and in scientific notation with sig. figures.

a) 4.060 + 120.23 + 4.1*10^-2

b) (140) / [7.2*10^3 * 16.43 * (16.43 - 14.26)]

2) How many sig. figures?

a) 100
b) 1.0*10^2
c) 1.00*10^3
d) 100.
e) 0.0048
f) 0.00480
g) 4.80*10^-3
h) 4.800*10^-3
i) 2001
j) 2.001*10^3
k) 0.0000101
l) 1000.
m) 22.04030

3) Use exponential notation to express #480 to:

1,2,3, and 4 sig. figures.

4) Perform the operation in sig. figures.

a) (0.102 * 0.0821 * 273) / 1.01
b) 0.14 * 6.022 * 10^23
c) 2.00*10^6/3.00*10^-7
d) 4.0*10^4 * 5.021*10^-3 * 7.34993*10^2

5) Rounnd each to 3 sig. figures and write in standard exponential notation.

a) 312.54
b) 0.00031254
c) 31,254,000
d) 0.31254
e) 31.254*10^-3

6) Do these in sig figures.

a) 97.381 + 4.2502 + 0.99195
b) 171.5 + 72.915 - 8.23
c) 8.925 - 8.904 / 8.925 * 100 (100 exact number)
d) (6.6262*10^-34 * 2.998 * 10^8) / 2.54*10^-9

7) Convert

a) How many kg in 1 teragram.
b) nanometers in 25 femtograms?
c) liters in 8.0 cubic deciliters

d) 8.43cm to milliliters.
e) 2.41*10^2cm to meters

f) 908oz. to kg
g) 12.8L to gallons
h) 125mL to quarts
i) 2.89gallons to milliliters
j) 4.48lb to grams
k) 550mL to quarts

Solution Preview

The following rules apply to determining the number of significant figures in a measured quantity:

1. All nonzero digits are significant--457 cm (three significant figures); 0.25 g (two significant figures).

2. Zeros between nonzero digits are significant--1005 kg (four significant figures); 1.03 cm (three significant figures).

3. Zeros to the left of the first nonzero digits in a number are not significant; they merely indicate the position of the decimal point--0.02 g (one significant figure); 0.0026 cm (two significant figures).

4. When a number ends in zeros that are to the right of the decimal point, they are significant--0.0200 g (three significant figures); 3.0 cm (two significant figures).

5. When a number ends in zeros that are not to the right of a decimal point, the zeros are not necessarily significant--130 cm (two or three significant figures); 10,300 g (three, four, or five significant figures). The way to remove this ambiguity is described below.

Use of standard exponential notation avoids the potential ambiguity of whether the zeros at the end of a number are significant (rule 5). For example, a mass of 10,300 g can be written in exponential notation showing three, four, or five significant figures:
1.03 x 10^4 g (three significant figures)
1.030 x 10^4 g ...

Solution Summary

The solution gives not only the answers but also the steps required to arrive at the answer.

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