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# Working with significant figures

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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

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#### 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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