# Significant Figures - Scientific Notation

Need to calculate the average of the following two figures, and be sure to keep significant figures.

19.5 + 20.40 = 39.9

39.9 /2 = 19.95

If the answer is 19.95, what is the answer using significant figures only?

Can the answer containing significant figures be put into scientific notation?

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#### Solution Preview

19.5 ==> 3 significant figures

20.40 ==> 4 significant figures

19.5 + 20.40 = (3 significant figures) = 39.9

39.9 ==> 3 significant figures

[ 39.9/2 ] =(3 significant figures) = 20.0 ==> the ...

#### Solution Summary

The answer is given step-by-step with explanation. The scientific notation significant figures are determined.

Measurement and Scientific Notation

1. In a density experiment, a student experimentally measures the following four values for the density of liquid ethanol: 0.772g/ml, 0.774g/ml, 0.785g/ml, and 0.775g/ml. The theoretical density of ethanol is 0.789 g/ml at 20ºC.

a. Compute the average density of ethanol.

b. Compute the % error for the average density (to 2 sig figs).

c. Compute the standard deviation for this data (to 2 sig figs).

d. Is this data accurate? precise? Explain.

2. Write the following measurements in scientific notation. Assume that terminal zeros of whole number are not significant. Remember that WebAssign uses the calculator notation of e instead of 10.

a. 850 g

b. 0.00025 L

c. 2350000 m

3. Using appropriate rules for rounding, round each of the following numbers to three significant figures:

a. 34.7823 m

b. 0. 003117 L

c. 3356.8 s

d. 1.2936 kg

Multiplication and Division

Perform the following calculations of measured numbers. Give the answers with the correct number of significant figures. Round your final answer only. Assume all numbers are measurements.

a. 57 x 0.55

b. 61.7 / 11

c. (2.327)(0.585)/((8.42)(0.0065))

d. 95.0 / 5.00

Addition and Subtraction

Perform the following calculations and give the answer with the correct number of significant figures.

a. 20.6 cm + 0.179 cm

b. 106.21 mL + 0.773 mL + 53 mL

c. 153.751 g - 15.57 g

4.Identifying each of the following numbers as measured or exact; give the number of significant figures in each. You may also type infinite or vague when appropriate.

a. 47.0 g

b. 10 pencils

c. 0.0005 cm

d. 550000 km

e. 3 eggs

5. Identify each of the following as an exact or a measured number.

(a) thickness of a book

(b) number of tea bags needed to make a pot of tea

(c) number of pencils in a pack

(d) number of eggs in a 3-egg omelet

6. Type of Measurement/Metric Unit/Abbreviation

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