# 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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#### Solution Summary

The expert examines measurement and scientific notations. The standard deviations for the data is computed.

Measurements and Conversions

1. Measure the height of a stack of 50 pennies (in centimeters).

2.Convert the height of the stack of pennies into meters

3.Calculate how many pennies would be needed to make a tower 1 billion meters tall. Give answer in both standard calculation and in scientific notation.