Scientific Measurement Conversion Problems Prentice Hall Chapter 3.3 Deborah Yager

Objectives  Construct conversion factors from equivalent measurements  Apply the technique of dimensional analysis to conversion problems  Convert complex units, using dimensional analysis

Conversion Factors A conversion factor is a ratio of equivalent measurements. The ratios (100 cm/1 m) and (1 m/100 cm) are examples of conversion factors.

When a measurement is multiplied by a conversion factor, the numerical value is generally changed, but the actual size of the quantity measured remains the same. The rule of multiplying by “1”: Every conversion factor is actually multiplying by “1”.

The scale of the micrograph is in nanometers. Using the relationship 10 9 nm = 1 m, you can write the following conversion factors.

Dimensional analysis is a way to analyze and solve problems using the units, or dimensions, of the measurements. Dimensional analysis provides you with an alternative approach to problem solving.

Converting Between Units Problems in which a measurement with one unit is converted to an equivalent measurement with another unit are easily solved using dimensional analysis. 3.3

Converting between units is the same as multiplying by “1”:

What is cm in micrometers?

Converting Complex Units Many common measurements are expressed as a ratio of two units. If you use dimensional analysis, converting these complex units is just as easy as converting single units. It will just take multiple steps to arrive at an answer.

1. 1 Mg = 1000 kg. Which of the following would be a correct conversion factor for this relationship? a)  1000 b)  1/1000 c)÷ 1000 d)1000 kg/1Mg

1. 1 Mg = 1000 kg. Which of the following would be a correct conversion factor for this relationship? a)  1000 b)  1/1000 c)÷ 1000 d)1000 kg/1Mg

2. The conversion factor used to convert joules to calories changes a)the quantity of energy measured but not the numerical value of the measurement. b)neither the numerical value of the measurement nor the quantity of energy measured. c)the numerical value of the measurement but not the quantity of energy measured. d)both the numerical value of the measurement and the quantity of energy measured.

2. The conversion factor used to convert joules to calories changes a)the quantity of energy measured but not the numerical value of the measurement. b)neither the numerical value of the measurement nor the quantity of energy measured. c)the numerical value of the measurement but not the quantity of energy measured. d)both the numerical value of the measurement and the quantity of energy measured.

3. How many  g are in g? a)1.34  10 –4 b)1.34  10 –6 c)1.34  10 6 d)1.34  10 4

3. How many  g are in g? a)1.34  10 –4 b)1.34  10 –6 c)1.34  10 6 d)1.34  10 4

4. Express the density 5.6 g/cm 3 in kg/m 3. a)5.6  10 6 kg/m 3 b)5.6  10 3 kg/m 3 c)0.56 kg/m 3 d) kg/m 3

4. Express the density 5.6 g/cm 3 in kg/m 3. a)5.6  10 6 kg/m 3 b)5.6  10 3 kg/m 3 c)0.56 kg/m 3 d) kg/m 3