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# Conversion Problems What strategies can I use to solve problems in Science? - PowerPoint PPT Presentation

Conversion Problems What strategies can I use to solve problems in Science?. A conversion factor is a ratio of equivalent measurements used to convert between units Measurement in numerator = measurement in denominator For example: 1m/100cm 1m = 100cm

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Conversion ProblemsWhat strategies can I use to solve problems in Science?

• A conversion factor is a ratio of equivalent measurements used to convert between units

• Measurement in numerator = measurement in denominator

• For example: 1m/100cm 1m = 100cm

• When a measurement is multiplied by a conversion factor, the numerical value changes, but the actual size does not. Why?

• A unique way of writing the number 1.

• In the same system they are defined quantities so they have unlimited significant figures.

• Equivalence statements always have this relationship.

• big # small unit = small # big unit

• 1000 mm = 1 m

• How do we decide what goes on top and what goes on the bottom?

• Generally, the units we want to convert TO: go on the top. The units we are converting FROM: go on the bottom. (SEE YOUR GIFT LABEL!)

• This ensures that the units we were given cancel

• Units must be on opposite sides of the fraction in order to cancel. Think John Travolta in Saturday Night Fever….

• For example: Convert 750dg to grams.

• First write down what you are given

• Then construct a conversion factor that causes your given units to cancel

• 750dg │ 1g = 75g

│10dg

• Where can we find the numbers we need?

• Write conversion factors for:

nm to m and m to nm

µL to L and L to µL

• A ruler is 12.0 inches long. How long is it in cm? ( 1 inch is 2.54 cm)

• in meters?

• A race is 10.0 km long. How far is this in miles?

• 1 mile = 1760 yds

• 1 meter = 1.094 yds

• Pikes peak is 14,110 ft above sea level. What is this in meters?

1 m

1 m

1 m

100 cm

100 cm

100 cm

100 cm

3

Units to a Power

• How many m3 is 1500 cm3?

1500 cm3

1500 cm3

• How many cm2 is 15 m2?

• 36 cm3 is how many mm3?

• Dimensional Analysis - A way to analyze and solve problems using the units, or dimensions of the measurements

• When converting between units it is often necessary to use more than one conversion factor.

• First convert from your given value to the base unit. Convert from the base unit to your unknown value.

• For example: What is 0.073cm in micrometers?

• 0.073cm │ 1m │106µm = 730µm

│100cm│ 1m

• Convert the following:

• 36cm to meters

• 3.72x10-3kg to grams

• 66.3L to cubic centimeter

• Convert the following:

4. 7.5x104nm to kilometers

5. 3.9x105mg to decigrams

6. 2.21x10-4dL to microliters

• 0.36m

• 3.72g

• 6.63x104cm3

• 7.5x10-8km

• 3.9x103dg

• 22.1µL

• When you are given a measurement expressed as a ration of two units, such as density or speed, multiple steps are needed.

• Convert one unit at a time!

• You must cube the conversion when converting a cubed unit

• For example: The density of manganese is 7.21g/cm3. What is the density of manganese expressed in units of kg/m3?

• Our gift label is upside down when converting the unit in the denominator of a fraction.

• 7.21g │ 1kg │ (100cm)3 = 7.21x103kg/m3

1cm3│1000g│ (1m)3

1 gal = 4 qt

1 L = 1.06 qt

1 lb = 454 g

1 mi =1760 yds

1 pint = 2 cups

1 qt = 2 pints

1 yd = 3 ft.

1 mile = 1.61 km

1 m = 1.094 yds

1 L = 1000 cm3

More Questions to Ponder milk. An American wishes to make the recipe has only measuring cups, which are marked in cups. If the density of milk is 1.03 g/cm

• Light travels at a speed of 3.00x1010cm/s. What is the speed of light in kilometers per hour?

• A bar of gold measures 4.5cm by 6.5cm by 1.6dm. Calculate the mass of the gold bar in kilograms. The density of gold is 19.3g/cm3

• What is the mass in kilograms, of 14.0L of gasoline? (assume that the density of gasoline is 0.680g/cm3)

Answers! milk. An American wishes to make the recipe has only measuring cups, which are marked in cups. If the density of milk is 1.03 g/cm

• 1.08x109km/hr

• 9.0kg

• 9.52kg