Kayla measures a distance of 50 inches. She needs to find the equivalent number of meters. Which conversion factors should she use? Check all that apply.
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Answers
Step-by-step explanation:
During your studies of chemistry (and physics also), you will note that mathematical equations are used in many different applications. Many of these equations have a number of different variables with which you will need to work. You should also note that these equations will often require you to use measurements with their units. Algebra skills become very important here!
Converting Between Units with Conversion Factors
A conversion factor is a factor used to convert one unit of measurement into another. A simple conversion factor can be used to convert meters into centimeters, or a more complex one can be used to convert miles per hour into meters per second. Since most calculations require measurements to be in certain units, you will find many uses for conversion factors. What always must be remembered is that a conversion factor has to represent a fact; this fact can either be simple or much more complex. For instance, you already know that 12 eggs equal 1 dozen. A more complex fact is that the speed of light is 1.86×105 miles/sec. Either one of these can be used as a conversion factor depending on what type of calculation you might be working with (Table 2.6.1).
Table 2.6.1: Conversion Factors from SI units to English Units
1 ounce (oz)
28.35 grams (g)
*mass
1 fluid once (oz)
2.96 mL
volume
2.205 pounds (lb)
1 kilogram (kg)
*mass
1 inch (in)
2.54 centimeters (cm)
length
0.6214 miles (mi)
1 kilometer (km)
length
1 quarter (qt)
0.95 liters (L)
volume
*pounds and ounces are technically units of force, not mass, but this fact is often ignored by the non-scientific community.
Of course, there are other ratios which are not listed in Table 2.6.1. They may include:
Ratios embedded in the text of the problem (using words such as per or in each, or using symbols such as / or %).
Conversions in the metric system, as covered earlier in this chapter.
Common knowledge ratios (such as 60 seconds = 1 minute).
If you learned the SI units and prefixes described, then you know that 1 cm is 1/100th of a meter.
1cm=
1
100
m=10−2m
or
100cm=1m
Suppose we divide both sides of the equation by 1m (both the number and the unit):
100cm
1m
=
1m
1m
As long as we perform the same operation on both sides of the equals sign, the expression remains an equality. Look at the right side of the equation; it now has the same quantity in the numerator (the top) as it has in the denominator (the bottom). Any fraction that has the same quantity in the numerator and the denominator has a value of 1:
100 cm
1 m
=
1000 mm
1 m
=
1×106μm
1 m
=1
We know that 100 cm is 1 m, so we have the same quantity on the top and the bottom of our fraction, although it is expressed in different units.
Performing Dimensional Analysis
Dimensional analysis is amongst the most valuable tools physical scientists use. Simply put, it is tr Conversions. This is how you c
Answer:
Step-by-step explanation:
During your studies of chemistry (and physics also), you will note that mathematical equations are used in many different applications. Many of these equations have a number of different variables with which you will need to work. You should also note that these equations will often require you to use measurements with their units. Algebra skills become very important here!
Converting Between Units with Conversion Factors
A conversion factor is a factor used to convert one unit of measurement into another. A simple conversion factor can be used to convert meters into centimeters, or a more complex one can be used to convert miles per hour into meters per second. Since most calculations require measurements to be in certain units, you will find many uses for conversion factors. What always must be remembered is that a conversion factor has to represent a fact; this fact can either be simple or much more complex. For instance, you already know that 12 eggs equal 1 dozen. A more complex fact is that the speed of light is 1.86×105 miles/sec. Either one of these can be used as a conversion factor depending on what type of calculation you might be working with (Table 2.6.1).
Table 2.6.1: Conversion Factors from SI units to English Units
1 ounce (oz)
28.35 grams (g)
*mass
1 fluid once (oz)
2.96 mL
volume
2.205 pounds (lb)
1 kilogram (kg)
*mass
1 inch (in)
2.54 centimeters (cm)
length
0.6214 miles (mi)
1 kilometer (km)
length
1 quarter (qt)
0.95 liters (L)
volume
*pounds and ounces are technically units of force, not mass, but this fact is often ignored by the non-scientific community.
Of course, there are other ratios which are not listed in Table 2.6.1. They may include:
Ratios embedded in the text of the problem (using words such as per or in each, or using symbols such as / or %).
Conversions in the metric system, as covered earlier in this chapter.
Common knowledge ratios (such as 60 seconds = 1 minute).
If you learned the SI units and prefixes described, then you know that 1 cm is 1/100th of a meter.
1cm=
1
100
m=10−2m
or
100cm=1m
Suppose we divide both sides of the equation by 1m (both the number and the unit):
100cm
1m
=
1m
1m
As long as we perform the same operation on both sides of the equals sign, the expression remains an equality. Look at the right side of the equation; it now has the same quantity in the numerator (the top) as it has in the denominator (the bottom). Any fraction that has the same quantity in the numerator and the denominator has a value of 1:
100 cm
1 m
=
1000 mm
1 m
=
1×106μm
1 m
=1
We know that 100 cm is 1 m, so we have the same quantity on the top and the bottom of our fraction, although it is expressed in different units.
Performing Dimensional Analysis
Dimensional analysis is amongst the most valuable tools physical scientists use. Simply put, it is tr Conversions. This is how you c
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