# How do I do that unit conversion?

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1 Name Date Period Furrey How do I do that unit conversion? There are two fundamental types of unit conversions in dimensional analysis. One is converting old units to new units with in the same system of measurements. The other is converting old units in one system of measurements to new units in a different system of measurements. How is the conversion made? The method used for unit conversions is the factor label method and the fundamental steps are:. Have your conversion chart. (The chart shows how many grams are in a kilogram, etc.) 2. Identify the old number and old units. (What is the number and units you are starting with?) 3. Identify the new units. (What is the unit you want to end with?) 4. Make a bridge between units. (The bridge is the conversion factor(s) required to get from the old units to the new units.) Eample : How many grams are in 2.4 kilograms? or 2.4 kg = g The base units in this problem are _grams.. The conversion chart of prefies and suffies shows that the prefi kilo- has a multiplier of 000. Prefi Multiplier to get base unit kilo- 000 centi-.0 milli The old number and units, what we are starting with, is 2.4 kg. This is placed over as shown: 2.4kg. This helps to visually organize the conversion to new units. We know that anything divided by is always itself. 3. The new units, what we want to end with, is _gram or g. 4. Make a bridge between the old units and new units. How many grams are in a kilogram? _000 _. 000g = kg. Set up the conversion factor, the bridge. A conversion factor is one item divided by another item that always equals like this: 000g kg = or kg 000g Which one do I use? These are both the same and both are equal to one. Choose the conversion factor that has the new units in the numerator (top) and the old units in the denominator (bottom). When you multiply, you want to keep the new units and cancel the old units. 2.4kg 000 kgg 2,400 the bottom, with the new units 2,400g. = 2,400g on top: = 2,400; on bottom: = ; the top is divided by, the kg units on top is canceled by the kg units on bottom leaving the final answer =.

2 Eample 2: How many liters are in 250 milliliters? or 250ml = liters The base units in this problem are _liters.. The conversion chart of prefies and suffies shows that the prefi milli- has a multiplier of.00. Prefi Multiplier to get base unit kilo- 000 centi-.0 milli The old number and units, what we are starting with, is 250ml. This is placed over as 250ml shown:. This helps to visually organize the conversion to new units. We know that anything divided by is always itself. 3. The new units, what we want to end with, is _liter or l. 4. Make a bridge between the old units and new units. How many milliliters are in a liter? _000 _. 000ml = l. Set up the conversion factor, the bridge. A conversion factor is one item divided by another item that always equals like this: 000ml l = or l 000ml Which one do I use? These are both the same and both are equal to one. Choose the conversion factor that has the new units in the numerator (top) and the old units in the denominator (bottom). When you multiply, you want to keep the new units and cancel the old units. =. 250ml l 000ml =.25 liters on top: 250 = 250; on bottom: 000 = ; the top is divided 250 by the bottom, the ml units on top is canceled by the ml units on bottom leaving the final answer 000 with the new units.25 liters. 2

3 Eample 3: How many centimeters are in Kilometers? or km = cm The base units in this problem are _meters.. The conversion chart of prefies and suffies shows that the prefi centi- has a multiplier of.0 and kilo- has a multiplier of 000. This eample has two different prefies hmmmmmm. Prefi Multiplier to get base unit kilo- 000 centi-.0 milli The old number and units, what we are starting with, is km. This is placed over as shown: 2.298km. This helps to visually organize the conversion to new units. We know that anything divided by is always itself. 3. The new units, what we want to end with, is _centimeter or cm. 4. Make a bridge between the old units and new units. How many centimeters are in a kilometer? _hmmmm, the chart does not show this, BUT it shows centi- to base units and it shows base units to kilo-_. 00cm = m and 000m = km. Set up two conversion factors, in the bridge, one conversion factor is from kilometers to meters and the second conversion factor is from meters to centimeters. Remember, a conversion factor is one item divided by another item that always equals. The two conversion factors are: 00cm m = or m 00cm = and 000m km or km 000m Which one of each pair do I use? Choose the conversion factors that have the new units in the numerator (top) and the old units in the denominator (bottom). When you multiply, you want to keep the new units and cancel the old units km 000 kmm 00cm m = 2,29,800 cm. Take a logical progression when using multiple conversion factors. In this eample, flow from the largest units to the smallest units, km > m > cm. On top: = 2,29,800; on bottom: = ; the top is divided by the bottom 2,29,800, the km units on top is canceled by the km units on bottom and the m units on top is canceled by the m units on bottom leaving the final answer with the new units _2,29,800 cm.. 3

4 Eample 4: How many kilograms are in 48,550,000 milligrams? or 48,550,000mg = kg The base units in this problem are _grams.. The conversion chart of prefies and suffies shows that the prefi milli- has a multiplier of.00 and kilo- has a multiplier of 000. This eample also has two different prefies. Prefi Multiplier to get base unit kilo- 000 centi-.0 milli The old number and units, what we are starting with, is 48,550,000 ml. This is placed over as shown: 48,550,000mg. This helps to visually organize the conversion to new units. We know that anything divided by is always itself. 3. The new units, what we want to end with, is _kilogram or kg. 4. Make a bridge between the old units and new units. How many kilograms are in a milligram? _hmmmm, once again, the chart does not show this, BUT it shows milli- to base units and it shows base units to kilo- _ 000mg = g and 000g = kg. Set up two conversion factors, in the bridge, one conversion factor is from kilometers to meters and the second conversion factor is from meters to millimeters. Remember, a conversion factor is one item divided by another item that always equals. The two conversion factors are: 000mg g = or g 000mg = and 000g kg or kg 000g Which of each pair do I use? Choose the conversion factors that have the new units in the numerator (top) and the old units in the denominator (bottom). When you multiply, you want to keep the new units and cancel the old units. 48,550,000mg g 000mg kg 000g = kg. Take a logical progression when using multiple conversion factors. In this eample, flow from the smallest units to the larges units, mg > g > kg. On top: 48,550,000 = 48,550,000; on bottom: =,000,000; the top is divided by the bottom, 48,550,000,000,000 the mg units on top is canceled by the mg units on bottom and g units on top is canceled by g units on bottom leaving the final answer with the new units kg.. 4

5 The first four eamples have been with in the metric system of measurements. The net series of eamples will be English to metric and metric to English conversions. There is not really a base unit in the English system of units because there is no such thing as a base 0 or multiple of 0 in the English system of units. An eample is length. The units for length in the English system of measurements are inches, feet, yards and miles. Eample 5: How many miles are in 0 kilometers? or 0 km = miles The base units in this problem are _meters to miles.. The conversion chart below shows a few of the conversions between the metric system and the English system of measurements. Length inches 2.54 centimeters (cm) centimeters 0.39 inches feet 0.30 meters meters 3.28 feet miles.6 kilometers kilometers 0.62 miles Mass and ounces grams Weight* grams 0.04 ounces pounds 0.45 kilograms kilograms 2.20 pounds * Weight as measured in standard Earth gravity Volume liters.06 quarts liters 0.26 gallons gallons 3.78 liters 2. The old number and units, what we are starting with, is 0 km. This is placed over as shown: 0km. This helps to visually organize the conversion to new units. We know that anything divided by is always itself. 3. The new units, what we want to end with, is _miles. 4. Make a bridge between the old units and new units. How many miles are in a kilometer? _0.62 _. km = 0.62 miles. Set up the conversion factor, the bridge. A conversion factor is one item divided by another item that always equals like this: 0.62miles km There is only one conversion factor that will work to go from kilometers to miles. The conversion factor will have the new units in the numerator (top) and the old units in the denominator (bottom). When you multiply, you want to keep the new units and cancel the old units. 0km bottom, 0.62miles km 6.2 = = 6.2 miles on top: = 6.2; on bottom: = ; the top is divided by the, the km units on top is canceled by the km units on bottom leaving the final answer with the new units 6.2 miles. A popular running race is the 0K which is 0 kilometers. Perhaps you have run in one of these races and always wanted to know how many miles you ran. 5

6 Eample 6: How many pounds are in kg? or kg = lbs The base units in this problem are _grams and pounds.. The conversion chart below shows a few of the conversions between the metric system and the English system of measurements. Length inches 2.54 centimeters (cm) centimeters 0.39 inches feet 0.30 meters meters 3.28 feet miles.6 kilometers kilometers 0.62 miles Mass and ounces grams Weight* grams 0.04 ounces pounds 0.45 kilograms kilograms 2.20 pounds * Weight as measured in standard Earth gravity Volume liters.06 quarts liters 0.26 gallons gallons 3.78 liters 2. The old number and units, what we are starting with, is kg. This is placed over as shown: 48.55g. This helps to visually organize the conversion to new units. We know that anything divided by is always itself. 3. The new units, what we want to end with, is _pounds or lbs. 4. Make a bridge between the old units and new units. How many pounds are in a kilogram? _2.2 _. kg = 2.2 lbs. Set up the conversion factor, the bridge. A conversion factor is one item divided by another item that always equals like this: 2.2lbs kg There is only one conversion factor that will work to go from kilograms to pounds. The conversion factor will have the new units in the numerator (top) and the old units in the denominator (bottom). When you multiply, you want to keep the new units and cancel the old units kg 2.2lbs = 06.8lbs on top: = 06.8; on bottom: = ; the top is divided kg 06.8, the kg units on top is canceled by the kg units on bottom leaving the final by the bottom, answer with the new units 06.8 lbs. = 6

7 Eample 7: How many liters are in 22 gallons? or 22 gallons = liters The base units in this problem are _gallons to liters.. The conversion chart below shows a few of the conversions between the metric system and the English system of measurements. Length inches 2.54 centimeters (cm) centimeters 0.39 inches feet 0.30 meters meters 3.28 feet miles.6 kilometers kilometers 0.62 miles Mass and ounces grams Weight* grams 0.04 ounces pounds 0.45 kilograms kilograms 2.20 pounds * Weight as measured in standard Earth gravity Volume liters.06 quarts liters 0.26 gallons gallons 3.78 liters 2. The old number and units, what we are starting with, is 22 gallons. This is placed over as 22gallons shown:. This helps to visually organize the conversion to new units. We know that anything divided by is always itself. 3. The new units, what we want to end with, is _liters. 4. Make a bridge between the old units and new units. How many liters are in a gallon? _3.78 _. kg = 2.2 lbs. Set up the conversion factor, the bridge. A conversion factor is one item divided by another item that always equals like this: 3.78l gallon There is only one conversion factor that will work to go from gallons to liters. The conversion factor will have the new units in the numerator (top) and the old units in the denominator (bottom). When you multiply, you want to keep the new units and cancel the old units. 22gallons 3.78l gallon divided by the bottom, = = 83.6 liters on top: = 83.6; on bottom: = ; the top is 83.6, the gallon units on top is canceled by the gallon units on bottom leaving the final answer with the new units 83.6 liters. When driving in a different country other than the United States or England and you need to fill the gas tank, the gas pump will be calibrated in liters and not gallon. You will know the volume of gas you are putting into the tank 7

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