6.1.3: Conversion Between the Metric and US Customary Systems of Measurement

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Leah Griffith, Veronica Holbrook, Johnny Johnson & Nancy Garcia
Rio Hondo College

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6.1.3 Learning Objectives

To estimate equivalence between the Metric Units and US Customary Units
To convert Metric Units to US Customary Units
To convert US Customary Units to Metric Units

Estimate equivalence between the Metric Units and US Customary Units

Before converting metric units to US customary units and vice versa, you need to familiarize the approximate metric equivalents of common customary units. The table below summarizes the commonly used metric and US customary units and their approximate equivalence. The notations enclosed are the abbreviations of each unit.

Metric Units	US Customary Units
Lengths
1 meter (m)	3.28 feet (ft. or ’)
1 kilometer (km)	0.62 mile (m)
1 centimeter (cm)	0.39 inch (in. or ”)
0.9144 meter (m)	1 yard (yd.)
1.852 kilometers (km)	1 nautical mile (nmi. or NM)
Weight
1 kilogram (kg)	2.2 pounds (lb. or #)
28.3 grams (g)	1 ounce (oz.)
1 milligram (mg)	0.002 teaspoon (tsp.)
Fluid Capacity
29.57 milliliters (mL)	1 fluid ounce (fl. Oz.)
1 liter (L)	4.23 cups (c)
3.79 liters (L)	1 gallon (gal.)
473.176 milliliters (mL)	1 pint (pt.)
0.95 liters (L)	1 quart (qt.)
158.987 liters (L)	1 barrel (bbl.)

Additional Common Conversions

Metric Units	US Customary Units
Area
6.45 square centimeters (cm²)	1 square inch (in²)
1 square meter (m²)	1.196 square yard (yd²)
4046.873 square meters (m²)	1 acre (ac.)
Volume and Capacity
16.39 milliliter (mL)	1 cubic inch (in³)
28.32 liters (L)	1 cubic foot (ft³)
764.55 liters (L)	1 cubic yard (yd³)
1233.482 cubic meters (m³)	1 cubic foot (ft³)

Convert Metric Units to US Customary Units

You have familiarized the commonly used equivalence between metric and US customary units. At this point, you will learn to convert metric units to US customary units.

To convert metric units to US customary units, use their estimate equivalence. Write the equivalence as a ratio, and multiply it to the given measurement (in metric) to convert. Be sure that the units of measure to convert cancels out. For instance, to convert liters to gallons, be sure to cancel out liters and retain gallons as the final unit.

Now, let us consider some examples.

Example 1

The official regulators of a shipment company classify a parcel weighing more than 51 pounds (lbs.) as a heavy shipment. Andrea packed 24 terracotta plant containers to be shipped to her customers. If each plant container weighs 1.3 kilograms (kg), will her package be classified as a heavy shipment?

Solution

To determine whether the parcel is a heavy shipment or not, you need to convert the total weight of the plant containers to pounds.

Compute for the total weight.

$ \text { Total Weight } = 24\times 1.3 \text{ kg}$

$= 31.2\text{ kg}$

Convert the total weight to pounds. Use the metric to US customary units’ equivalence: 1 kg = 2.2 lbs.

$31.2\cancel{\text{ kg}}\times\dfrac{ 2.2 \text { lbs}}{ 1\cancel {\text{ kg}}} = 68.64\text{ lbs}$

Since the total weight is more than 51 lbs., the shipment is considered heavy.

Try it Now 1

Angelica who lives in Las Vegas, Nevada, visited her friend in Canada. She knows that Canada uses the metric system, so their speed limits are posted in kilometers per hour. On her way, she sees a road sign that says, “max 60 km/h”. She knows the sign means “a maximum speed of 60 kilometers per hour” but she is unsure if this is over the speed limit in Las Vegas, Nevada. How can Angelica convert 60 km/h to miles per hour? Use the metric to US customary units’ equivalence: 1 kilometer (km) = 0.62 mile.

Answer: In Las Vegas, the limit is 65 miles per hour (mph). Since 37.2 mph is below this limit, 60km/h is not over the speed limit.

Example 2

Half of a meter of ribbon is required for wrapping presents enclosed in a rectangular box. How many presents using the same box size can be wrapped with 10 yards of ribbon?

Solution

Convert half a meter (0.5 m) to yards. Use the metric to US customary units’ equivalence: 1 yard = 0.9144 meter.

$0.5\cancel{ \text{ m} }\times\dfrac{ 1 \text { yd }}{ 0.9144 \cancel {\text{ m} }} = 0.5468\text{ yd }$

The result means that one present requires 0.5468 yards of ribbon. Calculate the number of presents by dividing 10 yards by 0.5468 yards.

$10\text { yds }\div \dfrac{ 0.5468 \text { yd }}{ 1 \text { present}} = 10\cancel {\text{ yd}}\times \dfrac{ 1\text { present}}{ 0.5468 \cancel {\text{ yd} }}= 18.29\text { presents }$

Approximately, 18 presents can be wrapped with 10 yards of ribbons.

Try it Now 2

Crystal and her friends are planning for a road trip, which they have determined to be 2,000 kilometers (km) long. They want to rent a van that can travel 100 km using 9 liters of gas. Suppose the gas price is $2.74 a gallon (gal.), how many gallons of gas they will need? How much money will the group of friends need to save for gas? Use the metric to US customary units’ equivalence: 4.405 liters (L)= 1 gallon (gal.).

Answer: The team needs 40.86 gallons of gas for the trip, which will cost them $111.96.

Try it Now 3

Christine plans to put up a short-course swimming pool at her house. A short-course swimming pool usually measures 22.86 meters in length, at least 18.29 meters in width, and 2.5 meters in depth. Convert the dimensions of the pool to inches. Use the metric to US customary units’ equivalence: 1 centimeter (cm) = 0.39 inch (in.) and 1 centimeter (cm) = 0.01 meter (m).

Answer: Approximately, the pool measures 891.54 in by 713.31 in by 97.5 in.

Try It Now 4

Drug dosage for children is based on body weights, milligrams per pound (mg/lb). A 5-year-old child with Meningitis who weighs 20 kilograms was prescribed Ceftriaxone. The dosage requirement is 220 milligrams per pound per day (mg/lb/day) once daily. The drug is prediluted in 40 mg/mL concentration. Calculate the dose in teaspoons. Use the metric to US customary units’ equivalence: 1 kilogram (kg) = 2.2 pounds (lb.) and 1 mg = 0.0002 tsp.

Answer: The dose is approximately 2 teaspoons.

Convert US Customary Units to Metric Units

You have learned how to convert metric units to US customary units. Now, you will learn to convert US customary units to metric units.

Example 3

Daniel drove 40 miles in two hours. What distance (in meters) did he cover in one minute? Use the US customary to metric units’ equivalence: 0.62 mile (mi.) = 1 kilometer (km), 1 km is equal to 1,000 meters (m), and 1 hour = 60 minutes.

Solution

Convert 40 miles in two hours to kilometers per hour.

$\dfrac{ 40 \cancel {\text{ mi} }}{ 2 \text { hrs }}\times\dfrac{ 1 \text { km }}{ 0.62 \cancel { \text{ mi} }} = 32.2581\text{ km/hr }$

Convert 32.2581 kilometers per hour to meters per hour.

$\dfrac{ 32.2581 \cancel {\text{ km }}}{ 1 \text { hr }}\times\dfrac{ 1000 \text { m }}{ 1 \cancel {\text{ km} }} = 32,258.1\text{ m/hr }$

Convert 32,258.1 meters per hour to meters per minute.

$\dfrac{ 32,258.1 \text { m }}{ 1 \cancel {\text{ hr} }}\times\dfrac{ 1 \cancel {\text{ hr} }}{ 60 \text { min }} = 537.635\text{ m/min }$

Daniel has covered 537.635 meters in one minute.

Try It Now 5

A supermarket has a car parking spot that is 9 feet wide and 18 feet long. Its ground-level parking has 50 parallel parking spots (side by side) of the same sizes. What is the area of the parking lot in square centimeters? Use the US customary units’ equivalence: 1 foot (ft.) = 12 inches (in.) and 1 square inch (in²) = 6.45 square centimeters (cm²). (Hint: You will need to use the formula to find the area of a rectangle)

Answer: The area of the parking lot is 7,523,280 square centimeters.

Example 4

Allison wants to bake a chocolate cake. The recipe requires 1¾ cups of all-purpose flour. A supermarket sells all-purpose flour in grams instead of cups. All-purpose flour comes in the following sizes: 80 grams, 400 grams, and 800 grams. If Allison plans to buy just enough flour for 1 recipe, which size will she buy? Use the US customary units equivalence: 1 cup (c.) = 8 ounces (oz.) and 1 ounce (oz.) = 28.3 grams (g).

Solution

Converting 1¾ to a fraction or decimal will help when converting cups to ounces. In this example 1¾ = 1.75 will be used.

$1.75\cancel{ \text{ cups} }\times\dfrac{ 8\text { oz }}{ 1\cancel {\text{ cup} }} = 14\text{ oz }$

Convert ounces to grams.

$14\cancel{ \text{ oz} }\times\dfrac{ 28.3\text { g }}{ 1\cancel {\text{ oz} }} = 396.2\text{ g }$

Since 80 grams is less than the required recipe amount and 800 grams is much higher than 396.2 grams, Allison must buy the 400 gram package.

Try It Now 6

Melody’s house garage is 45 feet long while David’s garage is 10 yards and 10 feet long. Which house has a longer garage? How much is the difference (in meters)? Use the US customary to metric equivalence: 3.28 feet (ft.) = 1 meter (m) and 1 foot (ft.) = 0.3333 yard (yd.)

Answer: Melody’s garage is longer by 1.52 meters.

Try it Now 7

How many liters of water are needed to fill an Olympic swimming pool with a total volume of 3,300 cubic yards? Assume that the water level is as deep as the pool. Use the US customary to metric units’ equivalence: 1 cubic yard (yd³) = 746.56 liters (L).

Answer: At most 2,463,648 liters of water are needed to fill the swimming pool.

Try It Now 8

Robert’s new car requires at most 57 liters of fuel. If the current average price for regular gas is $2.864 per gallon, how much will it cost him to fill his car’s tank? Use the US customary to metric units’ equivalence: 1 gallon = 3.79 liters

Answer: It will cost Robert approximately $43.32 to fill his car’s tank.