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3.22: Conversion Estimation Between Systems of Measure

Difficulty Level: At Grade Created by: CK-12
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Sarah is staying with her aunt in London for spring break. One night they decide to make Sarah's favorite recipe for roasted Brussels sprouts. Sarah's recipe calls for \begin{align*}1 \frac{1}{2}\end{align*} pounds of Brussels sprouts. The grocery store uses the metric system so Sarah has to weigh her Brussels sprouts in kilograms. How can Sarah estimate the number of kilograms of Brussels sprouts to buy so that she has the correct amount for her recipe?

In this concept, you will learn how to estimate equivalence between customary and metric units of measure.

Estimating Conversions Between Systems of Measure

There are two common systems of measurement used throughout the world.

  1. The customary system is the system of measurement primarily used in the United States. Units in this system include the inch, foot, mile, pound, and cup.
  2. The metric system is the system of measurement primarily used in science and in countries outside of the United States. Units in this system include the meter, liter, and gram.

Sometimes you will need to convert between the customary system and the metric system. The table below shows the approximate customary equivalent for common metric units.

Approximate Customary Equivalents for Common Metric Units
Metric Unit Customary Unit
1 centimeter 0.39 inch
1 meter 3.28 feet
1 kilometer 0.62 mile
1 milliliter 0.2 teaspoon
1 liter 4.23 cups
1 gram 0.04 ounce
1 kilogram 2.2 pounds

Notice how in this table all of the metric units are given in units of 1. So, for example, since 1 meter is about 3.28 feet, to convert 2 meters into feet just multiply 3.28 by 2 to get 6.56 feet.

Sometimes you will just want to get a general idea of what a metric measurement would be in the customary system of measurement or vice versa. If this is the case, you can use the table above and your estimation skills to determine an approximate equivalence.

Here is an example.

About how many inches is 14 centimeters?

First, look at the table to see how inches and centimeters are related. You can see that 1 centimeter is approximately 0.39 inch.

Now, because you are going from a metric unit to a customary unit, you will need to multiply the given value by the customary equivalent from the table.

\begin{align*}14 \times 0.39 = 5.46\end{align*}

The answer is there are approximately 5.46 inches in 14 centimeters.

Let's look at another example.

About how many kilograms is 7.7 pounds?

First, look at the table to see how kilograms and pounds are related. You can see that 1 kilogram is approximately 2.2 pounds.

Now, because you are going from a customary unit to a metric unit, you will need to divide the given value by the customary equivalent from the table.

\begin{align*}7.7 \div 2.2 = 3.5\end{align*}

The answer is there are approximately 3.5 kilograms in 7.7 pounds.

Examples

Example 1

Earlier, you were given a problem about Sarah and her Brussels sprouts recipe.

Her recipe calls for \begin{align*}1 \frac{1}{2}\end{align*} pounds of Brussels sprouts but the grocery store in London uses the metric system. Sarah needs to figure out how many kilograms of Brussels sprouts to buy.

First, Sarah should note that 1 kilogram is approximately 2.2 pounds.

Now, because she is going from a customary unit to a metric unit, she will need to divide the \begin{align*}1 \frac{1}{2}\end{align*} pounds by the customary equivalent from the table. Sarah should keep in mind that \begin{align*}1 \frac{1}{2}\end{align*} is equal to 1.5.

\begin{align*}1.5 \div 2.2 \approx 0.68\end{align*}

The answer is Sarah should buy approximately 0.68 kilogram of Brussels sprouts.

Example 2

About how many cups is 16 liters?

First, look at the table to see how cups and liters are related. You can see that 1 liter is approximately 4.23 cups.

Now, because you are going from a metric unit to a customary unit, you will need to multiply the given value by the customary equivalent from the table. Keep in mind that 4.23 is about 4, and 16 times 4 is equal to 64.

\begin{align*}16 \times 4.23 \approx 64\end{align*}

The answer is there are approximately 64 cups in 16 liters.

Example 3

About how many grams is 0.16 ounce?

First, look at the table to see how grams and ounces are related. You can see that 1 gram is approximately 0.04 ounce.

Now, because you are going from a customary unit to a metric unit, you will need to divide the given value by the customary equivalent from the table.

\begin{align*}0.16 \div 0.04 = 4\end{align*}

The answer is there are approximately 4 grams in 0.16 ounce.

Example 4

About how many kilograms is 6 pounds?

First, look at the table to see how kilograms and pounds are related. You can see that 1 kilogram is approximately 2.2 pounds.

Now, because you are going from a customary unit to a metric unit, you will need to divide the given value by the customary equivalent from the table. Keep in mind that 2.2 is about 2, and 6 divided by 2 is equal to 3.

\begin{align*}6 \div 2.2 \approx 3\end{align*}

The answer is there are approximately 3 kilograms in 6 pounds.

Example 5

About how many meters is 12 feet?

First, look at the table to see how meters and feet are related. You can see that 1 meter is approximately 3.28 feet.

Now, because you are going from a customary unit to a metric unit, you will need to divide the given value by the customary equivalent from the table. Keep in mind that 3.28 is about 3, and 12 divided by 3 is equal to 4.

\begin{align*}12 \div 3.28 \approx 4\end{align*}

The answer is there are approximately 4 meters in 12 feet.

 

Review

Estimate a customary equivalent for the following metric measurements.

  1. 4 kilograms to pounds
  2. 7.5 meters to feet
  3. 6 liters to cups
  4. 13.25 kilometers to miles
  5. 6 kilometers to miles
  6. 8 liters to cups
  7. 20 kilograms to pounds
  8. 12 meters to feet

Estimate a metric equivalent for the following customary measurements, round to the nearest hundredth where necessary.

  1. 4 quarts to liters
  2. 34 ounces to grams
  3. 52 pounds to kilograms
  4. 9 inches to centimeters
  5. 14 feet to meters
  6. 16 cups to liters
  7. 5 miles to kilometers

Review (Answers)

To see the Review answers, open this PDF file and look for section 3.22.

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Date Created:
Sep 23, 2015
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Aug 11, 2016
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