# 3.3.5: Customary and Metric Measurement Conversion

- Page ID
- 8747

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)## Estimation of Conversion to Metric Units

Billy is on a trip to Canada with his family. He is trying to get used to seeing all of the distances and speed limits on road signs given in terms of kilometers instead of miles! He sees a sign that says “maximum 50 km/h”. He knows that means 50 kilometers per hour, but he wonders if that is a fast speed or a slow speed. How can Billy **estimate** what 50 kilometers per hour would be in miles per hour?

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

**Estimating Conversion to Metric Units**

Recall that there are two primary systems of measurement that you can use.

- The
is the system of measurement primarily used in the United States. Units in this system include the inch, foot, mile, pound, and cup.**customary system** - The
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.**metric system**

You will encounter both metric units and customary units. Therefore, it’s important to develop a general idea of the equivalence between the two systems.

The table below shows the approximate metric equivalents for common customary units.

Customary Unit |
Metric Unit |

1 inch | 25.4 millimeters |

1 foot | 30.48 centimeters |

1 yard | 0.91 meter |

1 mile | 1.61 kilometers |

1 teaspoon | 4.93 milliliters |

1 cup | 0.24 liter |

1 pint | 0.47 liter |

1 quart | 0.95 liter |

1 gallon | 3.79 liters |

1 ounce | 28.35 grams |

1 pound | 0.45 kilogram |

Notice how in this table all of the customary units are given in units of 1. So, for example, since 1 foot is about 30.48 centimeters, to convert 2 feet into centimeters just multiply 30.48 by 2 to get 60.96 centimeters. If you had a measurement in centimeters and wanted to estimate the number of inches, you could reverse the process and divide by 30.48.

Often you will just want to get a general idea of what a given measurement would be in the other system of measurement. 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 cups are equal to 0.5 liter?

First, look at the table to see how cups and liters are related. You can see that 1 cup is approximately 0.24 liter.

Now, because you are going from a metric unit to a customary unit, you will need to divide the given value by the metric equivalent from the table. Keep in mind that 0.24 is approximately 0.25, and 0.5 divided by 0.25 is equal to 2.

0.5÷0.24≈2

The answer is there are approximately 2 cups in 0.5 liter.

Remember that this answer is not exact! You’re just looking to get a general sense for how the two systems of measurement are related.

Here is another example.

4 kilograms is equal to about how many pounds?

First, look at the table to see how pounds and kilograms are related. You can see that 1 pound is approximately 0.45 kilograms.

Now, because you are going from a metric unit to a customary unit, you will need to divide the given value by the metric equivalent from the table. Keep in mind that 0.45 is approximately 0.5, and 4 divided by 0.5 is equal to 8.

4÷0.45≈8

The answer is there are approximately 8 pounds in 4 kilograms.

**Examples**

Example 3.3.5.1

Earlier, you were given a problem about Billy and his trip to Canada.

He noticed a sign that said “maximum 50 km/h” and he wonders what 50 kilometers per hour is in miles per hour.

**Solution**

First, Billy should look to see how miles and kilometers are related. He should notice that 1 mile is approximately 1.61 kilometers.

Now, because he is going from a metric unit to a customary unit, he will need to divide the given value by the metric equivalent. He should keep in mind that 1.61 is approximately 1.6, and 50 divided by 1.6 is equal to about 31.

50÷1.61≈31

The answer is that 50 kilometers per hour is equal to approximately 31 miles per hour. This is a typical speed limit for a residential area.

Example 3.3.5.2

12 teaspoons is equal to about how many milliliters?

**Solution**

First, look at the table to see how teaspoons and milliliters are related. You can see that 1 teaspoon is approximately 4.93 milliliters.

Now, because you are going from a customary unit to a metric unit, you will need to multiply the given value by the metric equivalent from the table. Keep in mind that 4.93 is approximately 5, and 12 times 5 is equal to 60.

12×4.93≈60

The answer is there are approximately 60 milliliters in 12 teaspoons.

Example 3.3.5.3

4 gallons is equal to about how many liters?

**Solution**

First, look at the table to see how gallons and liters are related. You can see that 1 gallon is approximately 3.79 liters.

Now, because you are going from a customary unit to a metric unit, you will need to multiply the given value by the metric equivalent from the table. Keep in mind that 3.79 is approximately 3.75, and 4 times 3.75 is equal to 15.

4×3.79≈15

The answer is there are approximately 15 liters in 4 gallons.

Example 3.3.5.4

60 centimeters is equal to about how many feet?

**Solution**

First, look at the table to see how feet and centimeters are related. You can see that 1 foot is approximately 30.48 kilograms.

Now, because you are going from a metric unit to a customary unit, you will need to divide the given value by the metric equivalent from the table. Keep in mind that 30.48 is approximately 30, and 60 divided by 30 is equal to 2.

60÷30.48≈2

The answer is there are approximately 2 feet in 60 centimeters.

Example 3.3.5.5

3 cups is equal to about how many liters?

**Solution**

First, look at the table to see how cups and liters are related. You can see that 1 cup is approximately 0.24 liter.

Now, because you are going from a customary unit to a metric unit, you will need to multiply the given value by the metric equivalent from the table. Keep in mind that 0.24 is approximately 0.25, and 3 times 0.25 is equal to 0.75.

3×0.24≈0.75

The answer is there is approximately 0.75 liter in 3 cups.

**Review**

Estimate a metric equivalent for the following customary measurements.

- 5 cups to liters
- 5 yards to meters
- 6 inches to mm
- 15 pounds to kg
- 1 cup to liters
- 4 miles to km
- 5 feet to cm
- 12 feet to cm
- 8 inches to mm
- 28.5 ounces to grams
- 11.75 inches to millimeters
- 8 quarts to liters
- 15 pounds to kilograms

Solve the following problems.

- To join the swim team, Jessica swam every day. The distances she swam for the first four days were as follows: 1.65 km, 1,750 m, 185,000 cm, 1,950,000 mm. If the pattern continues, how many kilometers will she swim on the fifth day?
- Mrs. Roth is moving to a new apartment. She can lift exactly 22.5 kg. Which of the following objects can she lift: box of books (23,500 g), statue (2,450,000 cg), computer (2,550,000 mg), potted plant (22.55 kg)?

### Review (Answers)

To see the Review answers, open this PDF file and look for section 2.23.

### Vocabulary

Term | Definition |
---|---|

Customary System |
The customary system is the measurement system commonly used in the United States, including: feet, inches, pounds, cups, gallons, etc. |

Equivalence |
Equivalence is the condition of being equal in value or meaning. |

Estimate |
To estimate is to find an approximate answer that is reasonable or makes sense given the problem. |

Metric System |
The metric system is a system of measurement commonly used outside of the United States. It contains units such as meters, liters, and grams, all in multiples of ten. |

### Additional Resources

Practice: **Customary and Metric Measurement Conversion**

Real World Application: **Crossing the Border**