# 3.1.4: Introduction to Metric Units of Mass and Capacity

- Page ID
- 8737

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

Jesse works in the mailroom of a large company. Part of his responsibility is to make sure all mail is sent out with the correct postage. The postage depends on the size and weight of the mail. He is given a box that contains 10 books and some documents. Which metric unit of measurement should Jesse use to weight the package?

In this concept, you will learn to choose the appropriate metric unit of **mass** or **capacity** for the situation.

### Metric Units for Mass or Capacity

Grams, milligrams, and kilograms are metric units for measuring mass. To really understand each unit, you have to understand the size of each unit. Here are some examples of things that might weigh 1 of each metric unit of mass.

Unit |
Examples |

1 kilogram | 1 liter of water, dictionary |

1 gram | paperclip, one dollar bill |

1 milligram | a grain of sand, ant |

It would be best to measure heavier objects like people or textbooks in kilograms. Grams are often used to measure ingredients in baking recipes. Milligrams are very tiny units that are not used very often in everyday situation. Scientists are one group of people that might use milligrams to measure objects with very little mass.

Liters and milliliters are metric units for measuring capacity. Here are some examples of things that might weigh 1 of each metric unit of capacity.

Unit |
Examples |

1 liter | 1 liter of water, quart of milk |

1 milliliter | 20 drops, one-fifth of 1 teaspoon |

A liter would be used to measure much larger volumes of liquid, like the capacity of a car’s fuel tank. Millimeters are much smaller and would be used to measure very small amounts of liquid, like the amount of cough syrup you should take.

Think carefully about what is being measured before you decide on which unit to use.

### Examples

Example 3.1.4.1

Earlier, you were given a problem about Jesse in the mailroom.

Jesse needs to decide which metric unit he should use to weigh a box of books and documents.

**Solution**

First, think about the size and weight of the objects in the box.

Milligrams would be far too small of a unit. The books alone would probably weigh a few million milligrams. Even grams is really not ideal, since the total weight would be thousands of grams.

Jesse should use kilograms to weigh the package for postage.

Example 3.1.4.2

Choose the best unit of measurement.

Which unit of mass would you use to measure a handful of peanuts?

**Solution**

First, think about the size and weight of a handful of peanuts and then choose the best unit for measuring mass.

Peanuts are small, so the kilogram would be too much for a handful of peanuts. Peanuts may be small, but they are much larger than grains of sand. Milligrams would be too small to measure peanuts.

Grams would be the best unit to weigh a handful of peanuts.

Example 3.1.4.3

Choose the best unit of measurement: the weight of 5 pennies.

**Solution**

First, think about the size and weight of 5 pennies and then choose the best unit for measuring mass.

5 pennies would definitely weigh less than a kilogram and be too heavy for milligrams.

Grams would be the best unit to weigh 5 pennies, since each penny is about 2.5 grams.

Example 3.1.4.4

Choose the best unit of measurement: the amount of water in a bathtub.

**Solution**

First, think about the size of a bathtub and choose the best unit for measuring capacity.

Milliliters would be far too small to measure the amount of water a bathtub can hold.

Liters would be the better unit of capacity for the amount of water in a bathtub.

Example 3.1.4.5

Choose the best unit of measurement: the weight of a car.

**Solution**

First, think about the size and weight of a car and then choose the best unit for measuring mass.

A car is large and very heavy, so you will need the largest unit of the three choices.

Kilograms would be the best unit to weigh a car of the three.

### Review

Choose the best unit of either mass or capacity to measure each item.

- A dictionary
- A flea under a microscope
- A jug of apple cider
- An almond
- Drops of water from an eyedropper
- Ten dimes
- A bucket of water
- A baby bottle
- A handful of rice
- A large jug of water
- A water tower
- The water in a swimming pool
- The weight of a boat
- A handful of sand
- The weight of a backpack

### Review (Answers)

To see the Review answers, open this PDF file and look for section 4.19.

### Additional Resources

Videos:** **

PLIX Interactive: **Using the Right Units**

Practice: **Introduction to Metric Units of Mass and Capacity**

Real World Application: **Weighing In**