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2.21: Conversions of Length, Mass, Capacity in Metric Units

Difficulty Level: At Grade Created by: CK-12
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Charlotte is going on vacation with her parents and her 3 month old baby brother for a week. Her baby brother drinks 750 milliliters of formula each day. Charlotte’s mom has 6 liters of formula that she is bringing on the trip. How can Charlotte help her mom to figure out if she has enough formula for the trip?

In this concept, you will learn how to convert among metric units of measure using powers of 10.

Converting Metric Units of Measure

Recall that the metric system is the system of measurement primarily used in science and in countries outside of the United States.

In the metric system, the base unit of length is the meter (m). The base unit of mass is the gram (g). The base unit of capacity is the liter (L). The same prefixes are used throughout the metric system. The prefix of each unit of measurement indicates how that unit relates to the base unit.

  • “milli” means one thousandth. For example, there are 1000 millimeters in 1 meter.
  • “centi” means one hundredth. For example, there are 100 centimeters in 1 meter.
  • “kilo” means one thousand. For example, there are 1000 meters in 1 kilometer.

The metric system is based on powers of 10 just like our number system. To move between different units of length, mass, and capacity all you need to do is move the decimal point.

  • Any time you are going from a smaller unit of measure to a larger unit of measure you will need to divide or move the decimal point to the left.
  • Any time you are going from a larger unit of measure to a smaller unit of measure you will need to multiply or move the decimal point to the right.

The table below shows the most common metric conversions.

Common Metric Length Conversions
Kilometers (km) to Meters (m) \begin{align*}\times 1000\end{align*} Move decimal point 3 to the right
Meters (m) to Centimeters (cm)  \begin{align*}\times 100\end{align*} Move decimal point 2 to the right
Meters (m) to Millimeters (mm) \begin{align*}\times 1000\end{align*}  Move decimal point 3 to the right
Centimeters (cm) to Millimeters (mm)  \begin{align*}\times 10\end{align*} Move decimal point 1 to the right
Millimeters (mm) to Centimeters (cm)  \begin{align*}\div 10\end{align*} Move decimal point 1 to the left
Millimeters (mm) to Meters (m)  \begin{align*}\div 1000 \end{align*} Move decimal point 3 to the left
Centimeters (cm) to Meters (m)  \begin{align*}\div 100\end{align*} Move decimal point 2 to the left
Meters (m) to Kilometers (km)  \begin{align*}\div 1000 \end{align*} Move decimal point 3 to the left

The same conversions will work for grams and liters. Just use the prefixes to find the correct conversion.

Here is an example.

Convert 525 meters to centimeters.

First, notice that you are going from a larger unit to a smaller unit. This means you will need to multiply and move the decimal point to the right.

Next, remember that there are 100 centimeters in a meter. This means you will need to multiply by 100 or move the decimal point 2 to the right. Insert zeros into the blank spaces.

\begin{align*}525 \times 100=52,500\end{align*}

The answer is \begin{align*}525 \text{ meters} = 52,500 \text{ centimeters}.\end{align*}

Here is another example.

Convert 95,231 milligrams to kilograms.

First, notice that you are going from a smaller unit to a larger unit. This means you will need to divide and move the decimal point to the left.

Next, remember that there are 1000 milligrams in a gram and 1000 grams in a kilogram. This means there are 1,000,000 \begin{align*}(1000 \times 1000)\end{align*} milligrams in a kilogram. You will need to divide by 1,000,000 or move the decimal point 6 to the left.

\begin{align*}\frac{95231}{1000000}=0.095231\end{align*}

The answer is \begin{align*}95,231 \text{ milligrams} = 0.095231 \text{ kilograms}.\end{align*}

Examples

Example 1

Earlier, you were given a problem about Charlotte and her family trip with her baby brother.

Her brother drinks 750 milliliters of formula a day and her mom has 6 liters of formula packed for the 7 day trip. Charlotte wants to make sure they have enough formula.

First, Charlotte should figure out how many milliliters of formula her brother will need for the 7 days. He drinks 750 milliliters a day, so multiply 750 times 7.

\begin{align*}750 \times 7=5250\end{align*}

Her brother will need 5250 milliliters of formula for the trip.

Next, convert 5250 milliliters to liters. Charlotte should notice that she is going from a smaller unit to a larger unit. This means she will need to divide and move the decimal point to the left.

Now, Charlotte needs to remember that there are 1000 milliliters in a liter. This means she will need to divide by 1000 or move the decimal point 3 to the left.

\begin{align*}\begin{array}{rcl} 5250 \div 1000 &=& 5.250\\ 5250 \text{ milliliters} &=& 5.25 \text{ liters} \end{array}\end{align*}

The answer is that because Charlotte’s mom has 6 liters of formula and Charlotte’s brother will need 5.25 liters of formula, Charlotte’s mom has enough formula for the trip.

Example 2

Convert 150 grams to centigrams.

First, notice that you are going from a larger unit to a smaller unit. This means you will need to multiply and move the decimal point to the right.

Next, remember that there are 100 centigrams in a gram. This means you will need to multiply by 100 or move the decimal point 2 to the right. Insert zeros into the blank spaces.

\begin{align*}150 \times 100=15,000\end{align*}

The answer is \begin{align*}150 \text{ grams} = 15,000 \text{ centigrams}.\end{align*}

Example 3

Convert 500 meters to centimeters.

First, notice that you are going from a larger unit to a smaller unit. This means you will need to multiply and move the decimal point to the right.

Next, remember that there are 100 centimeters in a meter. This means you will need to multiply by 100 or move the decimal point 2 to the right. Insert zeros into the blank spaces.

\begin{align*}500 \times 100=50,000\end{align*}

The answer is \begin{align*}500 \text{ meters} = 50,000 \text{ centimeters}.\end{align*}

Example 4

Convert 120 meters to kilometers.

First, notice that you are going from a smaller unit to a larger unit. This means you will need to divide and move the decimal point to the left.

Next, remember that there are 1000 meters in a kilometer. This means you will need to divide by 1000 or move the decimal point 3 to the left.

\begin{align*}120 \div 1000=0.120 \ \text{or} \ 0.12\end{align*}

The answer is \begin{align*}120 \text{ meters} = 0.12 \text{ kilometers}.\end{align*}

Example 5

Convert 50 centiliters to liters.

First, notice that you are going from a smaller unit to a larger unit. This means you will need to divide and move the decimal point to the left.

Next, remember that there are 100 centiliters in a liter. This means you will need to divide by 100 or move the decimal point 2 to the left.

\begin{align*}50 \div 100=0.5\end{align*}

The answer is \begin{align*}50 \text{ centiliters} = 0.5 \text{ liters}.\end{align*}

Review

Convert the following metric units of length.

  1. 10 cm to millimeters
  2. 100 kilometers to meters
  3. 453 meters to kilometers
  4. 1,567 kilometers to meters
  5. 6,700 centimeters to meters
  6. 7.8 meters to centimeters

Convert the following measurements into milliliters.

  1. 65.57 liters
  2. 28.203 centiliters
  3. 0.009761 kiloliters

Convert the following measurements into centigrams.

  1. 29.467 grams
  2. 0.0562 milligrams
  3. 0.0450584 kilograms

Convert the following measurements into kiloliters.

  1. 89.96 liters
  2. 45,217 milliliters
  3. 3,120,700 centiliters

Review (Answers)

To see the Review answers, open this PDF file and look for section 2.21.

Resources

 

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Vocabulary

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.

Measurement

A measurement is the weight, height, length or size of something.

Proportion

A proportion is an equation that shows two equivalent ratios.

Ratio

A ratio is a comparison of two quantities that can be written in fraction form, with a colon or with the word “to”.

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