# 2.22: Comparison of Metric Measurements

Difficulty Level: At Grade Created by: CK-12
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Sarah and Laura both just joined the track team at school. So far they are really enjoying it! They are training for a meet next weekend where they will both be competing in long distance running events. Their coach told Sarah that she will be running in the 5000 m event. Laura will be running the 10k. At first, Sarah and Laura aren’t sure what this means. How can they figure out who will be running the longer distance?

In this concept, you will learn how to compare given metric units of measure.

### Comparing Metric Measurements

Sometimes you will want to compare different metric measurements. Knowing how to convert between metric units of measure and how to compare decimal numbers makes this possible.

You can compare two metric measurements in the same way that you compare decimal numbers. You just have to make sure that your measurements are in the same unit first.

Here are the steps for comparing metric measurements.

1. If necessary, convert one of the measurements so that both measurements are in the same unit.
2. Working from left to right, compare digits that have the same place value. Starting with the digit on the left and moving right, whichever number first has a larger digit is the larger number overall.

You can use an inequality symbol to show how two metric measurements are related.

Here is an example.

\begin{align*}4.56 \ g \ \underline{\;\;\;\;\;\;\;}\ 456 \ mg\end{align*}

First, you want both measurements to be in the same unit. It doesn’t matter which unit you convert. Let’s convert 4.56 g to mg.

Now, 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. Because there are 1000 milligrams in a gram, you will need to move the decimal point 3 to the right.

\begin{align*}\begin{array}{rcl} 4.56 \times 1000 &=& 4560 \\ 4.56 \ g &=& 4560 \ mg \end{array}\end{align*}

Next, rewrite your problem with both measurements in the same unit.

\begin{align*}4560 \ mg \ \underline{\;\;\;\;\;\;\;}\ 456 \ mg\end{align*}

Now, compare the two numbers. 4560 has a digit in the thousands place while 456 does not. 4560 is the bigger number. This means 4560 milligrams is more than 456 milligrams, so 4.56 grams is more than 456 milligrams.

The answer is \begin{align*}4.56 \ g > 456 \ mg\end{align*}.

### Examples

#### Example 1

Earlier, you were given a problem about Sarah and Laura's upcoming track meet.

Sarah will be running the 5000 m while Laura will be running the 10K. They are wondering who will have to run the longer distance.

First, Sarah and Laura need to know that 10K means 10 kilometers. With running races, the letter “K” is often used to mean kilometer. So they are comparing 5000 meters with 10 kilometers.

\begin{align*}5000 \ m \ \underline{\;\;\;\;\;\;\;}\ 10 \ km\end{align*}

Now, the girls will need both measurements to be in the same unit. They can convert 5000 meters to kilometers. Because there are 1000 meters in a kilometer, they will need to divide and move the decimal point 3 to the left.

\begin{align*}\begin{array}{rcl} \frac{5000}{1000} &=& 5 \\ 5000 \ m &=& 5 \ km \end{array}\end{align*}

Next, they can rewrite the problem with both measurements in the same unit.

\begin{align*}5 \ km \ \underline{\;\;\;\;\;\;\;}\ 10 \ km\end{align*}

Now, they can compare the two numbers. 5 is less than 10. This means 10 kilometers is more than 5 kilometers, so 10 kilometers is more than 5000 meters.

The answer is the 10K that Laura will be running is longer than the 5000 m that Sarah will be running.

#### Example 2

\begin{align*}743 \ km \ \underline{\;\;\;\;\;\;\;} \ 74,300,000 \ mm\end{align*}

First, you want both measurements to be in the same unit. It doesn’t matter which unit you convert. Let’s convert 74,300,000 mm to km.

Now, 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. Because there are 1,000,000 millimeters in a kilometer (1,000 millimeters in a meter and 1,000 meters in a kilometer means \begin{align*}1,000 \times 1,000 = 1,000,000 \text{ millimeters}\end{align*} in a kilometer), you will need to move the decimal point 6 to the left.

\begin{align*}\begin{array}{rcl} \frac{74,300,000}{1,000,000}& =& 74.3 \\ 74,300,000 \ mm & =& 74.3 \ km \end{array}\end{align*}

Next, rewrite your problem with both measurements in the same unit.

\begin{align*}743 \ km \ \underline{\;\;\;\;\;\;\;}\ 74.3 \ km\end{align*}

Now, compare the two numbers. 743 km has a digit in the hundreds place while 74.3 does not. 743 is the bigger number. This means 743 kilometers is more than 74.3 kilometers, so 743 kilometers is more than 74,300,000 millimeters.

The answer is \begin{align*}743 \ km > 74,300,000 \ mm\end{align*}.

#### Example 3

\begin{align*}45 \ cm \ \underline{\;\;\;\;\;\;\;}\ 500 \ mm\end{align*}

First, you want both measurements to be in the same unit. It doesn’t matter which unit you convert. Let’s convert 500 mm to cm.

Now, 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. Because there are 10 millimeters in a centimeter, you will need to move the decimal point 1 to the left.

\begin{align*}\begin{array}{rcl} \frac{500}{10} &=& 50 \\ 500 \ mm &=& 50 \ cm \end{array}\end{align*}

Next, rewrite your problem with both measurements in the same unit.

\begin{align*}45 \ cm \ \underline{\;\;\;\;\;\;\;}\ 50 \ cm\end{align*}

Now, compare the two numbers. Both numbers start with a digit in the tens place. 5 is greater than 4. This means 45 centimeters is less than 50 centimeters, so 45 centimeters is less than 500 millimeters.

The answer is \begin{align*}45 \ cm < 500 \ mm\end{align*}.

#### Example 4

\begin{align*}2 \ km \ \underline{\;\;\;\;\;\;\;}\ 400 \ m\end{align*}

First, you want both measurements to be in the same unit. It doesn’t matter which unit you convert. Let’s convert 400 m to km.

Now, 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. Because there are 1000 meters in a kilometer, you will need to move the decimal point 3 to the left.

\begin{align*}\begin{array}{rcl} \frac{400}{1000} &=& 0.4 \\ 400 \ m &=& 0.4 \ km \end{array}\end{align*}

Next, rewrite your problem with both measurements in the same unit.

\begin{align*}2 \ km \ \underline{\;\;\;\;\;\;\;}\ 0.4 \ km\end{align*}

Now, compare the two numbers. 2 is greater than 0.4. This means 2 kilometers is greater than 0.4 kilometers, so 2 kilometers is greater than 400 meters.

The answer is \begin{align*}2 \ km > 400 \ m\end{align*}.

#### Example 5

\begin{align*}6 \ L \ \underline{\;\;\;\;\;\;\;}\ 60,000 \ mL\end{align*}

First, you want both measurements to be in the same unit. It doesn’t matter which unit you convert. Let’s convert 60,000 mL to L.

Now, 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. Because there are 1000 milliliters in a liter, you will need to move the decimal point 3 to the left.

\begin{align*}\begin{array}{rcl} \frac{60,000}{1000} &=& 60 \\ 60,000 \ mL &=& 60 \ L \end{array} \end{align*}

Next, rewrite your problem with both measurements in the same unit.

\begin{align*}6 L \ \underline{\;\;\;\;\;\;\;}\ 60 L\end{align*}

Now, compare the two numbers. 60 is greater than 6. This means 6 liters is less than 60 liters, so 6 liters is less than 60,000 milliliters.

The answer is \begin{align*}6 \ L < 60,000 \ mL\end{align*}.

### Review

Compare or order the following measurements. Write <, >, or = for each blank.

1. \begin{align*}14 \ km \ \underline{\;\;\;\;\;\;\;} \ 56 \ m\end{align*}
2. \begin{align*}1.23 \ m \ \underline{\;\;\;\;\;\;\;} \ 123 \ km\end{align*}
3. \begin{align*}3.4 \ km \ \underline{\;\;\;\;\;\;\;} \ 340 \ m\end{align*}
4. \begin{align*}18 \ g \ \underline{\;\;\;\;\;\;\;} \ 0.18 \ kg\end{align*}
5. \begin{align*}27 \ m \ \underline{\;\;\;\;\;\;\;} \ 2700 \ km\end{align*}
6. \begin{align*}14 \ l \ \underline{\;\;\;\;\;\;\;} \ 2100 \ ml\end{align*}
7. \begin{align*}5 \ g \ \underline{\;\;\;\;\;\;\;} \ 0.0005 \ kg\end{align*}
8. \begin{align*}18 \ mm \ \underline{\;\;\;\;\;\;\;} \ 0.18 \ cm\end{align*}
9. \begin{align*}2.3 \ km \ \underline{\;\;\;\;\;\;\;} \ 2700 \ m\end{align*}
10. \begin{align*}3.48 \ cl \ \underline{\;\;\;\;\;\;\;} \ 0.348 \ l\end{align*}
11. \begin{align*}57.21 \ kg \ \underline{\;\;\;\;\;\;\;} \ 572,100 \ cg\end{align*}
12. \begin{align*}91.17 \ mm \ \underline{\;\;\;\;\;\;\;} \ 0.09117 \ m\end{align*}
13. \begin{align*}4.4 \ cl \ \underline{\;\;\;\;\;\;\;} \ 0.44 \ ml\end{align*}
14. Order the following measurements from least to greatest: 79,282 kg, 7,838,200 cg, 7,938,200 mg, 79,382 g.
15. Order the following measurements from least to greatest: 2,261,000 cl, 21,061 l, 21.06 kl, 21,161,000 ml.

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### Vocabulary Language: English

TermDefinition
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.

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