Title: LESSON: Measuring Units
Course: Mathematics Essentials Q1 > Section: Week 5

Metric Units

INTRODUCTION

Measuring Metric Length

READ: Equivalent Metric Units of Length

Equivalent Metric Units of Length

This lesson focuses on metric units of measurements. In the United States, we use the customary system of measurement more than we use the metric system of measurement. However, if you travel to another country or complete work in science class, you will need to know metrics.

What are the metric units for measuring length?

To measure length, we are measuring how long something is or you could say we are measuring from one end to the other end. That is the length of the item.

Here are the metric units of length from the smallest unit to the largest unit.

A millimeter is the smallest unit. Millimeters are most useful when measuring really tiny things. You can find millimeters on some rulers.

A centimeter is the next smallest unit. They can also be found on a ruler.

A meter is a little more than 3 feet. A meter is the unit that would be very helpful to a carpenter or to someone working in construction.

A kilometer is used to measure longer distances. You often hear the word kilometer mentioned when talking about a road race that 5k or 5 kilometers long.

How can we convert metric units of length?

When working with the customary units of length, inches, feet, etc, we know that we can convert them or change the units we are working with. For example, if you have 24 inches, it might make more sense to say that we have 2 feet. We can do the same thing when working with metric units.

Here is a chart to help us with the conversions.

Metric Unit | Equivalent To:
1 centimeter (cm) | 10 millimeters (mm)
1 meter (m) | 100 centimeters (cm)
1 kilometer (km) | 1000 meters (m)

Example 1

5 km = ____ m

Here we are converting kilometers to meters. How can we convert larger units to smaller units? We can convert larger units to smaller units by multiplying.

There are 1000 m in one kilometer.

Our answer is 5000 m.

Example 2

600 cm = ______ m

Here we are converting smaller units to larger units. How can we convert smaller units to larger units? We can convert smaller units to larger units by dividing.

There are 100 cm in one meter.

600 100 6

Our answer is 6.

READ: Equivalent Metric Units of Mass

Identify Equivalence of Metric Units of Mass

In the United States, the most common system of measurement is the Customary system of measurement. The Customary system of measurement for mass or weight is measured in pounds and tons. Outside of the United States and when people work with topics in science, people use a system called the Metric system. The metric system measures mass or weight differently from the customary system.

How do we measure mass in the Metric system?

In the metric system we use thee different units to measure mass or weight.

This text box lists the units of measuring mass from the largest unit, the kilogram to the smallest unit, the milligram. If you think back to when you learned about measuring length, the prefix “milli” indicated a very small unit. That is the same here as we measure mass.

How can we find equivalent metric units of mass?

The word equivalent means equal. We can compare different units of measuring mass with kilograms, grams and milligrams. To do this, we need to know how many grams equal one kilogram, how many milligrams equal one gram, etc. Here is a chart to help us understand equivalent units.

Here you can see that when we convert kilograms to grams you multiply by 1000.

When you convert grams to milligrams, you multiply by 1000.

To convert from a large unit to a small unit, we multiply.

To convert from a small unit to a large unit, we divide.

Example 1

5 kg = _____ g

When we go from kilograms to grams, we multiply by 1000.

5 kg = 5000 g

These two values are equivalent.

READ: Equivalent Metric Units of Capacity

Identify Equivalence of Metric Units of Capacity

When we think about capacity, we think about measuring liquids. In the Customary system of measurement, we measure liquids using cups, pints, ounces, gallons etc. In the Metric System of measurement, we measure capacity using two different measures, liters and milliliters.

Since there are only two metric units for measuring capacity, this text box shows them and their equivalent measures. Liters are larger than milliliters. Notice that prefix “milli” again.

When converting from large units to small units, you multiply.

When converting from small units to large units, you divide.

Example

4 liters = _____ milliliters

Liters are larger than milliliters, so we multiply by 1000.

4 liters = 4000 milliliters

READ: Choosing Appropriate Units of Measure

Choose Appropriate Metric Units of Measure

When you think about the metric units for measuring mass, how do you know when to measure things in grams, milligrams or kilograms? To really understand when to use each unit of measurement we have to understand a little more about the size of each unit.

Let’s compare grams with ounces. Grams and ounces measure really small things like a raisin.

Let’s compare kilograms with pounds. Kilograms and pounds measure bigger things, like a textbook.

What about milligrams?

Milligrams are very, very tiny. Think about how small a raisin is and we would use grams to measure that. Scientists are people who would measure the mass of very tiny items. These things would be measured in milligrams.

If you think about things that would be seen under a microscope, you would measure the mass of those items in milligrams.

A milligram is of a gram.

What about capacity? How do we choose the correct unit of measure to measure capacity?

There are two metric units for measuring capacity, milliliters and liters.

This comparison may seem a little more obvious that the units for mass. A milliliter would be use to measure very small amounts or ounces of water. A liter would be used to measure much larger volumes of water.

A milliliter is of a liter.

How about measuring length? The metric units of length are millimeter, centimeter, meter and kilometer. When is the best time to use each measurement?

A millimeter is the smallest unit. There are 10 mm in one centimeter, if an object is smaller than one centimeter, then you would use millimeters.

Who would use millimeters? A scientist measuring something under a microscope might use millimeters to represent a tiny specimen.

A centimeter is the next smallest unit. We can use a ruler to measure things in centimeters. If an object is the length of a ruler or smaller, then it makes sense to use centimeters to measure.

Meters are used to measure everything between the length of a ruler and the length of a far distance, like the distance between two cities or places.

Most household objects such as table, rooms, window frames, television screens, etc would be measured in meters.

READ: Converting Metric Units of Length, Mass and Capacity

Convert Metric Units of Length, Mass and Capacity

This section combines a couple of different skills that we have already learned. We have learned all about metrics and about how to convert metric units of length, mass and capacity. We have also learned how to multiply decimals using powers of ten such as 10, 100, 1000. How can we put these two skills together?

We can put them together by converting metric units using powers of ten. This will require us to move the decimal point as we did in earlier lessons.

Example

Convert 150 cm into mm by multiplying by a power of ten. We know that there are 10 mm in 1 cm. When we go from a larger unit to a smaller unit we multiply. Therefore, we are going to multiply 150 cm by 10.

150 cm 10 _____ mm

We know that when we multiply by 10 we move the decimal point one place to the right. The decimal point in a whole number is after the number. So we need to add a zero placeholder to 150.

150 cm = 1500 mm

We can do this when we convert from a smaller unit to a larger unit too. Let’s look at this one involving capacity.

Example

1250 milliliters = _____ L

We know that there are 1000 milliliters in one liter. We need to divide 1250 milliliters by 1000. To do this, we will move the decimal point three places to the left. The decimal point is after the number in a whole number.

1250 milliliters = 1.25 Liters

We can complete this with any unit of measure as long as we know the conversion equivalents and remember how to use powers of ten to move the decimal point to the left or to the right

EXAMPLE 1

Conversion between Metric Units

EXAMPLE 2

Converting within the Metric System

EXAMPLE 3

Applying the Metric System

CHECK Yourself! Unit Conversions

While we primarily use millimeters, centimeters, meters, and kilometers when talking about units of measure, there are other metric units of measure. See if you can take what you learned about metric conversion and the table below to answer question #5.

Metric Unit | Equivalent To
1 millimeter (mm) | 10 micrometers
1 centimeter (cm) | 10 millimeters
1 decimeter (dm) | 10 centimeters
1 meter (m)
100 centimeters

or

10 decimeters

or

10,000 millimeters

or

100,000 micrometers
1 dekameter (dam) | 10 meters
1 hectometer (hm) | 100 meters
1 kilometer (km) | 1000 meters