Convert Metric Units of Length, Mass and Capacity | Grade 5 Math | LevelKite

You already know how to convert customary units, such as changing feet to inches. To convert a measurement is to write the same amount in a different unit. Now you will convert units in the metric system. This is a set of units linked by 10, 100 and 1,000, the powers of ten you already know.

You will work with three kinds of measurement:

Length is how long something is. Its units here are the millimeter (mm), centimeter (cm), meter (m) and kilometer (km).
Mass is how much matter is in an object. You notice it as how heavy the object is. Its units here are the gram (g) and kilogram (kg).
Capacity is how much a container can hold. Its units here are the milliliter (mL) and liter (L).

Metric facts you will use

Kind of measurement	Fact	In words
Length	$1 \text{ cm} = 10 \text{ mm}$	One centimeter is as long as 10 millimeters.
Length	$1 \text{ m} = 100 \text{ cm}$	One meter is as long as 100 centimeters.
Length	$1 \text{ m} = 1{,}000 \text{ mm}$	One meter is as long as 1,000 millimeters.
Length	$1 \text{ km} = 1{,}000 \text{ m}$	One kilometer is as long as 1,000 meters.
Mass	$1 \text{ kg} = 1{,}000 \text{ g}$	One kilogram has the same mass as 1,000 grams.
Capacity	$1 \text{ L} = 1{,}000 \text{ mL}$	One liter holds as much as 1,000 milliliters.

Each fact in the table shows one amount written in two units. The unit written with 1 is the larger unit. It takes 10, 100 or 1,000 of the smaller unit to match it.

Picture a jump rope that is 2 m long. Each meter is 100 centimeters, so 2 meters are 2 groups of 100 centimeters: $2 \times 100 = 200$ . The rope is 200 cm long. The rope did not grow. You counted it with a smaller unit, so you needed more of them.

Now go the other way. A ribbon is 300 cm long. Every 100 centimeters make 1 meter, so you ask how many groups of 100 are in 300: $300 \div 100 = 3$ . The ribbon is 3 m long. A meter is a larger unit, so you needed fewer of them.

Key concept

Smaller unit: multiply. Larger unit: divide.

Converting never changes the amount. It changes only the unit and the number.

To change to a smaller unit, multiply. You need more of a smaller unit to show the same amount.
To change to a larger unit, divide. You need fewer of a larger unit to show the same amount.

Multiply or divide by the number in the fact that links the two units. For kilometers and meters, that number is 1,000, because $1 \text{ km} = 1{,}000 \text{ m}$ .

Worked example

Meters to kilometers

A hiking trail is 4,000 m long. How long is the trail in kilometers?

Find the fact that links meters and kilometers. It tells you how many of the smaller unit make one of the larger unit.
$1 \text{ km} = 1{,}000 \text{ m}$
Decide whether to multiply or divide. A kilometer is larger than a meter, so fewer kilometers cover the same trail. Changing to a larger unit means you divide.
Divide the number of meters by 1,000. This finds how many groups of 1,000 meters are in 4,000 meters, and each group is 1 kilometer.
$4{,}000 \div 1{,}000 = 4$
Check by going back the other way. 4 kilometers are 4 groups of 1,000 meters, which gives the length you started with.
$4 \times 1{,}000 = 4{,}000$

Answer

The trail is $4$ km long, because $4{,}000 \text{ m} = 4 \text{ km}$ .

More lengths, same rule

Convert	The new unit is	Fact to use	Calculation	Result
5 km to meters	smaller, so multiply	$1 \text{ km} = 1{,}000 \text{ m}$	$5 \times 1{,}000 = 5{,}000$	$5 \text{ km} = 5{,}000 \text{ m}$
8 cm to millimeters	smaller, so multiply	$1 \text{ cm} = 10 \text{ mm}$	$8 \times 10 = 80$	$8 \text{ cm} = 80 \text{ mm}$
700 cm to meters	larger, so divide	$1 \text{ m} = 100 \text{ cm}$	$700 \div 100 = 7$	$700 \text{ cm} = 7 \text{ m}$
6,000 mm to meters	larger, so divide	$1 \text{ m} = 1{,}000 \text{ mm}$	$6{,}000 \div 1{,}000 = 6$	$6{,}000 \text{ mm} = 6 \text{ m}$

The same rule works for mass and capacity. Each one needs just one fact: $1 \text{ kg} = 1{,}000 \text{ g}$ and $1 \text{ L} = 1{,}000 \text{ mL}$ .

7 kg to grams. Grams are smaller, so multiply: $7 \times 1{,}000 = 7{,}000$ . So $7 \text{ kg} = 7{,}000 \text{ g}$ .
3,000 g to kilograms. Kilograms are larger, so divide: $3{,}000 \div 1{,}000 = 3$ . So $3{,}000 \text{ g} = 3 \text{ kg}$ .
2 L to milliliters. Milliliters are smaller, so multiply: $2 \times 1{,}000 = 2{,}000$ . So $2 \text{ L} = 2{,}000 \text{ mL}$ .
9,000 mL to liters. Liters are larger, so divide: $9{,}000 \div 1{,}000 = 9$ . So $9{,}000 \text{ mL} = 9 \text{ L}$ .

The units changed from length to mass and capacity. The thinking stayed the same.

A conversion table lists the same amounts in two units, side by side. Each row shows one amount written two ways.

The numbers in the two columns follow a pattern, which is a rule that is true for every row. The pattern comes from the fact that links the two units. Once you know the pattern, you can fill in a missing cell. You can also read a conversion straight from the table.

The table below shows kilograms and grams. Two of its cells are missing.

Kilograms and grams

Kilograms (kg)	Grams (g)
1	1,000
2	2,000
3	3,000
6	?
?	8,000

Worked example

Complete and use a conversion table

In the table above, 1 kg, 2 kg and 3 kg sit next to 1,000 g, 2,000 g and 3,000 g. Two cells are missing: the grams for 6 kg and the kilograms for 8,000 g. Describe the pattern between the two columns and find both missing numbers. Then use the table to write 3,000 g in kilograms.

Describe the pattern. Look across the full rows: 1 goes with 1,000, 2 with 2,000 and 3 with 3,000. Each number of grams is 1,000 times the number of kilograms, which matches the fact that 1 kilogram is 1,000 grams.
$\text{number of grams} = \text{number of kilograms} \times 1{,}000$
Find the grams for 6 kg. Going from the kilograms column to the grams column changes to a smaller unit, so multiply by 1,000.
$6 \times 1{,}000 = 6{,}000$
Find the kilograms for 8,000 g. Going from the grams column to the kilograms column changes to a larger unit, so divide by 1,000.
$8{,}000 \div 1{,}000 = 8$
Use the table. Find 3,000 in the grams column and read across the same row to the kilograms column. Each row shows one amount in both units, so you do not need a new calculation.
$3{,}000 \text{ g} = 3 \text{ kg}$

Answer

The missing numbers are $6{,}000$ g next to 6 kg and $8$ kg next to 8,000 g. Each number of grams is 1,000 times the number of kilograms beside it, and the table shows that $3{,}000 \text{ g} = 3 \text{ kg}$ .

You can compare two measurements only when they use the same unit. A number by itself does not tell you the size. For example, 4 cm is longer than 35 mm, even though 4 is less than 35.

To compare, convert one measurement so that both use the same unit. Then compare the numbers. A handy choice is to change the larger unit to the smaller one, because then you multiply and the numbers stay whole.

Change 4 cm to millimeters: $4 \times 10 = 40$ , so $4 \text{ cm} = 40 \text{ mm}$ . Now both lengths are in millimeters, and 40 mm is greater than 35 mm. In symbols, $40 \text{ mm} > 35 \text{ mm}$ . So 4 cm is the longer length.

Worked example

Compare liters and milliliters

A bottle holds 3 L of juice. A jug holds 2,600 mL of juice. Which container holds more?

The units are different, so you cannot compare 3 and 2,600 yet. Choose to change liters to milliliters. Milliliters are the smaller unit, so you will multiply.
$1 \text{ L} = 1{,}000 \text{ mL}$
Multiply the number of liters by 1,000, because each liter is 1,000 milliliters. This writes the bottle's amount in milliliters.
$3 \times 1{,}000 = 3{,}000$
Now both amounts are in milliliters, so compare the numbers. 3,000 is greater than 2,600.
$3{,}000 \text{ mL} > 2{,}600 \text{ mL}$

Answer

The bottle holds more, because $3 \text{ L} = 3{,}000 \text{ mL}$ and $3{,}000 \text{ mL}$ is greater than $2{,}600 \text{ mL}$ .

Here is the idea to keep: converting changes the unit and the number, but never the amount. Multiply to change to a smaller unit, and divide to change to a larger unit. The fact that links the two units tells you whether to use 10, 100 or 1,000. This one rule works for length, mass and capacity. It fills in conversion tables, and it lets you compare two measurements once they share a unit.

Next, you will convert metric measurements that have decimal answers, add and subtract measurements given in mixed units, and solve word problems that take more than one step.