E. Spatial Sense · Spatial Sense: Angles, Triangles, Transformations and Area

Converting Metric Units: Bigger Units to Smaller Units

E2.2 A1About 40 minutes

Learning goals

I can describe the base ten relationships among metric units.
I can convert larger units into smaller units, such as km to m, m to cm, kg to g and L to mL.
I can solve problems that involve converting metric units.

Words to know

convert
To change a measurement into a different unit without changing its size. 2 m and 200 cm are the same length.

base unit
The main unit: metre (m) for length, gram (g) for mass, litre (L) for capacity.

prefix
The start of a unit's name that tells its size compared with the base unit: kilo-, hecto-, deca-, deci-, centi-, milli-.

decimetre (dm)
A tenth of a metre. 10 dm = 1 m and 1 dm = 10 cm.

Remember from Grade 4

You learned that kilo means 1000 times the base unit, centi means a hundredth, and milli means a thousandth. You know 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1000 g and 1 L = 1000 mL. Now you will see the pattern behind all of these and use it to solve problems.

Let's start with a cross-country race

Your school's cross-country race is 2 km long. The coach marks a flag every 100 m. How many flags is that?

To answer, you need the same unit for both numbers. 2 km = 2000 m. Then 2000 ÷ 100 = 20 flags.

Changing units like this is called converting.

The metric system is base ten

The metric system works just like place value. Each unit is 10 times the unit to its right, just as a ten is 10 ones and a hundred is 10 tens.

kilo- (k)	hecto- (h)	deca- (da)	base unit	deci- (d)	centi- (c)	milli- (m)
1000	100	10	1	one tenth	one hundredth	one thousandth
km	hm	dam	m	dm	cm	mm
kg	hg	dag	g	dg	cg	mg
kL	hL	daL	L	dL	cL	mL

Metric prefixes. Each column is 10 times the column to its right. The ones you'll use most are kilo-, the base unit, centi- and milli-.

A metre split into 10 decimetres. Each decimetre is 10 centimetres, and each centimetre is 10 millimetres. (Drawn smaller than a real metre, but in proportion.)

Converting bigger units to smaller units

When you change to a smaller unit, you need more of them, so you multiply.

km → m: multiply by 1000
m → cm: multiply by 100
m → mm: multiply by 1000
cm → mm: multiply by 10
kg → g: multiply by 1000
L → mL: multiply by 1000

Think of it like money: 3 loonies are worth 300 cents. Fewer big units, more small ones.

Each arrow goes from a bigger unit to a smaller one, so you multiply. For example, km to m is × 1000, and m to cm is × 100.

Worked example

Example 1: Whole numbers

Convert: (a) 7 km to m, (b) 4 m to cm, (c) 6 L to mL.

(a) Each km is 1000 m. 7 × 1000 = 7000 m.
(b) Each m is 100 cm. 4 × 100 = 400 cm.
(c) Each L is 1000 mL. 6 × 1000 = 6000 mL.

7000 m, 400 cm, 6000 mL

Worked example

Example 2: Decimals

Convert: (a) 2.5 km to m, (b) 3.75 m to cm.

(a) Split it up: 2 km = 2000 m. 0.5 km is half a kilometre, and half of 1000 m is 500 m. 2000 + 500 = 2500 m.
(b) 3 m = 300 cm. 0.75 m is 75 hundredths of a metre, and a hundredth of a metre is 1 cm, so 0.75 m = 75 cm. 300 + 75 = 375 cm.

2.5 km = 2500 m and 3.75 m = 375 cm.

Worked example

Example 3: A juice problem

You have 2 L of apple juice. Each glass holds 250 mL. How many glasses can you fill?

The units don't match. Convert the bigger unit: 2 L = 2 × 1000 = 2000 mL.
Now divide: 2000 ÷ 250. Four glasses make 1000 mL, so 2000 mL fills 8 glasses.
Check: 8 × 250 = 2000. ✓

8 glasses.

Worked example

Example 4: Compare

Which is longer: 1800 m or 2 km?

Convert 2 km to metres: 2 × 1000 = 2000 m.
Compare 1800 m and 2000 m.

2 km is longer, by 200 m.

Bigger number, smaller unit

Before you calculate, ask: "Am I going to a smaller unit? Then my number should get bigger." If you convert 5 km and get 0.005, something went wrong. A quick reasonableness check saves you from mistakes.

Just for fun

Lots of Ontario families buy milk in bags! A 4 L pack holds 4 × 1000 = 4000 mL. That's enough for 16 glasses of 250 mL each.

Hands-on activity

Kitchen and closet conversions

You need: food packages from the kitchen, a measuring tape or metre stick, and a pencil and paper.

Find 3 packages that show mass in kg (like flour, sugar or rice). Convert each to grams.
Find 3 containers that show capacity in L (like milk, juice or a 4 L bag of milk). Convert each to mL.
Measure the length of 3 things in m and cm (a bed, a table, a doorway). Write each length in cm only, then in mm only.
Make a chart: Item, Label, Converted.

Bonus: a recipe says 250 mL of milk. How many times could you make it from a 1 L carton?

(Bonus answer: 4 times, because 1000 ÷ 250 = 4.)

Math talk: "Why do we multiply when we change to a smaller unit?"

Your turn

6 km = ? m

4 m = ? cm

9 cm = ? mm

3 kg = ? g

5 L = ? mL

2.5 m = ? cm

A 3 L jug of water fills cups that hold 500 mL each. How many cups?

More practice: warm-up

7 m = ? cm

2 km = ? m

8 L = ? mL

5 cm = ? mm

10 kg = ? g

More practice: on your own

3.5 km = ? m

1.25 kg = ? g

4 m = ? mm

A 3 m ribbon is cut into pieces 25 cm long. How many pieces?

Which is more: 1500 g or 2 kg?

Challenge

A 5 km race is run on a track. One lap is 400 m. How many laps is the race?

A recipe uses 750 mL of milk. How many full batches can you make from a 4 L bag of milk? How much milk is left?

Put in order from shortest to longest: 0.8 km, 750 m, 85 000 cm.

Check your understanding

Quiz

How many metres are in 4 km?

3 m = ? cm

When you convert from a larger unit to a smaller unit, the number:

1.5 L = ? mL

How many 200 g scoops are in a 2 kg bag of flour?

Each metric unit is how many times the next smaller unit?

For parents and teachers

Big idea: The Ontario curriculum (E2.2) asks Grade 5 students to solve problems that involve converting larger metric units into smaller ones, and describe the base ten relationships among metric units. Students only need to convert in one direction (larger to smaller) this year.

Common difficulties:

Dividing instead of multiplying. Remind your child: smaller unit, bigger number.
Using the wrong factor. m → cm is × 100, but m → mm is × 1000. A place-value chart of prefixes helps.
Decimals. Split the decimal into whole units and a part: 2.5 km = 2 km + half a km.

How to help: Read labels together and convert: "This 4 L bag of milk is how many mL?" Social-emotional learning (A1) is woven in: checking answers for reasonableness and fixing mistakes calmly.