Chapter 10 · Measurement and data

Choose Units, Convert Time, and Compare Measurements

Learn to pick a sensible unit, decide when a conversion multiplies or divides, convert units of time, and compare measurements by changing them to the same unit.

14 min read

You use measurements every day, like how long recess lasts or how tall you are. A measurement has two parts: a number and a unit. The unit tells you what you are counting, such as minutes, feet or grams.

The same amount can be written with different units. A class that lasts $1$ hour also lasts $60$ minutes. Nothing about the class changed. Only the number and the unit changed.

To convert a measurement means to write the same amount with a different unit. In this lesson you will choose a sensible unit, decide whether a conversion multiplies or divides, convert units of time, and compare measurements that start in different units.

Start with the unit. A sensible unit fits the size of the thing you measure. It gives a number that is easy to read and easy to picture.

Think about how long a movie lasts. You could say $5{,}400$ seconds, but that number is hard to picture. You could also say $90$ minutes, which is much clearer. Both name the same length of time, but minutes are the sensible choice.

Two questions help you choose:

What kind of thing is it? Length, weight, liquid volume and time each have their own units.
How big is it? Use a small unit for a small amount and a large unit for a large amount.

Choosing a sensible unit

What you measure	Sensible unit	Why it fits
The length of a pencil	centimeters or inches	A pencil is short. A small unit of length gives an easy number.
The distance between two towns	kilometers or miles	The distance is long. A large unit of length keeps the number small.
How heavy a large dog is	kilograms or pounds	A large dog is heavy. Grams or ounces would give a huge number.
The water in a full bathtub	liters or gallons	A bathtub holds a lot. Milliliters or cups would give a huge number.
The time it takes to brush your teeth	minutes	Brushing is quick. In days, the number would be a tiny fraction.
How long a camping trip lasts	days	A camping trip is long. Seconds would give a huge number.

Now look at what happens to the number when you change the unit.

Picture $2$ hours. Cut each hour into minutes. Each hour holds $60$ minutes, so $2$ hours hold $2$ groups of $60$ minutes. That is $2 \times 60 = 120$ minutes. The unit got smaller, so you need more of them to fill the same time.

Now go the other way. Start with $120$ minutes and bundle them into hours. Every $60$ minutes make $1$ hour, so you get $120 \div 60 = 2$ hours. The unit got larger, so you need fewer of them.

The time itself never changed: $2$ hours and $120$ minutes are the same length of time.

Key concept

The size of the unit decides the number

For the same amount, a smaller unit gives a bigger number, and a larger unit gives a smaller number.

Converting to a smaller unit? You need more of them, so multiply.
Converting to a larger unit? You need fewer of them, so divide.

The number you multiply or divide by comes from a conversion fact. A conversion fact tells how many of the smaller unit make $1$ of the larger unit, such as $60$ minutes in $1$ hour.

Deciding whether to multiply or divide

Conversion	Is the new unit smaller or larger?	What that means	Number sentence
$5$ feet to inches	smaller	You need more inches, so multiply by $12$ .	$5 \times 12 = 60$ inches
$3$ gallons to quarts	smaller	You need more quarts, so multiply by $4$ .	$3 \times 4 = 12$ quarts
$4{,}000$ grams to kilograms	larger	You need fewer kilograms, so divide by $1{,}000$ .	$4{,}000 \div 1{,}000 = 4$ kilograms
$180$ minutes to hours	larger	You need fewer hours, so divide by $60$ .	$180 \div 60 = 3$ hours

You already know conversion facts for length, weight and liquid volume. Time has three facts of its own. They link the units of time in order from smallest to largest: seconds, minutes, hours, days.

These facts use $60$ and $24$ . They do not use $10$ , $100$ or $1{,}000$ the way metric facts do. Each fact links two units that sit next to each other. To move two units, such as from seconds to hours, take one step at a time.

Conversion facts for time

Conversion fact	Larger unit to smaller unit	Smaller unit to larger unit
$1$ minute = $60$ seconds	minutes to seconds: multiply by $60$	seconds to minutes: divide by $60$
$1$ hour = $60$ minutes	hours to minutes: multiply by $60$	minutes to hours: divide by $60$
$1$ day = $24$ hours	days to hours: multiply by $24$	hours to days: divide by $24$

Worked example

Hours to minutes

A train ride lasts $4$ hours. How many minutes does it last?

Name the two units. You start in hours and you want minutes. A minute is shorter than an hour, so you need more minutes than hours. That means you multiply.
Use the conversion fact 1 hour = 60 minutes. Each of the 4 hours holds 60 minutes, so find 4 groups of 60.
$4 \times 60 = 240$
Check the size of your answer. The number grew from 4 to 240. That makes sense, because the unit got smaller.
$4 \text{ hours} = 240 \text{ minutes}$

Answer

The train ride lasts $240$ minutes.

Worked example

Seconds to hours in two steps

A bike race lasts $7{,}200$ seconds. How many hours does it last?

Name the two units. You start in seconds and you want hours. An hour is much longer than a second, so you need fewer hours than seconds. That means you divide.
Seconds and hours are two units apart, so take one step at a time. First change seconds to minutes. Every 60 seconds make 1 minute, so divide by 60. The race lasts 120 minutes.
$7{,}200 \div 60 = 120$
Now change 120 minutes to hours. Every 60 minutes make 1 hour, so divide by 60 again. The race lasts 2 hours.
$120 \div 60 = 2$
Check the size of your answer. The number dropped from 7,200 to 2. That makes sense, because the unit got much larger.
$7{,}200 \text{ seconds} = 120 \text{ minutes} = 2 \text{ hours}$

Answer

The bike race lasts $2$ hours.

Now use conversions to compare. To compare measurements means to decide which amount is greater, or whether they are equal. To order them means to line them up from least to greatest, or from greatest to least.

A number tells you how many units there are. It does not tell you how big each unit is. So you can compare two numbers fairly only when they count the same unit.

Here is the plan:

Pick one unit for all the measurements. Any unit works, as long as every measurement uses it.
Convert each measurement to that unit.
Compare the numbers. Then give your answer with the measurements from the problem.

Worked example

Ordering times in three different units

A science club tests three flashlight batteries. Battery A lasts $2$ days. Battery B lasts $50$ hours. Battery C lasts $2{,}940$ minutes. Order the batteries from the shortest time to the longest time.

Pick one unit for all three times. Hours are a good choice, because days and minutes are each one step away from hours. Battery B is already in hours: 50 hours.
Convert Battery A to hours. An hour is shorter than a day, so you need more hours. Multiply by 24, because each day holds 24 hours. Battery A lasts 48 hours.
$2 \times 24 = 48$
Convert Battery C to hours. An hour is longer than a minute, so you need fewer hours. Divide by 60, because every 60 minutes make 1 hour. Battery C lasts 49 hours.
$2{,}940 \div 60 = 49$
Now all three times count hours, so you can compare the numbers. Put 48, 49 and 50 in order from least to greatest.
$48 < 49 < 50$
Match each number back to its battery. 48 hours is Battery A, 49 hours is Battery C and 50 hours is Battery B.

Answer

From the shortest time to the longest, the order is Battery A ( $2$ days), Battery C ( $2{,}940$ minutes), then Battery B ( $50$ hours).

Here is the idea to keep. A measurement is a number and a unit, and the size of the unit decides the number.

Choose a unit that fits the size of what you measure.
To convert to a smaller unit, multiply. To convert to a larger unit, divide.
For time, remember $60$ seconds in a minute, $60$ minutes in an hour and $24$ hours in a day.
To compare or order measurements, convert them to the same unit first.

Next, you will use these ideas to solve word problems with more than one step and to find and fix conversion mistakes.

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Multi-Step Conversion Problems: Solve, Check and Fix

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