Measurement Part One

Measurement Part One

Systems of Measurement

Every day we read or hear numbers that relate to the world around us. These numbers are often descriptions of things. For example, a common object like a car can be described using numbers in many ways:

How far has the car traveled? 124,349 kilometres

How old is the car? 6 years

How much is the car worth? $7,225

How much does the car weigh? 4,700 pounds

How hot or cold is the car right now? 21ºC

Whenever we describe things using numbers, we are using measurement. Often measurement can be done in more than one way. For example, the age of the car can be measured using years or months.

DESCRIPTION / QUALITY BEING MEASURED / MEASURED AMOUNT / ALTERNATIVE AMOUNT
How far has the car traveled? / Distance / 124,349 kilometres / 77,718 miles
How old is the car? / Time / 6 years / 72 months
How much is the car worth? / Value / $7,225 / 722,500¢
How much does the car weigh? / Weight (or mass) / 4,700 pounds / 2136 kilograms
How hot or cold is the car? / Temperature / 21º Celsius / 70º Fahrenheit

Usually, one way of measuring is the most common for a certain situation. The age of person is given in years, unless the person is very young, and then months or days would be used. The weight of a person in this country is usually given in pounds, but in many other countries people use kilograms. We often need to understand the situation in order to know what type of measurement to use.

We sometimes talk about using the Metric System of Measurement and the Imperial System of Measurement. Canada used the Imperial System until the early 1970’s, but now we use mainly the Metric System. Common exceptions to using metric are the weight of a person (usually measured in pounds) and height of a person (usually measured in feet and inches).

Types and Units of Measurement

The chart below shows the units that are typically used for various types of measurement in Canada and some common instruments used for measuring. This list is not complete.

Type Units System Measuring instrument

Distance kilometers metric car odometer

metres metric carpenter’s measuring tape

centimeters metric ruler

feet and inches Imperial ruler or tape

Time years, months, days both calendar

hours, minutes, seconds both clock, stopwatch

Speed kilometres per hour metric car speedometer

metres per second metric

Volume litres and millilitres metric measuring cup

cups Imperial measuring cup

Mass or weight kilograms metric grocery store scale

pounds Imperial bathroom scale

Value dollars and cents both usually counted manually

Temperature degrees Celsius metric thermometer

Distance

This ruler has both metric and Imperial scales. The top scale uses the centimetre as the unit of measurement, and the bottom scale uses the inch.

The left arrow above shows a distance of one centimetre from the 0 mark and the other arrow shows a distance of 6 centimetres from 0. One centimetre is about the width of a person’s baby finger.

Each centimetre (cm) is divided into 10 parts called millimetres (mm). There are 10 millimetres in 1 centimetre. One millimetre is about the width of a pencil lead.

The length of the entire pencil shown is 8 centimetres. Since each centimetre contains 10 millimetres, the length of the pencil can also be written as 80 millimetres.

The length of the nail below is 14.7 cm or 147 mm.

Notice that if we multiply the number of centimetres by 10 we get the number of millimetres. If we divide the number of mm by 10 we get the number of cm.

Measurement Practice

Measure the length of each of the following objects using a ruler and fill in the blanks with the correct numbers.

_____ cm _____ mm

Distance Units in the Metric System

Find a metre stick in your classroom and examine it. The stick is one metre long.

How many centimetres are on the stick? (1 cm is about the width of a small finger) ______

How many millimetres are on the stick? (1 mm is about the width of a pencil lead) ______

How many decimetres are on the stick? (1 decimetre has 10 centimetres and is

about the width of a person’s hand including the thumb) ______

You should be able to see that the metre stick has the following lengths:

1 metre = 10 decimetres = 100 centimetres = 1000 millimetres

The units can be written as follows:

1 m = 10 dm = 100 cm = 1000 mm

The names of the units in metric are made up of the word “metre” and a prefix. Each prefix means a particular value compared to the metre, which is the base unit.

Prefix Meaning

Milli + metre = millimetre (mm) or 0.001 of a metre

Centi + metre = centimetre (cm) or 0.01 of a metre

Deci + metre = decimetre (dm) or 0.1 of a metre

metre (m) 1 metre

Deca + metre = decametre (dam) 10 metres

Hecto + metre = hectometre (hm) 100 metres

Kilo + metre = kilometre (km) 1000 metres

Converting Distance Measurements Within the Metric System

To help you change a value from one metric unit of measurement to another, the following Metric Staircase is useful.

Kilometre, at the top, is the largest unit on the staircase. Millimetre, at the bottom, is the smallest. Because kilometres are so large compared to millimetres, it takes one million millimetres to equal a single kilometre.

1 km = 1,000,000 mm

Each step down is a multiplication by 10. As you know, multiplying by 10 is simply moving the decimal one space to the right.

1 km = 10 hm = 100 dam = 1000 m = 10,000 dm = 100,000 cm = 1,000,000 mm

Examples:

3 km = 30 hm = 300 dam = 3000 m = 30,000 dm = 300,000 cm = 3,000,000 mm

12 km = 120 hm = 1200 dam = 12,000 m = 120,000 dm = 1,200,000 cm = 12,000,000 mm

0.002 km = 0.02 hm = 0.2 dam = 2 m = 20 dm = 200 cm = 2000 mm

Example: Change 5 hectometres into metres. 5 hm = ??? m

Solution: Starting at hectometres, how many steps do you take to get to metres? Two steps to the right (down the stairs) means to multiply by 10 twice:

5 hm = 50 dam = 500 m

Example: Change 0.54 kilometres into decimetres. 0.54 km = ??? dm

Solution: Starting at kilometers, how many steps do you take to get to decimetres? Four steps down means to multiply by 10 four times:

0.54 km = 5.4 hm = 54 dam = 540 m = 5400 dm

Example: How many decimetres are in 3.052 decametres?

Solution: 3.052 dam = ??? dm

Starting at decametres, move two steps to the right. Because you moved two steps to the right, simply move the decimal point two places to the right.

3.052 dam = 305.2 dm

To change a smaller unit into a larger unit, start at the smaller unit and keep dividing by 10 until you reach the larger unit. As you know, the shortcut for dividing by 10 is to move the decimal point one place to the left.

For example, to change 10 millimetres into metres, begin at mm and move left (up) three steps.

10 mm = 1 cm = 0.1 dm = 0.01 m

Examples: 43 cm = ??? hm

Solution: 43 cm = 4.3 dm = 0.43 m = 0.043 dam = 0.0043 hm

Because hectometres is four steps to the left of centimetres, the shortcut is to move the decimal four places to the left.

Practice Converting Metric Distances

Remember: To change from a larger unit to a smaller unit, multiply. To change from a smaller unit to a larger unit, divide.

Moving to the right on the staircase means you need to move the decimal to the right.

Moving to the left on the staircase means you need to move the decimal to the left.

Changing from a larger unit to a smaller unit. Changing from a smaller unit to larger unit.

1. 4.5 km = ______hm 13. 78 cm = ______dm

2. 63.2 dam = ______m 14. 8579 mm = ______hm

3. 74.02 hm = ______cm 15. 41 hm = ______km

4. 9 km = ______m 16. 0.5 dam = ______hm

5. 0.24 cm = ______mm 17. 0.003 m = ______dam

6. 0.5 dm = ______cm 18. 4889 cm = ______hm

7. 4.55 m = ______mm 19. 780 dm = ______km

8. 98 m = ______dm 20. 15.2 dam = ______km

9. 0904 dm = ______mm 21. 5.6 cm = ______m

10. 77 dam = ______dm 22. 0.88 mm = ______dm

11. 0.0002 cm = ______mm 23. 4899.02 mm = ______km

12. 0.005 hm = ______cm 24. 7 dam = ______km

Convert the following.

1. 3855 cm = ______hm 5. 0.05 dam = ______dm

2. 6 dm = ______mm 6. 97.05 m = ______mm

3. 354 mm = ______m 7. 47 km = ______dam

4. 0.25 km = ______hm 8. 3.2 hm = ______km

Complete the following

1. 7cm 4mm = ______mm

2. 5m 9cm = ______cm

3. 4m 8dm 2cm = ______cm

4. 3km 2m = ______km

5. 4km 17m 52cm = ______m