Mathematics 1 ESO. IES Don Bosco (Albacete). European Section 1

Unit 6: THE METRIC SYSTEM

6.1.- THE METRIC SYSTEM

The metric system, also known as the Systme International dUnits (SI), was

developed in the late 1700s to standardize units of measurement in Europe.

The metric system is used in nearly every country in the world except the

United States.

The world since 1970: Green = metric, black = English Imperial system

The simplicity of the metric system stems from the fact that there is only one

unit of measurement (or base unit) for each type of quantity measured (length, mass, etc.).

The three most common base units in the metric system are the metre, the

gram, and the litre. With these simple measurements we can measure nearly

everything in the world.

Examples:

The length of this guitar

is about 1 metre.

This dictionary has a mass

of about 1 kilogram.

This jug has exactly

1 litre of water in it.

But what if we want to talk about really big or really small objects?

The measurement of very large and very small objects is expressed as multiples

of ten of the base unit.

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For example, rather than saying that the Nile River is 6,650,000 metres long, we

can say that it is 6,650 thousand-metres long. This would be done by adding the

prefix kilo (meaning 1,000) to the base unit metre. So the length of the Nile

River is 6,650 kilometres.

Metric numbers

In the Metric System we use metric number prefixes like kilo (a thousand), milli (one thousandth) and so on.

The table below shows the prefixes used for talking about big and small

numbers.

Name The number Prefix Symbol

trillion 1,000,000,000,000 tera T

billion 1,000,000,000 giga G

million 1,000,000 mega M

thousand 1,000 kilo k

hundred 100 hecto h

ten 10 deca da

unit 1

tenth 0.1 deci d

hundredth 0.01 centi c

thousandth 0.001 milli m

millionth 0.000 001 micro billionth 0.000 000 001 nano n

trillionth 0.000 000 000 001 pico p

Example 1:

You put your bag on a set of scales and it shows 2,000 grams, we can call that 2

kilograms, or simply 2 kg.

Example 2:

The doctor wants you to take 5 thousandths of a litre of medicine (a thousandth

is one thousand times smaller), he is more likely to say take 5 millilitres?, or write it down as 5 ml.

Exercise 1:

Copy and complete.

a) 1 hm = ____ m c) 1 l = ____ dl e) 1 g = ____ mg g) 1 dl = ____ cl

b) 1 dal = ____ l d) 1 m = ____ cm f) 1 hl = ____ dal h) 1 dm = ____ mm

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Converting units

The metric system is called a decimal-based system because it is based on multiples of ten. Any measurement given in one metric unit can be converted to

another metric unit in a simple way.

This is the metric conversion stair chart:

Example: 1.2 cm = 0.012 m

Example: 5.3 kg = 5300 g

Exercise 2:

Copy and complete.

a) 2462 m = _____ km e) 1.6 kl = _____ dal i) 0.58 m = _____ dm

b) 4.2 dal = _____ hl f) 0.52 hm = _____ m j) 234 ml = ____ l

c) 256 cg = _____ g g) 5.4 l = _____ cl k) 46 cg = _____ dg

d) 400 mm = _____ dm h) 75 cg = _____ g l) 0.08 m = _____ cm

For every step upward on the chart you are dividing by 10 or moving the

decimal one place to the left.

When you move down the stairs you are multiplying by 10 for each step or

moving the decimal one place to the right.

We move two steps up on the chart, so we divide by 100,

that is, we move the decimal point two places to the left.

We move three steps down on the chart, so we multiply

by 1000, that is, we move the decimal point three places

to the right.

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Exercise 3:

Convert into metres.

a) 1 km 6 hm 7 dam c) 2 dm 7 cm 8 mm

b) 6 hm 5 m 6 dm d) 3 hm 5 dm 9 mm

6.2.- LENGTH MEASUREMENT

Length is a measure of distance. You can measure how long things are, or how tall, or how far apart they are. Those are all examples of length measurements.

Examples:

This fork is 20 cm long. The thickness of a plastic

id card is about 1 mm.

A fingernail is about

1 cm wide.

The base unit for length is the metre. One metre is one ten-millionth of the

distance from the Earths equator to the North Pole.

The most common length measurements are millimetres, centimetres, metres

and kilometres.

Exercise 4:

Give the most sensible unit for measuring the following lengths.

a) The width of a table.

b) The thickness of 10 sheet of paper on top of each other.

c) The length of football field.

d) The distance from one city to another.

e) The height of an adult person.

Exercise 5:

There are 35 English books in the pile on teachers desk. If each book is 8 mm

thick, what is the height of the pile in centimetres?

One metre equals roughly

one long step of an adult man.

One kilometre equals

ten minutes walk.

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Exercise 6:

Ethan lives at one end of Park Avenue. Brian lives at

the other end of the avenue. It is 5.8 kilometres

from one end of Park Avenues to the other. If

Ethan walks 2.79 kilometres toward Brians house,

how many metres does he have to walk to get

there?

Exercise 7:

The police went on a wild chase to catch the man speeding through town in a

black car. At times their speeds exceeded one hundred forty-three km per hour.

At that rate, how many kilometres would the car go in 35 minutes?

Exercise 8:

Dylan is the best athlete in his school. He can pole vault up

to five metres and seventy-three centimetres. If he would

like to be able to pole vault up to six and twelve

hundredths metres, how many more centimetres does he

need to pole vault to reach his goal?

Exercise 9:

The diagram is a plan of the floor of a school

hall. For an assembly the hall is filled with

chairs.

The chairs are arranged in two blocks. You need a gap of 0.6 m between rows of

seats. You need to leave a border of 1 m around each block. How many chairs can

you fit in the school hall?

6.3.- VOLUME AND CAPACITY MEASUREMENT

Capacity is a measure of the amount of liquid a 3-D shape contains.

Volume is the amount of space a 3-D shape or substance occupies or contains.

The volume of a container is generally understood to be the capacity of the

container rather than the amount of space it occupies.

Each chair needs this amount of space.

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The base unit for volume is the litre. One litre is the capacity of a cubic decimetre.

The two most common volume measurements are

millilitres and litres.

Other volume measurements:

Cubic metre (m3): a cube that is 1 metre on each side. Cubic centimetre (cm3): a cube that is 1 cm on each side.

3 31 m 1000 dm 1000 l= = 3 31 dm 1000 cm= 3 3

31 l 1 dm 1000 cm 1 cm 1 ml1 l 1000 ml

= = =

=

Exercise 10:

Give the most sensible unit for measuring the capacity of each of the following.

a) A swimming pool.

b) A fridge.

c) A bottle of perfume.

d) A cars petrol tank.

e) A garden watering can.

Exercise 11:

In Tusco a 3 litre bottle of Coke costs 1.59. A 340 ml can costs 39 p. Which is

the best value and why?

1 litre = 1 dm3

20 drops of water

makes about 1 millilitre A teaspoon of liquid

is about 5 millilitres.

31 m 1000 l=

31 dm 1 l=

31 cm 1 ml=

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Exercise 12:

To make a fruit punch for a party, Tammy mixes three 1

litre boxes of orange juice with two 1 litre boxes of

pineapple juice and ten 500 ml bottles of lemonade. What is

the total volume of the fruit punch?

Exercise 13:

Convert into litres: 2 m3 75 dm3 590 cm3.

Exercise 14:

A large coffee urn contains 15 litres of tea and is used to fill cups with 125 ml

of tea in each.

a) How many cups can be filled from a full urn of tea?

b) If 40 cups have been filled from a full urn, what volume of tea is left in

the urn?

6.4.- MASS MEASUREMENT

Mass is a measure of the amount of matter in an object. Mass is linked to weight. The base unit for mass is the gram. One gram is the weight of 1 cm3 of pure water.

The most common mass measurements are grams, kilograms and tonnes.

A paperclip weighs

about 1 gram.

The weight of 7 apples

is about 1 kilogram. This car weighs about 2 tonnes.

Exercise 15:

Give the most sensible unit for measuring the weight of each of the following.

a) A sugar lump.

b) A sack of potatoes.

c) A ballpoint pen.

d) A lorry.

e) A light bulb.

1 kg = 1000 g 1 tonne = 1000 kg

g

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Exercise 16:

The total weight of a van and its load is 5 tonnes. If the van carries 10 crates,

each having a weight of 270 kg, find the weight of the van when empty.

Exercise 17:

A man who weighs 80 kg loads 12 crates, each of weight 55 kg, on a trolley of

weight 260 kg. He them pushes the full trolley into a lift cage where there is

notice as follows:

Is it safe to start the lift?

Exercise 18:

Twelve coloured pencils, each of weight 8 g, are contained in a

cardboard packet of weight 29 g.

a) What is the weight of the full packet?

b) How many of the same packets would together weigh 1 kg?

6.5.- AREA MEASUREMENT

The area of a shape is the amount of space it covers.

The base unit for area is the square metre.

A square metre is the area of a square that is 1 m on each

side.

Multiples and divisors of the square meter are shown in the following table:

km2 hm2 dam2 m2 dm2 cm2 mm2

1 000 000 m2 10 000 m2 100 m2 0.01 m2 0.0001 m2 0.000001 m2

Examples:

A square hectometre (hm2) is the area of a square that is 1 hm on each side.

A square decimetre (dm2) is the area of a square that is 1 dm on each side.

A square centimetre (cm2) is the area of a square that is 1 cm on each side.

Load not to exceed 1 tonne

The area covered by a large umbrella

is roughly one square metre

Mathematics 1 ESO. IES Don Bosco (Albacete). European Section 9

Look at this picture in order to understand the equivalences between these

units.

The square metre is divided into 10 rows of 10 square

decimetres. 2 2 21m 10 10 dm 100 dm= =

The same thing happens to the other units. For example:

2 2 21dm 10 10 cm 100 cm= =

2 2 21cm 10 10 mm 100 mm= =

2 2 21dam 10 10 m 100 m= =

Converting units

To convert units you can use this stair chart:

Example: 1275 dm2 = 12.75 m2

Example: 5 hm2 = 50000 m2

For every step upward on the chart you are dividing by 100 or moving the

decimal two places to the left.

When you move down the stairs you are multiplying by 100 for each step or

moving the decimal two places to the right.

We move one step up on the chart,

so we divide by 100,

We move two steps down on the chart,

so we multiply by 10000

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Land units

Hectares and square kilometres are commonly used to measure land.

A hectare (ha) is an area equal to a square that is 100 metres on each side.

Hectares and square hectometres are the same.

Exercise 19:

Give the most sensible unit for measuring the area of each of the following.

a) Portugal.

b) A house.

c) A sheet of paper.

d) A television screen.

e) A football pitch.

Exercise 20:

Copy and complete.

a) 5.1 km2 = _____ hm2 f) 53000 m2 = _____ dam2

b) 825 hm2 = _____ km2 g) 420 cm2 = _____ mm2

c) 0.03 hm2 = _____ m2 h) 52800 mm2 = _____ dm2

d) 12500 m2 = _____ ha i) 5 m2 4 dm2 7 cm2 = _________ m2

e) 3500 ha = _____ km2 j) 5 km2 48 hm2 25 dam2 = ___________ m2

2 21 ha 1hm 10000 m= =

21km 100 ha=

The surface of Spain is about 2500000 km 50000000 ha= .

METRIC AND IMPERIAL MEASURES

You can measure length, mass and capacity using metric and imperial units.

You can convert between metric units by multiplying or dividing by 10, 100, 1000,

Length is a measure of distance.

Metric units millimetre (mm) centimetre (cm) metre (m) kilometre (km)

=10 mm 1 cm =100 cm 1 m =1000 m 1 km

Imperial units inch () foot () yard ( )=3 ft 1yd mile

Equivalents 5 miles 8 km

1 inch 2.5 cm 1 yard 1 m 1 foot 30 cm

Mass is a measure of the amount of matter in an object. Mass is linked to weight.

Metric units gram (g) kilogram (kg) tonne (t)

=1000 g 1 kg =1000 kg 1 tonne

Imperial units ounce (oz) pound (lb) stone ton

Equivalents 1 ounce 30 g

1 lb 454 g 1 kg 2.2 lb

Capacity is a measure of the amount of liquid a 3-D shape wild hold.

Metric units millilitre (ml) centilitre (cl) litre

=1000 ml 1 litre =100 cl 1 litre

Imperial units pint gallon

Equivalents 1 pint 600 ml

1.75 pint s 1 litre 1 gallon 4.5 litres

Example:

Calculate the approximate length of a 12 inch ruler in

a) centimetres b) millimetres

a) 1 2.5 cm b) 1 cm = 10 mm 12 =2.5 12 30 cm 30 cm =30 10 300 mm

means approximately equal to

1 metre is a bit longer than 1 yard

10

cm mm

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METRIC AND IMPERIAL MEASURES. WORKSHEET

1. Choose one of these metric units to measure each of these items.

a) your height c) your weight e) weight of a suitcase g) quantity of drink in a can i) weight of an elephant

b) amount of tea in a mug d) length of a suitcase f) distance from Paris to Madrid h) amount of petrol in a car j) weight of an apple

Write the appropriate abbreviation next to your answer.

2. Convert these measurements to the units shown.

a) 20 mm = _______ cm c) 450 cm = _______ m e) 0.5 cm = _______ mm g) 6000 g = _______ kg i) 2500 kg = _______ t

b) 400 cm = _______ m d) 4000 m = _______ km f) 4.5 kg = _______ g h) 6500 g = _______ kg j) 3 litres = _______ ml

3. Convert these distances to miles.

4. Convert these measurements to centimetres.

a) 1 inch b) 5 inches c) 6 inches d) 12 inches e) 36 inches 5. Use 1 kg 2.2 lb to convert these weights to pounds.

a) 2 kg b) 40 kg c) 50 kg d) 0.5 kg e) 2.5 kg 6. Use 1 oz 30 g to convert ounces to grams in these recipes.

7. The speed limit on a motorway in the UK is 70 miles per hour. Calculate the speed limit in kilometres per hour.

millimetre gram millilitre centimetre kilogram centilitre metre tonne litre kilometre