measurement measuring length, capacity, weight conversion of units involving length

MeasurementMeasuring Length, Capacity, Weight Conversion of Units Involving length

By Mr. Gerzon B. Mascariñas

Math Prayer

Dear Lord, May we add purity to the world. Subtract evil from our lives. Multiply good works for your son, Jesus. Divide our gifts and share them with others. Amen.

Objectives:• Trace the history and development of

measurement.

• Name instrument used in measuring length.

• Distinguish the appropriate units used in measuring.

• Convert one unit of measurement to another using dimensional analysis.

• Solve real-life problems involving measurement.

Concept MapMathematics

Quantitive (in nature)

Measurement

Dev’t Units Instruments

English Metric (SI) Nature Standard

• Have you ever imagined yourself living in a world where there is no common understanding of how long a certain is?

• Or how heavy a certain object is?

• Or maybe how brief a certain instance is?

• What do you think would life be without standard measurement?

History of Measurement• Early human beings – made use of

the parts of the human body for measuring.

1. Span It is the distance from the tip of the

little finger to the tip of the thumb of an outstretched hand.

2. PalmIt is the distance across the base of the four fingers that form the palm.

3. Digit It is the thickness or width of the index finger.4. Foot

It is the length of a foot.

5. Cubit It is the distance from the tip of the middle finger of the outstretched hand to the front of the elbow.6. Pace

It is the distance of one full step.

The body measures depend upon the person who is performing the measuring. Hence, different persons have different lengths of arms and hands.

The English System of Measurement• Different systems for the same

purpose developed and became established in different parts of the world.

• Through royal decrees, England was able to standardized its system of units of measurement.

• King Henry I – decreed that a yard was a distance from his nose to the end of his thumb on his outstretched hand.

• Queen Elizabeth I – changed the measure of the mile from 5,000 feet to 5, 280 feet

Familiar Units in the English System• Length

12 inches = 1 foot

3 feet = 1 yard

5 feet = 1 pace

5, 280 feet = 1 mile

220 yards = 1 furlong

8 furlongs = 1 mile

125 paces = 1 furlong

Weight16 ounces = 1 pound

2, 000 pounds = 1 ton

Capacity3 teaspoons = 1 tablespoon

16 tablespoon = 1 cup

8 ounces = 1 cup

2 cups = 1 pint

2 pints = 1 quart

Customary Length

• A mile is about half the length of Talladega Super Speedway.

• Talladega is 2.9 miles long.

Talladega Super Speedway

This represents

about 1 mile.

Customary Length

• A yard is about the length of a walking stick.

Customary Length

• A foot is about the length of a floor tile.

Customary Length

• An inch is about the length of a drink bottle top.

Customary Capacity 1 gallon

Meet Mr. Gallon

4 quarts

Meet Mr. Gallon

8 pints

Meet Mr. Gallon

16 cups

Customary Weight

• A small car weighs about a ton.

Customary Weight

• A bag of coffee weighs about 1 pound.

Customary Weight

• An ounce weighs the same as 8 nickels.

The Metric System of Measurement

• During the French revolution, a group of French scientists thought of creating a more simplified system of measurement that would provide convenience converting from smaller or larger version of the unit.

• The International Metric System was developed and introduced in Europe in the times of Napoleon

• Metric system is a “base-10” or “decimal system”.

The Metric System of Measurement• Metric system uses prefixes to

indicate units larger or smaller than a given base unit. Each prefix is a multiple of 10.

• Prefix is a word or letter written in front of a basic metric unit to specify the fraction or multiple of the unit

The following table shows some examples of these units

1000 100 10 1 0.1 0.01 0.001

Prefixes Kilo(k) Hecto(h) Deca(da) Basic Unit Deci(d) Centi(c) Milli(m)

Length km hm dam Metre (m) dm cm mm

Mass kg hg dag Gram (g) dg cg mg

Capacity kl hl dal Litre (l) dl cl ml

29

Prefixes Symbol Name Equivalence

Kilo k thousand 1, 000

Hecto h hundred 100

Deca da ten 10

Deci d One-tenth 0.1

Centi c One-hundredth 0.01

Milli m One-thousandtth 0.001

SI PrefixesPrefixes Symbol Name Power

of TenPrefixes Symbol Name Power

of Ten

yotta Y Septillion 1024 deci d tenth 10-1

zetta Z Sextillion 1021 centi c hundredth 10-2

exa E Quintillion 1018 milli m Thousandth 10-3

peta P Quadrillion

1015 micro μ Millionth 10-6

tera T Trillion 1012 nano n Billionth 10-9

giga G Billion 109 pico p Trilllionth 10-12

mega M Million 106 femto f Quadrillionth

10-15

kilo K Thousand 103 atto a Quintillionth 10-18

hecto H Hundred 102 zepto z Sextillionth 10-21

deca da Ten 101 yocto y Septillionth 10-24

One 100 One 100

Metric Units – Length, Distance

m

The base unit for measuring distance is the metre (m)We use metres to measure:• The height of a door• The length of a corridor• The length and width of a room


km m

We use kilometres (km) for longer distances, such as:• The distance between cities (for example, between

Madrid and Barcelona, or Manchester and Leeds)• The distance to the next services on the motorway• The distance from the Earth to the moon (400 000 km)


km m mm

We use millimetres (mm) for very small things:

• The thickness of a coin• The diameter of a screw

Metric Units – Weight/Mass

g

The base unit for measuring weight is the gram (g)

• A sugar cube weighs a few grams• We use grams to weigh sliced ham (200 g)


kg g

A more familiar unit for weight is the kilogram (kg):

• A bag of sugar weighs 1 kg• A normal wash-load is 1.5 kg• My weight is about 81 kg


kg g mg

We use milligrams (mg) for very small things:

• The amount of paracetamol in a tablet

Metric Units – Capacity/Volume

l

The base unit for measuring distance is the litre (l)

• A large bottle of Coke contains 2 l:• The petrol tank of an average car holds 40 l


kl l

• Kilolitres (kl) are rarely used in everyday life• The capacity of a swimming pool could be

measured in kl but is more commonly measured in thousands of litres instead


kl l ml

• A teaspoon is about 5 ml• A can of coke is bout 330 ml


kl l cl ml

• A bottle of wine is 75 cl• A drinking cup (paper) is about 20 cl

The International System of Measurement

• The International Bureau of Weights and Measures in France works in the development and improvement of the metric system.

• In 1960, the General Conference on Weights and Measures adopted the modernized metric system and called it

Le Systeme International d’Unites(International System of Units) or SI

Book Exercises

• Answer Vocabulary and Concepts, Practice and Application I, II AND III on pages 23 – 24.

Answer Key:Vocabulary and Concepts:1. i

2. h

3. g

4. j

5. f

6. d

7. a

8. b

9. c

10. e

Practice and ApplicationI. Complete each of the following.

1. 1 kiloliter = ___ liter

2. 1 dekaliter = ___ liter

3. 1 hectometer =___ meter

4. 1 centiliter = ___ liter

5. 1 milliliter = ___ liter

6. 1 decimeter = ___ meter

Answer Key:II.

7.10

8.0.1

9.100

10. 1000

11. 10

12. 10

Answer Key:III.

13. 0.33

14. 3,300

15. 0.0033

16. 0.033

17. 330

18. 33

Class ActivityFind the measure of each item in the leftmost

column using the indicated units of measurement and measuring instrument and record the results.

Units of Measurement/Measuring Instrument

Item Span Ruler (cm) Meterstick (m)

1. Width of the teacher’s table

2. Height of the student’s chair

3. Width of the door

4. Height of blackboard

5. Length of the classroom

Converting Measurements• Dimensional analysis – a method

of calculating that uses numbers in the form of fractions, which enables us to convert from one type of unit to another.

• It consists of three components:The given unit,The desired unit,The conversion factor

Example:Suppose the black board is 4 meters

long. You want to find its length in centimetres.

The given unit - meterThe desired unit - centimeterThe conversion factor - 100 cm = 1 m 1 m

100 cm

4 m x =

Note that we can cancel units when multiplying fractions since they behave like numbers.

4 m x = 400cm

Rules in Changing Units1. To change from a larger unit to

a smaller unit, multiply.

2. To change from a smaller unit to a larger unit, divide.

Examples:1. Convert 5.237 dam to cm. The given unit, The desired unit,

The conversion factor

1 dam = 1,000 cm Solution: 5.237 dam x =

5.237 x 1,000 cm = 5, 237 cm

Examples:2. Convert 750 mm to m. The given unit, The desired unit,

The conversion factor

1 m = 1,000 mm Solution: 750 mm x = 750 m 1,000 = 0.75 m

We are going to use our We are going to use our knowledge about multiplying knowledge about multiplying

and dividing by 100 to and dividing by 100 to convert centimetres to metres convert centimetres to metres

and to convert metres to and to convert metres to centimetres.centimetres.

There are 100 centimetres in 1 metre

When we change from cm to m we divide by:-

Remember!When we divide by 100 the units move two places to the right.

H T U th hth th

4 2 7 0 0 0 ÷100

This is how we change 427cm into metres:-




H T U th hth th

4 2 7 0 0 ÷100





H T U th hth th

4 2 7 0 ÷100


Therefore:-Therefore:-

427cm = 4.27m427cm = 4.27mH T U t h th

3 2 6

H T U t h th

3 2 6

H T U t h th

4 7 6

H T U t h th

1 6 5 3

H T U t h th

0 4 7 6

H T U t h th

1 6 5 3

÷100÷100

÷100÷100

÷100÷100

cmcm mm

354cm354cm

15.4cm15.4cm

779cm779cm

52.4cm52.4cm

939cm939cm

395cm395cm

25.8cm25.8cm

3.54m3.54m

0.154m0.154m

7.79m7.79m

0.524m0.524m

9.39m9.39m

3.95m3.95m

0.258m0.258m

÷10÷1000

Convert from centimetres to metresConvert from centimetres to metres

To change from metres to To change from metres to centimetres we MULTIPLY BY 100.centimetres we MULTIPLY BY 100.

REMEMBERREMEMBER

When we multiply by 100 we When we multiply by 100 we move each digit two places to the move each digit two places to the left:-left:-

H T U t h th

3 5 1

3.51m = 3.51m =

To change from metres to To change from metres to centimetres we MULTIPLY BY centimetres we MULTIPLY BY 100.100.

REMEMBERREMEMBER

When we multiply by 100 we When we multiply by 100 we move each digit two places to move each digit two places to the left:-the left:-

H T U t h th

3 5 1

3.51m = 3.51m =

To change from metres to centimetres To change from metres to centimetres we MULTIPLY BY 100.we MULTIPLY BY 100.

REMEMBERREMEMBER

When we multiply by 100 we move When we multiply by 100 we move each digit two places to the left:-each digit two places to the left:-

H T U t h th

3 5 1

3.51m = 3.51m =


REMEMBERREMEMBER


H T U t h th

3 5 1

3.51m = 3.51m =

To change from metres to To change from metres to centimetres we MULTIPLY BY 100.centimetres we MULTIPLY BY 100.

REMEMBERREMEMBER

When we multiply by 100 we When we multiply by 100 we move each digit two places to the move each digit two places to the left:-left:-

H T U t h th

3 5 1

3.51m = 3.51m =


REMEMBERREMEMBER


H T U t h th

3 5 1

3.51m = 3.51m =


REMEMBERREMEMBER


H T U t h th

3 5 1

3.51m = 3.51m = 351cm351cm

5.4m5.4m

6.2m6.2m

12.7m12.7m

3m3m

7.6m7.6m

0.54m0.54m

0.3m0.3m

540cm540cm

620cm620cm

1270cm1270cm

300cm300cm

760cm760cm

54cm54cm

30cm30cm

x100x100

Try changing these measurements in metres into centimetresTry changing these measurements in metres into centimetres

Approximate English and Metric Equivalents

1 inch (in.) = 2.54 centimeters (cm)

1 foot (ft.) = 30.48 centimeters(cm)

1 yard (yd.) = 0.9 meter (m)1 mile (mi.) = 1.6 kilometers (km)

Convert the following: a.15 inches to centimetersb.138 miles to kilometersc.35,400 millimeters to inches

English System

12 inches (in.) = 1 foot (ft.)3 feet (ft.) = 1 yard (yd)36 inches (in.) = 1 yard (yd)5, 280 feet (ft.) = 1 mile (mi.)1,760 yards (yd.) = 1 mile (mi.)

Convert the following: a.45 inches to feetb.15,400 feet to milesc.16 inches to yards

Problem Solving

1. My grandparents walk 1.5 kilometers every morning. What is the total distance that they walk in meters?

2. The speed limit in many subdivisions is 30 kph. How many miles per hour is this?

1 mile = 1.6 km

Quiz # 1 July 2, 2012I. Identification1. What did the early civilizations use in

measuring?

2. It is the distance across the hand from the tip of the thumb to the tip of the little finger of an outstretched hand.

3. What is the metric system’s basic unit of length?

4. Who was the king of England decreed that a yard was the distance from the tip of his nose to the end of his thumb on his outstretched hand.

5. It is a word or letter written in front of a basic metric unit to specify the fraction or multiple of the unit.

6. How many meters in 1 micrometer.

7. What is the value of hecto?

8. Which metric unit of measure is most appropriate to use in measuring the length of a chalk? (e.g. 12 ___long)

9. What is the basic unit of weight?

10. What is the basic unit of capacity/volume?

II. Computation• Convert the given measurement to the

unit indicated.

1.48 dm to km

2.12 dam to m

3.18 m to ft.

4.160 in. to hm

5.3.54 yrd to mi.

III. Problem Solving

1.Express 86 kilometers per hour in miles per hour.

2. A notebook is 0.37 decimeters thick. How thick is the notebooks in millimeters?

Quiz # 1 Answer KeyI. Identification1. What did the early civilizations use in

measuring?

Ans: Natural measures or body parts

2. It is the distance across the hand from the tip of the thumb to the tip of the little finger of an outstretched hand.

Ans: span or dangkal

3. What is he metric system’s basic unit of length?

Ans: meter

4. Who was the king of England decreed that a yard was the distance from the tip of his nose to the end of his thumb on his outstretched hand.

Ans: King Henry I

5. It is a word or letter written in front of a basic metric unit to specify the fraction or multiple of the unit.

Ans: Prefix

6. How many meters in 1 micrometer.

Ans: one-millionth meter or

0.000001 meter

7. What is the value of hecto?

Ans: 100

8. Which metric unit of measure is most appropriate to use in measuring the length of a chalk? (e.g. 12 ___long)

Ans: cm or centimeter

9. What is the basic unit of weight?

Ans: gram

10. What is the basic unit of capacity/volume?

Ans: liter

II. Computation• Convert the given measurement to the

unit indicated.

1.48 dm = 0.0048 km

2.12 dam = 1.2 m

3.18 m = 59.06 ft.

4.160 in. = 0.04064 hm

5.3.54 yrd = 0.002 mi.

III. Problem Solving

1.Express 86 kilometers per hour in miles per hour.

Ans: 53.75 mi/hr

2. A notebook is 0.37 decimeters thick. How thick is the notebooks in millimeters?

Ans: 37 mm

Assignment

• Answer Practice and Application I, II and III on page 33

measurement measuring length, capacity, weight conversion of units involving length

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