Measurement Chapter Video Playlist

(1)

Measurement Chapter

Applied Math

(2)

Overview

 Section 1 – _{English System and Introduction to}

Measurement Conversion

 Section 2 – _{Metric System}  Section 3 – _Tolerance

 Section 4 – _{Convert between measurement systems}

(English metric)

 Section 5 – _{Using/reading different measuring}

instruments

(3)

Section 1 Introduction to the Measurement

Conversion Process

(4)

$10.00

11 grams

$10.95

1 ½ ounces

(5)

Reference Information

26 mm float height.

(6)

Reformat Computed

Measurements

144,695 sq ft

673 ft

215 ft

(7)

Measurement Conversion

 One technique for any situation:

– English System

– Metric System

(8)

Introduction

Measurement

Theory

x One = Equivalent

3 ft x 1 = 3 ft

4 ₄

3 ft

1 12 ft

₄

x

12 in

₌

1 ft

3 ft

(9)

Overview

1000 cubic inches is _____ gallons.

1000 cu in

1 x

231 1 gal

=

1 x 231

1000 x 1 gal

=

231 1000 gal

= 4.3 gal

cu in

(10)

Measurement

Conversion

(11)

60 in

20 in

Sheet Metal - Steel

Area of metal = Length x Width

Area of metal = 60 in x 20 in

Area of metal = 1,200 sq in

(12)

1,200 sq in

1

Example 1

Metal: 1,200 square inches

Change to square feet…

x

________

sq in

144 sq in

₌

_{1 sq ft}

=

1,200 x 1 sq ft

1 x 144

8.3 sq ft

1,200 sq ft

(13)

10.3 lb

1

Gas Can after pit stop: 10.3 lbs (tare wt.) How many gallons are still in the gas can?

x ________

lb

6.1 lb

=

1 gal

= 10.3 gal

1.7 gal

_6.1

(14)

£112

1

Product from a website in Great Britain: £112 What is this price in United States dollars (USD)?

x ________

£

0.5664

£

=

$ 1 USD

= $112

_0.5664

$197.74

(15)

Homework

 The Basics…

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Measurement

(19)

Multi-step Problems 1 of 2

 3.5 days = _____ minutes

3.5 days

1 x

_____

day(s)

1 day = 24 hr

1 hr = 60 min

x

_____

hr = 5040 min5040 min₁

Plan: Days

(20)

 2.8 lb= _____ g (grams)

2.8 lb

1 x

_____

lb

1 lb = 16 oz

1 oz = 28.3 g

x

_____

oz = 1267.84 g1267.8 g₁

Multi-step Problems 2 of 2

Plan: lb

(21)

Homework

 Multi-step Problems

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Measurement

Section 1 – Convert mixed units of measure.

(25)

Why convert mixed units?

 Arithmetic is easier…

20 ft 9 in

4 ft 2 in

18 ft 7 in 8 ft 10 in

Overall length = ? 249 in

50 in

223 in 20.75 ft 106 in 4.2 ft

(26)

Mixed Units 1 of 1

 4 lbs 5 oz = _____________ lbs

5 oz

1 x _______oz

16 oz = 1 lb

= 5 lb 16

0.3125 lb

(27)

Homework

 Mixed Units

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Measurement

(32)

 Rates – two measurements needed to

describe something…

Product Pricing:

$ per gallon $ per foot

Pay: dollars per hour

Productivity: frames per hour

Properties of metal:

pounds per cubic inch pounds per foot

Steel: 0.283 lbs per cubic inch

(33)

Rates

1a of 3

 $32.67 per foot= _____ $/inch

price

length1 foot$32.67 x

foot

1 foot = 12 in

= $32.67 12 in

$2.72/inch

Flat Stock, Steel, 4140, ¾” x 2”

If a small project requires 30” of this flat stock, how much does it cost?

(34)

Rates

1b of 3

 $4.25 per gallon= _____ $/L

price quantity

$4.25

1 gallon x

gallon

1 gallon = 3.79 L

= $4.25

(35)

Rates

1c of 3

 $15.51 for 3 ft= _____ $/inch

price length $15.51

3 foot x

foot

1 foot = 12 in

= $15.51 36 in

$0.43/inch

Rod, Steel, 4140, 5/8” Dia x 3 Ft Long

If a small project requires 105” of this steel rod stock, how much does it cost?

(36)

Invoice from hospital: Doctor’s fee for surgery was $2,780. The surgery lasted for 1 ¾ hrs.

What is the pay per minute?

Rates

2 of 3

(37)

Invoice from hospital: Doctor’s fee for surgery was $2,780. The surgery lasted for 1 ¾ hrs.

What is the pay per minute?

Rates

2 of 3

$2,780 1.75 hrsx

1 hr = 60 min

hr

= $2,780

(38)

 12 gauge shotshell has an advertised muzzle velocity of

1250 ft/sec.

 Convert to: miles/hour

distance time 1250 ft

1 sec x

(39)

 12 gauge shotshell has an advertised muzzle velocity of

1250 ft/sec. Convert to: miles/hour

x

_____

ft

5280 ft = 1 mile

60 sec = 1 min

x

_____

sec ₌4500000 mi

5280 hr

852.3 mi/hr

1250 ft

1 sec x

_____

min

60 min = 1 hour

(40)

Homework

 Rates

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Measurement

(44)

Metric System

 Used worldwide

 One basic unit of measurement is used

for each physical quantity.

 Based on the number 10…no fractions!

Length

Metric System English System meter Inches, feet, yards

(45)

Base Units of Measure

 Length

meter (m)

 Mass

gram (g)

 Volume

(46)

Changing the Base Unit

liter 11,127,061 liters

(47)

If you need larger units of

measure than the base…

(48)

Create

larger units of measure

(49)

If you need larger units of

measure than the base…

You can create them by multiplying the base measurement by multiples of 10.

You identify each new, larger unit of

measure by adding a prefix to the base unit.

(50)

Prefixes

to indicate larger units of measure

liter liter

deka

liter

hecto

liter

(51)

Equivalencies

liter liter

deka

liter

hecto

liter

(52)

kilo base unit

deka

hecto deci centi milli

(53)

Changing the Base Unit

meter

Piston Diameter 0.0889 meters

(54)

meter meter deci meter centi meter milli

1 meter = 10 decimeters

1 meter = 100 centimeters

1 meter = 1000 millimeters

(55)

kilo base unit

deka

hecto deci centi milli

(56)

Metric System

(57)

Metric Conversions

Using Conversion Fractions 1 of 1

 Convert 1.5 meters to centimeters.

1.5 m

1 x _m

base centi

deka hecto

kilo deci milli

1 m = 100 cm

1

100 cm _{150 cm}

1

150 cm

(58)

Metric System

Conversion Shortcut Method

(59)

Metric Conversions

Using Prefix Chart to Convert 1 of 3

 Convert 3200 grams to kilograms.

kilo hecto deka base

unit deci centi milli

(60)

Metric Conversions

 Convert 0.65 liters to milliliters.

kilo hecto deka base

unit deci centi milli

(61)

Metric Conversions

 Convert 850 centimeters to kilometers.

kilo- hecto- deka- base

unit deci- centi milli

(62)

Assignment List

 Section 2 – Convert Metric Units

of Measure

(63)

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Measurement

(65)

Tolerance

_23.75”

(66)

Tolerance

23.75”  0.125”

Maximum: 23.75 + 0.125

=23.875”

Minimum: 23.75 - 0.125

=23.625”

X

_X

23.885” _23.621”

23.760” 23.680” 23.870”

+

(67)

-Tolerance Interval

1.55” 1.56”

1.54”

Standard Maximum Minimum

1.55”  0.01”

(68)

 Determine the:

Upper Limit Lower Limit

Tolerance Interval

0.785”  0.0005”

0.785 + 0.0005 = 0.7855” 0.785 - 0.0005 = 0.7845”

2(0.0005) = 0.001”

0.7855” 0.7845”

(69)

 Determine the:

Tolerance Interval

130 lb x 3% =

130 + 3.9 = 133.9 lb 130 – 3.9 = 126.1 lb

2(3.9) = 7.8 lb

3.9 lb

130 lb x .03 =

(70)

 Determine the:

Tolerance Interval

2500   2%

2500 x 2% =

2500   50 

2500 + 50 = 2550 

2500 – 50 = 2450 

2(50) = 100 

50 

(71)

 Determine the: Upper Limit Lower Limit Tolerance Interval Oil-Dry 20 lbs

20 lbs  0.15 lbs 0.00 lbs

20 + 0.15 = 20.15 lbs 20 - 0.00 = 20 lbs

(72)

Assignment List

Section 3 – Tolerance

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Measurement

Section 4 - Converting between measurement systems

Engine Displacement:

(77)

English to Metric

Conversions

1 of 3

 20 ounces = _____ grams

English Length Weight Volume Area Pressure Metric Metric Prefixes Area Volume Temperature Conversions

English < - > Metric

Length Mass “Weight” Area Volume 20 oz 1 x

_____

oz

1 oz = 28.3 grams

1

(78)

English to Metric

Conversions

2 of 3

 3.4 kg = _____ oz

Length Mass “Weight” Area Volume 3.4 kg 1 x

_____

kg

1 lb = 0.454 kg

0.454 1 lb

= 119.8 oz

x

_____

lb 1

16 oz

1 lb = 16 oz

(79)

English to Metric

Conversions

3 of 3

 120 km/hr = _____ mi/hr

Length Mass “Weight” Area Volume dist. time 120 km

1 hr x km

1 mile = 1.61 km

1.61

(80)

Homework

PS-8, 9, 10

Section 4 – Convert between English and

Metric

_____ Practice Set 8 (p. 24) # 1 – 5, 6, 8, 10, 11

_____ Practice Set 9 (p. 25) # 1, 5

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Measurement Chapter

(89)

MEASUREMENT

(90)

(91)

Determine the Scale

Goal: What is the measurement indicated by the smallest division (tick mark) on the scale?

500 ml

400

300

200

(92)

16 spaces or divisions

1”

Determine the Scale

Rulers

inch per division

 16 =

1st: Pick a convenient whole number interval.

2nd: Count the number of divisions in the interval.

(93)

Each division = 1/16 inch

Reading English Rulers

1 of 3

5” 16

(94)

Determine the Scale

1” interval 10 divisions

1” ÷ 10 divisions = _{1/10 inch or}_{0.1” per division} 4

or

4.3”

or 0.7”

3” 10

(95)

Reading English Rulers

Using “landmarks” Landmark: 16/32” Landmark: 8/32” Landmark: 32/32” 2

1 17₃₂ in. 7₃₂ in. ₂ 29

(96)

Practice

 Worksheets:

(97)

Determine the Scale

Measuring Liquids

 Graduated Cylinders

(98)

Measuring Liquids

Determine Scale 1

500 ml

400

300

200

100

1 division = ___ ml

100 ml

100 ml ÷ 5 divisions =

20

20 ml per division

440 ml

(99)

Practice

 Worksheet:

(100)

1 cm2 cm

Reading Metric Rulers

cm

(101)

Reading Metric Rulers

cm

In 1 cm, there are 10 divisions

(102)

Reading Metric Rulers

cm

(103)

Reading Metric Rulers

mm

1 mm 2 mm 3 mm 4 mm 5 mm 6 mm 7 mm 8 mm 9 mm 10 mm

(104)

Reading Metric Rulers

mm

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(105)

Practice

 Worksheets:

(106)

Homework

PS 11, 12

(107)

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Dial Caliper

english scale

(110)

Micrometers

Reading the Scale

(111)

Micrometer Barrel

1” ÷ 10 = 0.1”

(112)

Micrometer Barrel

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(115)

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Practice

 Worksheets

(117)

Quizzes

(118)

The End

 Written by Peter C. Esser

 Southwest Wisconsin Technical College  2006-2015