01 Measurement Chapter Lecture Tech Math 1A Version pptx

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Measurement Unit

Tech Math 1A

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Overview

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

Measurement Conversion

 Section 2 – _{Metric System}

 Section 3 – _{Convert between measurement systems}

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Section 1 Introduction to the Measurement

Conversion Process

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$10.00

11 grams

$10.95

1 ½ ounces

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Relate to Difficult

Concepts

• What does a million dollars look like?

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Reference Information

Shop Manual 26 mm float height.

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Reformat Computed

Measurements to Suit Needs

144,695 sq ft

673 ft

215 ft

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Measurement Conversion

 One technique for any situation:

– English System – Metric System

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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

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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

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Measurement

Conversion

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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

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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

144

Charge customer $2.85 per square foot.

8.3 sq ft x $2.85/sq ft

(14)

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

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£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

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Homework

 Measurement Chapter

– Worksheet 1 – Introduction to

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Measurement

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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

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 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

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Homework

 Worksheet 2 - Additional

Measurement Conversion Practice

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Measurement

Section 1 – Convert mixed units of measure.

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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

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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

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Homework

 Worksheet 2 – Additional

Measurement Conversion Practice

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Measurement

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 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

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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?

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Rates

1b of 3

 $4.25 per gallon= _____ $/L

price quantity

$4.25

1 gallon x

gallon

1 gallon = 3.79 L

= $4.25

(29)

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?

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 12 gauge shotshell has an advertised muzzle velocity of

1250 ft/sec.

 Convert to: miles/hour

distance time 1250 ft

1 sec x

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 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

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Homework

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Measurement

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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

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Base Units of Measure

 Length

meter (m)  Mass

gram (g)  Volume

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Changing the Base Unit

liter 11,127,061 liters

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If you need larger units of

measure than the base…

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Create

larger units of measure

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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

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Prefixes

to indicate larger units of measure

liter liter

deka

liter

hecto

liter

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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.

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Equivalencies

liter liter

deka

liter

hecto

liter

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kilo base unit

deka

hecto deci centi milli

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Changing the Base Unit

meter

Piston Diameter 0.0889 meters

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meter

deci

meter

centi

meter

milli

1 meter = 10 decimeters

1 meter = 100 centimeters

1 meter = 1000 millimeters

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kilo base unit

deka

hecto deci centi milli

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Metric System

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Relating Units of Measure

Building your own conversion factors

 How many centimeters in a meter?

 How many millivolts in a volt?

 Etc…

base centi deka

hecto

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Relating Units of Measure

1 of 3

 How do millimeters compare to centimeters?

base centi deka

hecto

kilo deci milli

(50)

Relating Units of Measure

2 of 3

 How do milliliters and deciliters compare?

base centi deka

hecto

kilo deci milli

(51)

Relating Units of Measure

3 of 3

 How do kilovolts and volts relate?

base centi deka

hecto

kilo deci milli

(52)

Homework

 Worksheet 4 – Metric System

 Problems 1 – 5 _{(establish relationship between}

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Metric Conversions

Using Conversion Fractions 1 of 3

 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

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Metric Conversions

 Convert 55 millimeters to centimeters.

55 mm

1 x _mm

base centi deka

hecto

kilo deci milli

1 cm = 10 mm

10

1 _{55 cm}

10

5.5 cm

=

(55)

Metric Conversions

 Convert 2500 grams to kilograms.

2500 g

1 x _g

base centi deka

hecto

kilo deci milli

1 kg = 1000 g

1000

1 kg _{2500 kg}

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Homework

 Problems 6 – 12 _{(practice converting metric}

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Metric System

Conversion Shortcut Method

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Metric Conversions

Using Prefix Chart to Convert 1 of 3

 Convert 3200 grams to kilograms.

kilo hecto deka base

unit deci centi milli

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Metric Conversions

 Convert 0.65 liters to milliliters.

unit deci centi milli

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Metric Conversions

 Convert 850 centimeters to kilometers.

kilo- hecto- deka- base

unit deci- centi milli

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Homework

 Problems 6 – 12 _{(practice converting metric}

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Temperature Conversion

To convert from Celsius to Fahrenheit :

F = C + 32

9

5

Sample: 2525 C = _____  F

F = 25 + 32

F = 45 + 32

F =

77 

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Temperature Conversion

To convert from Fahrenheit to Celsius :

C = (F - 32)

5

9

Sample: 130130 F = _____  C

C = (130 - 32)

C = (98)

C =

54.4 

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Homework

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Details

 Informational Handout: U.S. Metric

Association Correct SI-metric Usage

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Homework

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ADDITIONAL PREFIXES

The metric system provides for more prefixes in order to communicate very

large

numbers or very small numbers…

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ADDITIONAL PREFIXES

The metric system provides for more prefixes in order to communicate very

large

numbers or very small numbers…

unit deci centi milli Mega

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giga (G) 1 09 _{1 billion}

---mega (M) 1 06 _{1 million}

---kilo (k) 1 03 _{1 thousand}

hecto (h) 1 02 _{1 hundred}

deka (da) 1 01 _{1 ten}

Base Unit 1 00 ₁

deci (d) 1 0-1 _{1 tenth}

centi (c) 1 0-2 _{1 hundredth}

milli (m) 1 0-3 _{1 thousandth}

---micro (µ) 1 0-6 _{1 millionth}

---nano (n) 1 0-9 _{1 billionth}

---pico (p) 1 0-12 _{1 trillionth}

This will be included in Worksheet 4 on page 5.

Goal – Focus upon and learn the

powers of 10

associated with the most common metric prefixes.

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Calculator Speed Tips

 Perform a computation with 50.5

megawatts (MW).

50.5 MW 50,500,000

M = mega = 106

(71)

Calculator Speed Tips

 Perform a computation with 3.85

microvolts (µV).

3.85 µV 0.00000385 V

µ = micro = 10-6

(72)

Calculator Speed Tips

 Perform a computation with 250

milliamps (mA).

250 mA 0.25 A

m = milli = 10-3

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Application

Use:

P

=

VI

Find P when V = 250 µV and I = 30mA

P= 0.0000075 w

P= 7.5 µw

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Homework

Worksheet 4 – Metric System

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More speed tips

 270,000,000,000

 13,800,000

 0.000000092

 0.00000476

thinking in blocks of three

270 EE 9

13.8 EE 6

103

109

92 EE -9

4.76 EE -6

10-3

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Homework

Worksheet 4 – Metric System

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Measurement

Section 3 - Converting between measurement systems

Engine Displacement:

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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

(79)

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

.454 1 lb

= 119.8 oz

x

_____

lb 1

16 oz

1 lb = 16 oz

(80)

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

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Homework

 Worksheet 7 – Convert from

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The End

 Written by Peter C. Esser

 Southwest Wisconsin Technical College

 2006-2013