Conversions Steps to Fool Proof Conversions 1 2

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Conversions

Conversions

Steps to Fool Proof Conversions 1. 2. 3. 4. Write what you want to

Steps to Fool Proof Conversions 1. 2. 3. 4. Write what you want to convert with unit Add a multiplication sign Draw a horizontal line Whatever unit you don’t want goes on the opposite side of the line from where it was written 5. Place whatever unit you do want on the other side of the horizontal line 6. Add the conversion factor � A 1 goes beside the prefix if you are using conversion factors

34 m = _____ km

34 m = _____ km

46 inches = _____ Feet

46 inches = _____ Feet

80 km/hr = ______ m/s

80 km/hr = ______ m/s

7 2. 9 x 10 nl = _______ GL

7 2. 9 x 10 nl = _______ GL

Significant Digits

Significant Digits

Measurements § Every measurement is wrong! § To a certain degree § Examples: ▫

Measurements § Every measurement is wrong! § To a certain degree § Examples: ▫ Your Birthday ▫ Height

Measurement • Every measurement has a degree of uncertainty • The uncertainty is based

Measurement • Every measurement has a degree of uncertainty • The uncertainty is based on: ▫ The measuring device ▫ The skill of the measurer

Ways to indicate How Accurate a Number Is 1) Tolerance Intervals 2) Percent Error

Ways to indicate How Accurate a Number Is 1) Tolerance Intervals 2) Percent Error 3) Significant Digits

Tolerance Intervals Tolerance is the greatest range of variation that can be allowed 25

Tolerance Intervals Tolerance is the greatest range of variation that can be allowed 25 0. 5 would be between 24. 51 to 25. 49 25 0. 05 would be between 24. 951 to 25. 049 25 0. 005 would be between 24. 9951 to 25. 0049

Tolerance Intervals • Used on blueprints and in machining to indicate accuracy

Tolerance Intervals • Used on blueprints and in machining to indicate accuracy

Activity: Tolerance a Part Design a square piece with a square hole through it’s

Activity: Tolerance a Part Design a square piece with a square hole through it’s centre. Key Dimensions: • How must the length of the piece be toleranced • How big must the square hole through the piece be to accommodate the square peg Criteria: • The square piece must sit inside a container that was toleranced 20 m lm on each side • The square peg is dimensioned 2 m 0. 1 m

Percent Error • Indicates a percentage that the value may be out by

Percent Error • Indicates a percentage that the value may be out by

Sample Problem • You buy an 8 foot 2 x 4. You measure the

Sample Problem • You buy an 8 foot 2 x 4. You measure the board to be 94. 5 inches long. What is the percentage error for the length of the board? • 12 inches = 1 foot

Significant Digits The accuracy is determined by the right most digit 25 would be

Significant Digits The accuracy is determined by the right most digit 25 would be between 24. 51 to 25. 49 25. 0 would be between 24. 951 to 25. 049 25. 00 would be between 24. 9951 to 25. 0049

 • Significant Digits: Uses the number of digits in the number to express

• Significant Digits: Uses the number of digits in the number to express the uncertainty of the number ▫ 1 x 101 is less accurate than 12 ▫ 12 is less accurate than 12. 0 ▫ 12. 0 is less accurate than 12. 00

Rules for Significant Digits • All non-zero digits are significant • All zeros contained

Rules for Significant Digits • All non-zero digits are significant • All zeros contained between non-zero digits are significant ▫ i. e. 207 – 3 sd • All trailing zeros to the right of a decimal are significant ▫ i. e. 3. 000 – 4 sd

When are zeroes not significant? • All leading zeros to the left of the

When are zeroes not significant? • All leading zeros to the left of the first non-zero digit are not significant ▫ i. e. 0. 00058 – 2 sd

 • Exact numbers have infinite significant digits ▫ How many cars do I

• Exact numbers have infinite significant digits ▫ How many cars do I have? 1

Examples a. ) 125. 9 b. ) 230 c. ) 0. 00658 d. )

Examples a. ) 125. 9 b. ) 230 c. ) 0. 00658 d. ) 500. 3

Examples: a. ) 125. 9 b. ) 230 c. ) 0. 00658 d. )

Examples: a. ) 125. 9 b. ) 230 c. ) 0. 00658 d. ) 500. 3 - 4 s. d. - 3 s. d. - 4 s. d.

Defining Cylindricity - Extra • http: //www. youtube. com/watch? v=Zu. ECC 8 RM Z

Defining Cylindricity - Extra • http: //www. youtube. com/watch? v=Zu. ECC 8 RM Z 40

Interchangeable Parts • Muskets were originally designed by expert gun smiths who made one

Interchangeable Parts • Muskets were originally designed by expert gun smiths who made one gun at a time • If it broke and needed servicing, the gun would have to be sent back to an expert gunsmith

Early US Attempts • In 1801, Eli Whitney built ten guns from the same

Early US Attempts • In 1801, Eli Whitney built ten guns from the same parts, disassembled all of them in front of congress and then reassembled them from a pile of parts • The concept was great but each part was still handmade by skilled craftsmen

Changes that Allowed Interchangeability • New machines (lathes, mills, etc) • Development of jigs

Changes that Allowed Interchangeability • New machines (lathes, mills, etc) • Development of jigs to control the path of the tool and fixtures to hold the piece in place • Blocks and gauges to determine the accuracy of the finished parts

How to Improve Accuracy • Improve the measuring instrument ▫ The smaller the unit

How to Improve Accuracy • Improve the measuring instrument ▫ The smaller the unit on the measuring device, the more precise the measurement • Know how to measure ▫ Always look straight down on the measuring device

How to Improve Accuracy • Repeat ▫ Measure several times to get a good

How to Improve Accuracy • Repeat ▫ Measure several times to get a good average value ▫ “Measure twice, cut once” • Measure under controlled conditions ▫ Objects can shrink or expand based on measuring conditions

Why wouldn’t you make everything very, very accurate? • Cost • Waste of time

Why wouldn’t you make everything very, very accurate? • Cost • Waste of time • Not needed • The more accurate a measurement must be, the more it costs to do so

Bibliography • Britton. "Geometric Dimensioning and Tolerancing. " Lecture. http: //synthetica. eng. uci. edu/~mccarthy/mecha

Bibliography • Britton. "Geometric Dimensioning and Tolerancing. " Lecture. http: //synthetica. eng. uci. edu/~mccarthy/mecha nicaldesign 101/GDand. T. pdf. 1 Feb. 2013

Operations with Significant Digits

Operations with Significant Digits

Adding and Subtracting • Use the lowest number of decimal places from the numbers

Adding and Subtracting • Use the lowest number of decimal places from the numbers given in the problem • 2. 35 + 7. 669 = 10. 019 �According to the rule, we can only keep 2 decimal places = 10. 02

12. 875 – 8. 3 = 20. 876 – 5 =

12. 875 – 8. 3 = 20. 876 – 5 =

Multiplying and Dividing • Use the lowest number of significant digits form the numbers

Multiplying and Dividing • Use the lowest number of significant digits form the numbers given in the problem 3. 4 x 2. 35 = 7. 99 2 SD 3 SD = 2 SD = 8. 0

780 / 23 = 200. 600 x 0. 0012 =

780 / 23 = 200. 600 x 0. 0012 =

Scientific Notation • Used to express numbers with the proper number of significant digits

Scientific Notation • Used to express numbers with the proper number of significant digits • 1. 32 x 1010 (3 s. d) ▫ Only one digit to the left of the decimal place ▫ Only leave the number of sig digs you want in the numerical portion

Finding the exponent • Every time you move the decimal to the left, the

Finding the exponent • Every time you move the decimal to the left, the exponent goes up 1 • Every time you move the decimal to the right, the exponent goes down 1 • 3, 567, 000 (with 3 SD) • 0. 000, 056, 0 (with 3 SD)

In this course, • The number of significant digits in your answer should be

In this course, • The number of significant digits in your answer should be the same as the lowest number of significant digits in the question • Ex: If each students has 0. 50 cents and there are 100 students, how much money do they have?