1.4 Dimensional Analysis

This section is all about conversions.We are going to be using conversion facts to make conversion “chains.”

We will be working with different units in terms of:

You will need to make use of some formulas. Pretty much, all the info you need, can be found in the appendix. You are going to be using this information A LOT. I strongly suggest you make a copy and maybe laminate it so it lasts longer. This way you don’t have to keep flipping back and forth in your text.

The best way for me to teach you conversions is through lots of examples. But first:

Rounding: I need to give you a quick tutorial on the type of rounding we will be doing in this class. You might consider it the “conventional” method as opposed to rounding used in an engineering sense.

1) Rounding decimals. You need to know place value. If you don’t you will likely get most of your answer wrong; so, please learn it.

Once you can find the place value, look one digit to the right.If it is 5 or more, round up.If it is less than 5, round down.

If you need practice, click on the picture to the right. It will take you to MathATube.com where you can practice some problems.

English EnglishMetric MetricEnglish Metric

Linear – measuring distance, 1 dimensional (ft, m) Area – 2 dimensional (sq ft or ft2, m2) Volume – 3 dimensional (cu ft or ft3, m3)

Practice on Rounding: Round each value as directed.

124.89903Nearest whole number ___________________

Nearest hundred ___________________

Nearest hundredth ___________________

Nearest ten ___________________

Nearest tenth ___________________

Nearest thousandth ___________________

Nearest ten thousandth ___________________

0.0908277

Nearest whole number ___________________

Nearest hundred ___________________

Nearest hundredth ___________________

Nearest ten ___________________

Nearest tenth ___________________

Nearest thousandth ___________________

Nearest ten thousandth ___________________

2) Changing decimals to fractions (to the nearest 1/2, 1/4, 1/8, 1/16, 1/32, etc.). We discussed this once before, but let’s review.

Once you have the decimal -a) Multiply the decimal portion of the number by the denominator of the

fraction you want. This gives you the numerator. b) If necessary, round to the nearest whole number.

Demonstration: The length of a piece of metal is 18.6349 inches. Give this dimension to the nearest 16th of an inch.

18.6349 inches = 18 whole inches plus ???? 16ths more. So forget about the 18 and concentrate on the decimal portion.

Multiply 0.6349 times 16 = 10.1584 This is how many 16ths there are in 0.6349 in.

Now, round to the nearest whole number (the nearest whole 16th). 10.1584 ≈10

Final Answer: 18.6349 ≈ 18-10/16 in But, are we done?...Probably not. Simplifying further makes sense. Final answer 18-5/8 in

This process works EVERY TIME!

You will need the appendix in the back of your text for the following examples.Example 1A circuit board measures 15” wide by 11” tall. Convert the dimensions into centimeters rounded to one decimal place.

Example 2Usain Bolt's 9.58sec at world championships shatters 100- meter record ... Aug 16, 2009 Berlin Germany ... Lightning Bolt captures another world record ... Convert Usain Bolt’s speed to MPH (miles per hour) for his time of 9.58 seconds in the 100 meter dash.

Example 3Find the weight of the beam cut from a Douglas fir tree weighing 36 lbs/ft3

(pounds per cubic foot). Be careful with the units!

Example 5 (1.4.1: Calculating concrete volume, from your

text)Find the volume of concrete in yd3 needed for a sidewalk that is4 in deep by 6 ft wide by 100 ft long. Pay close attention to the units.

Example 6 (1.4.3: Converting from metric to standard weight, from

your text)A length of steel tubing is labeled to weigh 8700 grams, convert this weight to pounds to determine how much trouble it will be to lift.

Extra Practice: Odd problems from end of section exercises.

Homework: You are assigned all of the even numbered problems (17 problems). You must give a complete chain for each problem. The chain must include the correct values and units.Section 1.4:

1. 96.5 cm

2. 61 13”16

3. 1295.4 mm

4. 29’ 6 5”16

5. 1.79 miles

6. 5 5”8 = 14.3 cm, 4

3”8 = 11.1 cm, 8

1”4 =

21.0 cm, 2 1”2 = 6.4 cm

7. 184 mm = 7 1”4 , 122 mm = 4

13”16 , 30 mm

= 1 3”16

8. 109.68 cm2

9. 1.64 ft2

10. 13,939 ft2

11. 8.67 yd2

12. .51 m2

13. 53.82 ft2

14. 10.8 oz

15. 37.4 gallons

16. 6.19 yd3

17. 946 cm3

18. 6,912 in3

19. 3.9 yd3

20. 4,428 ft3

day

21. 11.41 ftyr

22. 8.0 mileshour

23. 39.5 mileshour

24. 0.84 gL

25. 12.3 mileshour

26. 12.1 ms

27. a. 8,951.0 ozft3

b. 316.3 g¿3

c. 49,282.7 gft3

d. 490.1 lbsft3

e. 4.6 gcm3

28. 96.9 lbs

29. 580 lbs

30. 9 grains

31. 588 lbs

32. 83.4 lbs

33. 67.6 lbs

34. 368 mg of protein, 883.2 mgday