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 answers 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.
Great website for tons of math stuff you need to know “Adapted Mind”.
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: Problems 4,10,17,23,24,26,27,28,32,34(10 problems). You must give a complete conversion chain for each problem. The chain must include the correct values and units. Don’t forget to include units on your final answer.
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