SIGNIFICANT FIGURES & FUZZY NUMBERS
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 For example, something measured as 3 inches isn't 3 inches. It may be close to 3 inches but never exactly 3 inches. You could say it was more like 3 and 1/16 inches. But even that is not exact. It is only accurate to the nearest 1/16 inch. Example 2: A cake recipe calls for 1 quart of milk. You know that 4 cups equals 1 quart, so you measure out 4 cups. Do you have a quart? In theory you should, but measurements are not exact, so you will not have exactly a quart. You are close enough for baking a cake, but for more critical recipes, the inaccuracies can cause problems. Even if you measured a quart directly without measuring four cups, you still could not get exactly one quart. You can only get as close as the measuring tools and your ability to read them allow. The Hubble telescope is a good example. Engineering had the correct theoretical sizes needed for the curvature of the mirror that collects and focuses the light. Measuring the curvature of the mirror was another matter. The builders of the mirror made large measurement mistakes that caused the mirror to have a blurred image. This required a second mirror to correct the previous measurement mistakes. The picture below illustrates before and after images from the telescope.

# Measurement

 Measurement is important to everyone: Athletes, artists, aviators, architects, accountants, archeologists,... and that's just the "A's" A measurement, however, is only good if you know its accuracy. Unfortunately, the accuracy of a measurement isn't always made clear. The purpose of the following exercises is to teach you how to make the accuracy of your measurements clear.

 Measurements reported as 1 decimeter, 1.0 decimeters, and 1.00 decimeters may seem the same, but their accuracies are very different.[Note: a decimeter is one tenth of a meter. Sizes shown are close to actual sizes.] 1 decimeter implies that it could actually range from a half (0.5) decimeter to just under 1.5 decimeters. It's been rounded to the nearest whole decimeter. The ".0" in 1.0 decimeter implies accuracy to the nearest tenth. The actual length could range from 0.95 decimeters (which got rounded up to 1.0) to just under 1.05 decimeters (which got rounded down to 1.0) The ".00" in 1.00 decimeter implies accuracy to the nearest hundredth. The actual length could range from 0.995 decimeters (which got rounded up to 1.00) to just under 1.005 decimeters (which got rounded down to 1.0) As you can see, measurements that include more decimal places increase the accuracy tremendously.

 Which of the following measurements is more accurate? 3 miles 3.4 miles 3.37 miles
 If you were a carpenter and a customer called and said he wanted a floor-to-ceiling bookshelf and the height of the wall was 8 feet, what would you do? A. Build a bookshelve to as close to 8 feet as you could. B. Build a resizable bookcase that could stretch from 6 feet to 10 feet. C. Ask the customer to clarify his accuracy, by measuring to the nearest 1/4". D. Go measure the height yourself.
Significant Numbers
(also called Significant Figures or "Sig Figs" for short)

 An atlas says the distance from Phoenix to Honolulu is 3,300 miles. You also learned in your geography class that continental drift causes the US to separate from the Hawaii at 2 centimeters per year. How far will Phoenix be from Honolulu in 10 years? A. 3,300 miles plus 20 centimeters. B. Still 3,300 miles. C. Convert 3,300 miles to centimeters, then add 20.
 A newspaper reports that a certain basketball player will make a total of 12 million dollars next year from playing and from endorsement of products. The player said he will donate exactly \$50,000 to charity. How much will he have left? A. \$11,950,000. B. Still 12 million dollars. C. Between \$12,450,000 and \$11,450,000. D. Around 12 million.
 A celebrity's accountant reports that his client made \$17,245,820.28 last year and gave \$15.25 to his least favorite charity. How much did he have left after this specific charity donation? A. 17 million dollars. B. \$17,245.805.03 C. \$15.25 is too small to bother.

 Bill Gates, who owned Microsoft, was reported in the newspaper to be worth 15 billion dollars. Let's say you buy Windows Vista software for \$90 and Bill's share is two dollars. How much is he worth now? A. \$15,000,000,002. B. Still 15 billion C. \$2 is insignificant compared to billions.

 You tell your friend you can both park in your one car garage if the total length of your two cars is less than 35' 6 3/4". You measured your Jaguar at 18' 3 1/4". Your friend said his car was 17 feet in length. Should you close the garage door? A. Yes, their total length is only 35' and 3 1/4". That's 3 1/2" to spare. B. No.
 You just tested your pool and the results indicated the chlorine concentration at 50 ppm (parts per million, which means 50 chlorine atoms for every 1 million H20 molecules.) However, your friend spills his 12 ounces of beer into your 2,000 gallon pool. What is the concentration of chlorine now? A. Less than 50 ppm. B. Still 50 ppm. The extra 12 ounces is too small to affect reading. C. 50 ppm chlorine, 1 ppm alcohol.
 When adding or subtracting two amounts, does the following statement make sense? If the inaccuracy of one amount is larger than the other amount, don't bother in doing the addition or subtraction. For example, in the picture a measurement of '9 cm.' is only accurate to the nearest whole centimeter, which means it could vary from 8.5 cm. to just under 9.5 cm. (a range of 1 cm) The other number is .4 cm., which is smaller than the 1 centimeter variation. In other words, if we tried to add the two together to get 9.4, we are indicating our answer to be accurate the nearest tenth of a centimeter. However, we can't because our measurement of 9 cm. was not measured that accurately.