Imagine that you are playing the Between game with a partner. Player A picks a decimal number between 5 and 6 -- say, 5.7 -- crosses out the number 5, and writes down 5.7 in its place. Player B picks a number between 5.7 and 6, such as 5.9, crosses out the number 6, and writes down 5.9. Now Player A must pick a number between 5.7 and 5.9 -- i.e., 5.8 -- and replace Player A's previous number (5.7) with it. Play continues for a total of 10 rounds (the above describes three rounds).
Imagine that the Between game was a measuring task where you were trying to become more accurate with each measurement. What does this game tell you about the nature of measurement?
Problem H2
Suppose that a scale of 1 in.:20 ft. was used for building a model train. What does this mean? If a railcar is 40 ft. long, how long is the scale model?
Problem H3
A science class wants to create insects that are larger than life. They found that a queen ant is 0.5 in. long. The large model they plan to create is 5 ft. long. What is the scale factor for the ant model?
Problem H4
Here is your car's gas gauge:
a.
Suppose your full gas tank holds 16 gallons. Put an arrow on the gas gauge to show how much gas you would have left in your tank if you filled it up and then took a drive that used 6 gallons:
b.
Your gas tank said "Empty," but you were low on cash. You used your last $4 to buy gas, paying $1.139/gallon. Suppose a full tank holds 14 gallons. Put an arrow on the gas gauge to show how much gas you had in your tank after your purchase:
c.
You filled up your tank this morning, then took a drive in the country to enjoy the fall colors. Your odometer said that you had gone 340 miles, and you have been averaging about 31 miles/gallon. If your gas gauge looked like this when you got home, how much does your gas tank hold when it is full?
Problem H5
Suppose that you had the following 10 measurements (in centimeters) of the same object:
31.9
32.0
31.9
32.1
32.0
32.2
32.4
32.3
32.5
32.4
a.
With these data, what would you give as the best approximation? Explain why you give that approximation. What would be the precision unit for your best estimate?
Think about finding the mean or an average data value of the set. Close Tip
Suppose that you made five measurements in addition to the 10 listed above:
32.1
32.2
32.3
32.3
32.4
b.
What is your best approximation now?
Suppose that you made a total of 20 measurements -- the 15 above and the following five:
32.0
32.9
32.4
32.2
32.1
c.
What is your best approximation now? Did it change?
d.
In general, what effect on a best approximation do you expect if the results of more and more measurements are reported?
Problem H6
Take a piece of paper and measure its length and width. What level of precision will you use to measure? What is the accuracy of your measure in terms of the relative error?
Remember, the level of precision depends on the measuring instrument and its unit of measure. Accuracy depends on relative error. You can record the accuracy as a percent by subtracting the relative error from 1 and writing the resulting decimal as a percent. Close Tip
