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Learning Math Home
Session 2: Solutions
Session 2 Part A Part B Part C Homework
measurement Site Map
Session 2 Materials:

A B C 


Solutions for Session 2 Homework

See solutions for Problems: H1 | H2 | H3 | H4 | H5 | H6

Problem H1

The fact that this game does not reach an "ending" (with no moves available) shows that there can always be a more accurate measurement, and therefore the act of measuring can never be exact.

<< back to Problem H1


Problem H2

This means that all lengths in the model are 1 in. long for every 20 ft. in the original model. If the original railcar is 40 ft. long, we can set up the following proportion to calculate the model's length:

Solving the equation for x would give us x = 2. So the model's length will be 2 in.

<< back to Problem H2


Problem H3

The scale factor is 5 ft.:1/2 in. For easier calculations, we can convert the ratio into inches. Since 1 ft. = 12 in., the scale factor would be 60:1/2, or 120:1.

<< back to Problem H3


Problem H4


One way to do this is to partition the gas gauge into 16 equal parts by dividing it in half four times (2 • 2 • 2 • 2 = 16). You can then count 6 gallons. Another way is to note that 6/16 = 3/8, so partitioning the gauge into eighths is sufficient.


One way to solve this problem would be as follows: Filling up the entire tank would cost $1.139 • 14 = $15.94. Four dollars is one-fourth of $16, so it is just a little more than one-fourth of $15.94. The arrow should be just slightly above one-fourth full.


First you need to find out how much gas you used for 340 miles:

340 31 = 10.97

So approximately 11 gallons were used. Next, look at the needle position: It is approximately one-third of the way from "Empty" to the first quarter mark. Further subdividing the gauge into 12ths, we see that the needle is about 1/12 of the way from "Empty." Since about 11 gallons were used, and 11/12 of the tank is empty, the tank therefore holds about 12 gallons when full.

<< back to Problem H4


Problem H5


The best approximation might be about 32.2 cm, which is in the center of the data set. The average (mean) of the 10 measurements is 32.17 cm. The precision unit appears to be tenth (or 1 mm), as all 10 measurements are recorded to the nearest 0.1 cm.


The mean of the 15 measurements is 32.2 cm. Again, the precision unit might be 0.1 cm. Our approximation, however, is better now since we have more measurements.


The mean is now 32.23 cm. Even though the measurement errors are pretty high, this gives us even more confidence that the actual measure is close to 32.2 cm.


With more measurements we will get an increasingly better approximation.

<< back to Problem H5


Problem H6

The level of precision depends entirely on the measuring instrument. If we use a measuring stick with 1-in. precision, the maximum error is 0.5 in.

The accuracy can be obtained by subtracting the relative error from 1 and writing the resulting decimal as a percent. For the longer side of the paper, the relative error is 0.5/11, or about 0.045 (so, the accuracy is 1 - 0.045 = 0.95, or 95%). The relative error for the shorter side is 0.5/8.5, or about 0.059 (so the accuracy is 1 - 0.059 = 0.94, or about 94%), which is less accurate. A measuring stick with more partitions will give more precise and more accurate measurements.

<< back to Problem H6


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