# Assignment: Metric system

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## Assignment: Metric system

Assignment: Metric system

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Assignment: Metric system
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1. Using a metric ruler, determine the length of the items in Table 1.1 below:

In the final column, you are to estimate your measurement precision. To do this, measure each item a second or even third time. How close are the measurements? If there is a range of values for the length you measure, record the average difference between measurement values as your uncertainty. If your measured value for a given object appears the same after repeated measurements, this does not necessarily mean that your uncertainty is zero. Look closely at your ruler or measurement device and estimate the smallest unit of length that you would be able to discriminate with it. Every measurement device has limits. For instance, very few people use a ruler with a precision greater than 1/3 or 1/2 of a millimeter; in many cases, even this precision is difficult or impossible to obtain. Typically +/- 1 mm is standard for measuring flat objects with a ruler, but this uncertainty can be expected to go up when the object has significant curvature or its length is not quite so well defined.

To measure the circumference (length around) of your head or thigh, wrap a piece of string around it and mark where the string meets itself. Then lay the string out flat and measure the length with your ruler.

Table 1.1. Metric measurements and uncertainties.

 meters cm mm inches Uncertainty ? Your favorite shoe .254 25.4 254 10 2.54 Your index finger 0.0762 7.62 76.2 3 7.62 A pencil 0.1524 15.24 152.4 6 1.524 Fingernail of your pinky 0.003175 0.3175 3.175 1/8 .3175 Width of a credit card The circumference of your thigh The circumference of your head

2. Measure and record volume in Table 1.2.

Estimate the rough volume of your head by using the circumference (denoted C) and multiplying out this formula (based on the volume of a sphere =4pr3/3 = C3/(6p2)):

Volume ? 1/59 × C × C × C = C3/59

Estimate the uncertainty in your head volume (?V, called “delta V”) calculation by using the uncertainty in your measurement of the circumference of your head (denoted ?C) and multiplying through the following formula:

?V ? 3/59 × C × C × ?C = 3/59 × C2 × ?C

Table 1.2. Head volume and uncertainty estimates.

 Circumference (C) Uncertainty in Circumference (?C) Head Volume   ? 1/59 C3 Uncertainty in Head Volume (?V) ? 3/59 × C2 × ?C

3. Complete the conversions in Table 1.3. The first row has been done.

Table 1.3. Length conversions.

 Length km m miles feet 2.0 km 2.0 2,000 1.24 6,562 705 m 705 3.25 miles 3.25 300 ft 300

4. Complete the conversions in Table 1.4.

Table 1.4. Mass conversions.

 Weight kg g pounds (lbs) 5.0 kg 5.0 400 g 400 50 pounds 50

5. Complete the conversions in Table 1.5.

Table 1.5. Volume conversions.

 Volume liters ml gallons 6.0 liters (l) 6.0 600 ml 600 3 gallons 3

6. Complete the conversions in Table 1.6.

Table 1.6. Temperature conversions.

 Temperature °C °F 100 °C 100 27 °C 27 -2 °C -2 27 °F 27 95 °F 95 -40 °F -40

7. Population biologists use the term “Doubling time” to refer to how long it takes a population to double in size. This concept is particularly useful when the average time for a given individual to reproduce is fairly constant in a species. Consider a bacterial population that can reproduce by dividing into two daughter cells (binary fission) from an original single individual cell. Assume a doubling time of ten minutes and fill out the following table. At time zero there is one bacterium, ten minutes later there are two bacteria, ten minutes after that there are 4 bacteria, etc. Fill in the blanks in Table 1.7.

Table 1.7. Population growth.

 Number of Bacteria 1 8 First exceeds 10,000 Time 0 30 min 1 hour 2 hour
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