Measurement - Review

1. What is the purpose of using the rules for significant digits when doing calculations?

2. A student performs an experiment where several mass measurements are made using a triple beam balance.  After collecting the data she notices that when no mass is on the beam it does not read zero!  What type of error will her data have?  Will the precision of her work be affected?  Will the accuracy of her work be affected?  Explain. (i.e. Demonstrate you know the meaning of accuracy and precision.)

3. An experiment to measure the speed of sound is performed repeatedly and the resulting best value and mean deviation are reported as 342 m/s ± 8 m/s.  The accepted value is 343 m/s.  Which type of error is more prevalent – random or systematic?  Explain.

4. Circle the significant digits in the following:

a. 6700 km             b. 0.0080900 m           c. 3.040 ´ 10⁷ m                      d. 2100.20 L

5. Make the following conversions:  (2.54 cm = 1 in)

a. 109.7 in to m      b. 3.0 L to in³   c. 150 km/h to ft/min

d. 10.5 g/cm³ to kg/m³        e. 3500 ft² to m²

6. Perform the following calculations and indicate the result with appropriate significant digits and correct units.

a. (45.7 cm) - (13.56 cm)              b. (45.0 m) ´ (2.00 m)

c. (99 L) + (7 L)                             d. (1700 g) ¸ (876.0 mL)

7. Write the following with a metric prefix.  (These are “hypothetical units” – just for fun!)

a. 3.50 x 10⁸ Ryan              b. 9.99 x 10¹¹ frog                    c. 4.12 x 10^-6 soft

d. 0.082 gans                     e. 2470 manjaro                       f. 1.275 x 10^-7 way!

8. The volume of a canister is measured several times with the following results:  3.575 L, 3.642 L, 3.600 L, 3.618 L, 3.624 L, 3.622 L, and 3.614 L.  (a) Determine the best value. 
(b) Determine the average absolute deviation.  (c) What, if anything, can be said about the accuracy and precision of these results?  Explain.

9. An experimenter determines absolute zero to be -272.3° C.  (a) Given that the accepted value is -273.15° C, determine the relative error.   (b) What, if anything, can be said about the accuracy and precision of this experiment using only this information?  Explain.

10. Using a unit approach determine the mass of the earth based upon its gravitational effect on the moon.  Use the speed of the moon in its orbit, 1.04 km/s, the distance to the moon,
390 Mm, and the gravitational constant, 6.67 x 10^-11 m³/kg s².

11. A car’s ability to accelerate is tested by measuring time to go from zero up to a certain speed.  The table below shows the data that was collected.  Produce a graph of this data – let time be the x-variable and speed be the y-variable.  This is a good example of a graph on which the type of relation is not entirely obvious.  Therefore you will try two different curve fits on the same data set.  (a) Using a ruler, draw a line of best fit through the data and determine the equation.  (b) The line that you drew draws attention to the fact that this data is somewhat curved and may follow a relation of the type y = kÖx.  Add a column to the table and determine the best value for k.  (c) Neither of these two equations is a perfect fit.  Discuss some of the signs that show each equation is an imperfect fit.  Which do you think is better?

Time (s)	Speed (mph)
0.0	0.0
1.9	30.0
3.0	40.0
4.3	50.0
5.9	60.0
7.7	70.0
10.2	80.0

1.

2.

3.

4. a. 6700 km

    b. 0.0080900 m

    c. 3.040 ´ 10⁷ m

    d. 2100.20 L

5. a. 2.786 m

    b. 180 in³

    c. 8200 ft/min

    d. 10500 kg/m³

    e. 330 m²

6. a. 32.1 cm

    b. 90.0 m²

    c. 106 L

    d. 1.9 g/mL

7. a. 350 MegaRyan

    b. 999 Gigafrog

    c. 4.12 microsoft

    d. 82 milligans

    e. 2.47 kilomanjaro

    f. 127.5 nanoway!

8. a. 3.614 L

    b. 0.015 L

    c.

9. a. 0.3%

    b.

10. 6.32 ´ 10²⁴ kg

11. a. v = (7.4 mph/s)t + (12 mph)

          where v = speed, t = time

      b. v =(24 mph s^-1/2)Öt

          where v = speed, t = time

      c.