Download Sacramento State University

Sacramento State University
PHYSICS 1
Shea - Fall 2007
HOMEWORK 1
1. Assume the following numbers (in units of meters) appear in the register of your calculator as a
result of doing a calculation. Express the numbers in scientific notation retaining three significant
figures. a) .0098746005 b) 987,234.03 c) 1.207654 d) 100 E(6) e) 1.230345 E(-2) Describe in words
how you determine the number of significant figures for a number written in scientific notation. Give
an example to support your description.
[Note: When recording answers from your calculator for physics problems it is generally acceptable to
give results to two/three significant figures when it is not clear how many significant figures there are
in each number used in the calculation. In some cases you can use the context of the problem to
determine a reasonable number of significant figures but it is always considered to be poor practice to
record six or seven significant digits from your calculator in an answer to a problem where you used
numbers in the problem with say three significant figures.]
2. Repeat problem (1) but now list the result in units of centimeters to three significant figures. Does
changing units change the number of significant digits? Discuss.
3. For the measured quantities written below, identify the number of significant figures and rewrite in
scientific notation. Be sure to explain any assumptions you make about the quantities, remembering
that scientific notation must clearly indicate the number of significant figures.
a) 2,400 g b)0.007863 cm c) 1050.0 x 102 L d) 203.2 s e) 405,000 min
4. In physics it is often useful to check the answer you get on your calculator or make an order of
magnitude approximation of the answer to see if the result is reasonable. For practice to develop this
skill make a numerical approximation of the following calculation to one significant figure (do not use
a calculator and show your approximations): a) (0.0987)(9.34) b) (4325)/(-2.10)
c) (145.3)(0.23)/(840) d) (.0023)(-6.43)(-345.0)/(-3.45) e) Square root of (8.12) f) Sq of (-8.34XE(3))
After doing this approximation, compare it to the number you get using your calculator and comment.
For the next two problems use your calculator to get the answer and write it down as preliminary
answer with more significant digits than is justified. Then write the final answer with the correct
number of significant digits in scientific notation with appropriate units.
5. Significant digits in addition and subtraction: Write each of the following expressions as a single
number in scientific notation with the result to the correct number of significant figures. Remember
that the sum can not be more precise than the least precise number in the sum. [Note that the least
precise number is not necessarily the number with the least number of significant digits.]
a) 3.241x103 cm+ 4.0x102 cm b) 5480 s + 6.754x102 s + 1104.2 s c) 52.4 g - 1.255 g - 10 g
6. Significant figures in multiplication and division: Write each of the following expressions as a single
number in scientific notation with the result to the correct number of significant figures. Remember
that the result of a calculation when multiplying and/or dividing is only as precise as the factor with
the smallest number of significant figures.
a) 5.2 cm x 3.1 cm b) 5.243 m/s x 0.0031 s c) 2.000 +0.01 and 2.000 x 0.01
d) (2341 x 0.165 )/(13 x 324)
Note: When solving physics problems it is good practice to do the complete calculation on your
calculator entering more significant figures then might be justified and at the end record five or six
significant figures for your preliminary answer. Then for your final answer round this number off to
the correct number of significant figures and rewrite it in scientific notation form with units.
7. You measure the dimensions of a small box and get the following results: length 8.3 cm, width 2.432
cm and height 3.0 cm. What is the volume of the box? Would you report 1 or 2 significant figures?
Explain
Due: Tuesday September 11 at the beginning of class.