Measurements 1
Measurements
Objective: To measure the volume of different solid objects, calculate the density of the objects, and
find the standard deviation and the percent error.
Theory: For measurement in any scientific experiment there is a certain amount of precision that may
be obtain using the instruments provided. These limitations to the accuracy of the instruments
used may be caused by the instruments themselves or by the observer conducting the
experiment. These uncertainties in the measurements must be regulated so that if two
experimenters measure a quality, the results that are calculated may correlated. To maintain a
correlation, significant figures are used. For a number such as 1117 there are four significant
figures, for 11 there are two significant figures. However, for 20 there is one significant figure
and here we employ scientific notation, 2.0 โ 101. For multiplying or dividing measurements we
use the use the number with least amount of significant figures which correlates to the less
accurate number.
1028
14 =73.428571428571428571428571428571โ
73
When adding and subtracting, the number with the least amount of digits after the decimal
place is used.
172.25โ13.875=158.375โ158.38
Standard deviation shows the amount a variation or dispersion from the expected value or
average. The percent error from the standard value indicates the error in the experiment in
relation to the values that have been set to be the standard of the value.
๐ฅ๎ชง=1
๐โ๐ฅ๐
๐
๐=1 =๐ฅ1+๐ฅ2+๐ฅ3+๐ฅ4โฆโฆ+๐ฅ๐
๐=๐๐ฃ๐๐๐๐๐
๐=โโ(๐ฅ๐โ๐ฅ๎ชง)2
๐
๐=1๐โ1 =โ(๐ฅ1โ๐ฅ๎ชง)2+(๐ฅ2โ๐ฅ๎ชง)2+(๐ฅ3โ๐ฅ๎ชง)2โฆ+(๐ฅ๐โ๐ฅ๎ชง)2
๐โ1
= ๐ ๐ก๐๐๐๐๐๐ ๐๐๐ฃ๐๐๐ก๐๐๐ ๐๐๐ ๐ ๐ ๐๐๐๐ ๐๐ข๐๐๐๐ ๐๐ ๐ก๐๐๐๐๐
% ๐๐๐๐๐ =|๐ฅ๎ชงโ๐ฅ๐
๐ฅ๐ |โ100
Perform the indicated operation giving the answer to the correct amount of significant digits.
A. 15.3 x 7.9 = ________ D. 15.3 รท 7.9=____________
B. 16.47 - 4.2 = _______ E. 1.2 x 10-3 - 0.001=_______
C. 3.14 + 360 = ________
1.2x10^2
1.9
12.
0.0002
363.
