MEASUREMENT IN THE SCIENTIFIC METHOD

Good experiments have good measurements with
properly recorded data.

Bad measurements create incorrect data.
Incorrect data = bad results = wrong conclusions.
HIT THE TARGET
WHAT MAKES A GOOD MEASUREMENT?

Accuracy –
 how

close your measurement is to the correct value
Precision –
 how
close one measurement is to all other
measurements in the experiment
ERROR

ALL MEASUREMENTS HAVE ERROR
-Error is a measure of how far off you are from correct
Error mainly comes from measuring tools.
 Accuracy depends on the tools used.

ERROR


A guess must be made when recording error…
How long is the box?
I know the measurement is at
least 5 cm…
0
c
m
1
2
3
4
5
6
7
8
But since there are not marks between the
centimeters, that is all we know for sure…
So we guess…5.8cm, the last digit shows our guess
Since each person guesses different, the last digit shows our error
ERROR

When reading measurement data you can tell where
the guess was made by how many decimal places the
measurement has…more decimal places = more
accurate

The guess is ALWAYS the last digit
ERROR

To Get less error, we use a tool with smaller guesses…
0
1
2
3
4
5
6
7
8
What is the measurement with a more accurate
tool?
5.91 cm…the 1 is a guess
MINIMIZING ERROR
Use precise and accurate tools – your measurement can
only be as precise & accurate as your tool.
 Using proper measuring technique

USING MEASUREMENTS

Since our measurements all have error, when we
use them in calculations, we have to carry the
error through…

How do we do this you ask?

Significant Figures…
SIGNIFICANT FIGURES

Significant figures - show accuracy in
measurements & calculations

JUST BECAUSE IT IS ON YOUR CALCULATOR
SCREEN DOES NOT MAKE IT SIGNIFICANT!
RULES FOR IDENTIFYING SIG. FIGS. IN A
MEASUREMENT

All non-zero digits are significant
1, 2, 3, 4, 5, 6, 7, 8, 9

Leading zeros are place holders and not
significant
0.0000000000000000002

Trailing zeros are only significant if they are to
the right of the decimal
1000000  zeros are not significant
1.00000  zeros are significant

Zeros between two significant figures, or
between a significant digit and the decimal are
significant
101  zero is signigicant
10.0  all zeros are significant
10000.  all zeros are significant
SIGNIFICANT FIGURES

So, is there an easy way to figure this out
without memorizing the rules…
SIG FIG TOOL
We will use our great nation to identify the sig figs in a
number…
On the left of the US is the Pacific and on the right is the
Atlantic
P
A
SIG FIG TOOL
If we write our number in the middle of the country we
can find the number of sig figs by starting on the correct
side of the country…
If the decimal is Present, we start on the Pacific side
If the decimal is Absent, we start on the Atlantic side
We then count from the first NON zero till we run out of
digits…
P
0.05600
A
SIG FIG TOOL EXAMPLES
P
105200
A
4
This number has _____
sig
figs
SIG FIG TOOL EXAMPLES
P
105200.
A
6
This number has _____
sig
figs
CALCULATIONS WITH SIGNIFICANT FIGURES

Since our measurements have error, when we
use them in calculations, they will cause our
answers to have error.

Our answer cannot be more accurate than our
least accurate measurement.

This means that we have to round our answers
to the proper accuracy…
CALCULATIONS WITH SIGNIFICANT FIGURES

When we add or subtract, our error only makes a
small difference. So, when adding or subtracting
we base our rounding on the number of decimal
places.
 Rule
for Adding and Subtracting –
 the
answer must have the same number of decimal
places as the measurement used in the calculation that
has the fewest decimal places
CALCULATIONS WITH SIGNIFICANT FIGURES

When we multiply or divide, our error makes a
large difference. So, when multiplying or dividing
numbers, we round based on significant figures.
 Rule
for Multiplying and Dividing –
 the
answer must have the same number of significant
figures as the measurement used in the calculation that
has the fewest significant figures
EXAMPLE 1
35.0 cm + 2.98 cm – 7 cm = ?
30.98 cm
This is what your calculator gives you…
However, as we just discussed, the answer cannot be more
accurate than your least accurate measurement…
The least accurate measurement is 7 cm…
So by the adding rule, our answer must be rounded to zero
decimal places, or the ones place
Which gives us the answer of
31 cm
EXAMPLE 2
3.0 x 89.54 ÷ 0.000000001 = ?
268620000000
We have to round to proper sig figs…
So we get
300000000000
Or in scientific notation
3 x 1011
EXAMPLE 3

What if we have both add/sub and mult/div in the
same problem?
(2.4 m + 5 m) ÷ (1.889s – 3.9 s) = ?
Order of opperations means we do the addition and
subtraction first…
(7.4 m) ÷ (-2.011s)
We have to round these before we go on to the
division…
7 m ÷ -2.0 s
Now divide
-3.5 m/s
Now Round
-4 m/s
Presentation created by:
Mr. Kern
THE END
Information gathered from years of scientific
research and data collection
Assignment provided by :
Glencoe Publishing Company