Transcript File

INTRODUCTION TO SIGNIFICANT FIGURES
SIGNIFICANT FIGURES
Scientist use significant figures to determine
how precise a measurement is
 Significant digits in a measurement include all
of the known digits plus one estimated digit

FOR EXAMPLE…

Look at the ruler below

Each line is 0.1cm
You can read that the arrow is on 13.3 cm
However, using significant figures, you must
estimate the next digit
That would give you 13.30 cm




UNCERTAINTY IN MEASUREMENT Measurements are made one
place beyond where the measuring device is marked. For example, a
ruler marked to the nearest tenth of a centimeter can be read to the
hundredths place by estimating how far between the lines the
measurement falls.

Device is marked to the ONES place, so read to the TENTHS place
Measurement: 6.2 cm
the 2 in the tenths place is ESTIMATED --------------------------- cm .1 .2 .3 .4 .5 .6 .7 .8 .9 Device is marked to the
TENTHS place, so read to the HUNDREDTHS place Measurement:
0.48 cm
the 8 in the hundredths place is ESTIMATED ------------------------------------- cm 10 20 30 40 50 60 70 80 90 Device is marked to the
TENS place, so read to the ONES place Measurement: 67 cm
the
7 in the ones place is ESTIMATED
LET’S TRY THIS ONE

Look at the ruler below
What can you read before you estimate?
 12.8 cm
 Now estimate the next digit…
 12.85 cm

THE SAME RULES APPLY WITH ALL
INSTRUMENTS
The same rules apply
 Read to the last digit that you know
 Estimate the final digit

LET’S TRY GRADUATED CYLINDERS

Look at the graduated cylinder below

What can you read with confidence?
56 ml
Now estimate the last digit
56.0 ml



ONE MORE GRADUATED CYLINDER

Look at the cylinder below…
What is the measurement?
 53.5 ml

RULES FOR SIGNIFICANT FIGURES
RULE #1
All non zero digits are ALWAYS significant
 How many significant digits are in the
following numbers?

•274
•3 Significant Figures
•25.632
•5 Significant Digits
•8.987
•4 Significant Figures
RULE #2
All zeros between significant digits are
ALWAYS significant
 How many significant digits are in the
following numbers?

504
3 Significant Figures
60002
5 Significant Digits
9.077
4 Significant Figures
RULE #3
All FINAL zeros to the right of the decimal
ARE significant
 How many significant digits are in the
following numbers?

32.0
3 Significant Figures
19.000
5 Significant Digits
105.0020
7 Significant Figures
RULE #4
All zeros that act as place holders are NOT
significant
 Another way to say this is: zeros are only
significant if they are between significant digits
OR are the very final thing at the end of a
decimal

FOR EXAMPLE
How many significant digits are in the following numbers?
0.0002
6.02 x 1023
100.000
150000
800
1 Significant Digit
3 Significant Digits
6 Significant Digits
2 Significant Digits
1 Significant Digit
RULE #5
All counting numbers and constants have an
infinite number of significant digits
 For example:
1 hour = 60 minutes
12 inches = 1 foot
24 hours = 1 day

HOW MANY SIGNIFICANT DIGITS ARE IN THE
FOLLOWING NUMBERS?
0.0073
100.020
2500
7.90 x 10-3
670.0
0.00001
18.84
2 Significant Digits
6 Significant Digits
2 Significant Digits
3 Significant Digits
4 Significant Digits
1 Significant Digit
4 Significant Digits
RULES ROUNDING SIGNIFICANT DIGITS
RULE #1





If the digit to the immediate right of the last
significant digit is less that 5, do not round up
the last significant digit.
For example, let’s say you have the number
43.82 and you want 3 significant digits
The last number that you want is the 8 – 43.82
The number to the right of the 8 is a 2
Therefore, you would not round up & the
number would be 43.8
ROUNDING RULE #2




If the digit to the immediate right of the last significant
digit is greater that a 5, you round up the last
significant figure
Let’s say you have the number 234.87 and you want 4
significant digits
234.87 – The last number you want is the 8 and the
number to the right is a 7
Therefore, you would round up & get 234.9
ROUNDING RULE #3






If the number to the immediate right of the last
significant is a 5, and that 5 is followed by a non zero
digit, round up
78.657 (you want 3 significant digits)
The number you want is the 6
The 6 is followed by a 5 and the 5 is followed by a non
zero number
Therefore, you round up
78.7
ROUNDING RULE #4





If the number to the immediate right of the last
significant is a 5, and that 5 is followed by a zero, you
look at the last significant digit and make it even.
2.5350 (want 3 significant digits)
The number to the right of the digit you want is a 5
followed by a 0
Therefore you want the final digit to be even
2.54
SAY YOU HAVE THIS NUMBER
2.5250
(want 3 significant digits)
 The number to the right of the digit you want is
a 5 followed by a 0
 Therefore you want the final digit to be even
and it already is
 2.52

LET’S TRY THESE EXAMPLES…
200.99
(want 3 SF)
201
18.22
(want 2 SF)
18
135.50
(want 3 SF)
136
0.00299
(want 1 SF)
0.003
98.59
(want 2 SF)
99
SCIENTIFIC NOTATION
Scientific notation is used to express very large
or very small numbers
 I consists of a number between 1 & 10 followed
by x 10 to an exponent
 The exponent can be determined by the
number of decimal places you have to move to
get only 1 number in front of the decimal

LARGE NUMBERS







If the number you start with is greater than 1, the
exponent will be positive
Write the number 39923 in scientific notation
First move the decimal until 1 number is in front –
3.9923
Now at x 10 – 3.9923 x 10
Now count the number of decimal places that you
moved (4)
Since the number you started with was greater than
1, the exponent will be positive
3.9923 x 10 4
SMALL NUMBERS







If the number you start with is less than 1, the
exponent will be negative
Write the number 0.0052 in scientific notation
First move the decimal until 1 number is in front –
5.2
Now at x 10 – 5.2 x 10
Now count the number of decimal places that you
moved (3)
Since the number you started with was less than 1,
the exponent will be negative
5.2 x 10 -3
SCIENTIFIC NOTATION EXAMPLES
Place the following numbers in scientific notation:
99.343
9.9343 x 101
4000.1
4.0001 x 103
0.000375
3.75 x 10-4
0.0234
2.34 x 10-2
94577.1
9.45771 x 104
GOING FROM SCIENTIFIC NOTATION TO
ORDINARY NOTATION
You start with the number and move the
decimal the same number of spaces as the
exponent.
 If the exponent is positive, the number will be
greater than 1
 If the exponent is negative, the number will be
less than 1

GOING TO ORDINARY NOTATION EXAMPLES
Place the following numbers in ordinary notation:
3 x 106
6.26x 109
5 x 10-4
8.45 x 10-7
2.25 x 103
3000000
6260000000
0.0005
0.000000845
2250
SIG FIGS: ADDITION AND SUBTRACTION
The answer can only be as precise as the least
precise of the measurements to be added or
subtracted. The answer must be rounded to the
place of precision of the least precise of the
measurements.
 33.5 cm + 7.88 cm + 0.977 cm = 42.357 cm
ROUNDED = 42.4 cm tenths hundredths
thousandths Since TENTHS goes out the least
far, round the answer to the nearest TENTH

SIG FIGS: MULTIPLICATION AND DIVISION
The answer can contain only as many
significant figures as the measurement with
the least number of significant figures.
 67.23 cm X 9.22 cm = 619.584 cm2 ROUNDED
= 620. cm2 4 sig figs 3 sig figs Rounding the
answer to 3 sig figs, you need to put the
decimal point to show that the 0 is a sig fig.

Accuracy and Precision in Measurements
Accuracy: how close a measurement
is to the accepted value.
Precision: how close a series of
measurements are to one another or
how far out a measurement is taken.
A measurement can have high precision, but
not be as accurate as a less precise one.
30