Significant figures or
Significant digits
• ANY numbers generated by means of a
measurement (length, volume, time, etc)
should be expressed in the correct number of
significant figures.
• This reflects how close the measured values
are to the true values.
1
Significant Figures (digits)
= reliable figures obtained by
measurement
= all digits known with certainty plus one
estimated digit
Taking the measurement
• Is always some uncertainty
• Because of the limits of the instrument you
are using
EXAMPLE: mm ruler
Is the length of the line between 4 and 5 cm? Yes,
definitely.
Is the length between 4.0 and 4.5 cm? Yes, it
looks that way.
But is the length 4.3 cm? Is it 4.4 cm?
• It is important to be honest when reporting a
measurement, so that it does not appear to
be more accurate than the equipment used to
make the measurement allows.
• We can achieve this by controlling the number
of digits, or significant figures, used to report
the measurement.
As we improve the sensitivity of the equipment used
to make a measurement, the number of significant
figures increases.
Postage Scale
3g
1g
1 significant
figure
Two-pan
balance
2.53 g
0.01 g
3 significant
figures
Analytical
balance
2.531 g
0.001g
4 significant
figures
Which numbers are Significant?
How to count them!
Non-Zero integers
• Always count as significant figures
1235 has 4 significant digits
Zeros – there are 3 types
Leading zeros (place holders)
The first significant figure in a measurement
is the first digit other than zero counting
from left to right
0.0045g
(4 is the 1st sig. fig.)
“0.00” are place holders.
The zeros are not significant
Captive zeros
Zeros within a number at always significant –
30.0809 g
All digits are significant
Trailing zeros – at the end of numbers but to the right of the
decimal point
2.00 g - has 3 sig. digits (what this means is that
the measuring instrument can measure exactly to two
decimal places.
100 m has 1 sig. digit
Zeros are significant if a number contains decimals
Exact Numbers
Are numbers that are not obtained by
measuring
Referred to as counting numbers
EX : 12 apples, 100 people
Exact Numbers
Also arise by definition
1” = 2.54 cm or 12 in. = 1 foot
Are referred to as conversion factors that allow
for the expression of a value using two
different units
Significant Figures
Rules for sig figs.:
•Count the number of digits in a measurement from left to
right:
•Start with the first nonzero digit
•Do not count place-holder zeros.
•The rules for significant digits apply only to measurements
and not to exact numbers
Sig figs is short for significant figures.
Determining Significant Figures
State the number of significant figures in the following measurements:
2005 cm
4
0.050 cm
2
25,000 g
2
0.0280 g
3
25.0 ml
3
50.00 ml
4
0.25 s
2
1000 s
1
0.00250 mol
3
1000. mol
4
Rounding Numbers
• To express answer in correctly
• Only use the first number to the right of the
last significant digit
Rounding
• Always carry the extra digits through to the
final result
• Then round
EX:
Answer is 1.331 rounds to 1.3
OR
1.356 rounds to 1.4
Significant Figures
Rounding off sig figs (significant figures):
Rule 1: If the first non-sig fig is less than 5, drop all non-sig fig.
Rule 2: If the first sig fig is 5, or greater that 5, increase the last
sig fig by 1 and drop all non-sig figs.
Round off each of the following to 3 significant figures:
12.514748
12.5
192.49032
192
0.6015261
14652.832
0.602
14,700