Transcript Sig Digs- Sci 10

All measurements are subject to
uncertainties. All instruments used are
influenced by external circumstances,
and the accuracy of a measurement may
be affected by the person making the
reading.
In everyday language, the words precise and
accurate mean roughly the same thing . . . not
in science.
A measurement is accurate if it is close to the
accepted value.
The accuracy of an individual
measurement depends on the
quality and performance of the
instrument used to make the
measurement.
The precision of a measurement is the degree of exactness
to which it can be reproduced. After taking a lot of
measurements, you will find that they are close to each
other.
The precision of an instrument is
limited by the smallest division on
the measurement scale.
For example,
A measurement of the mass of the
clock made with this scale would
be more precise
than a
measurement
made with this
one.
When you read any measuring
device, you always record the
measurement by . . . .
reading the smallest division on the scale and then
“guessing at” or estimating, the tenth of the smallest
division.
Record the correct readings on the ruler.
a) 13.50 cm
c) 14.35 cm
b) 11.10 cm
d) 12.26 cm
e) 12.63 cm
= estimated digit
Record the correct readings from the thermometers.
32.6 °C
8.95 °C
8.2 °C
- 8.3 °C
= estimated digit
I can “sig dig” it.
Grooovy baby!
Significant digits are all those
digits obtained from a properly taken
measurement: all of the certain digits plus the
one estimated digit.
The number of significant digits indicates the precision of
the measurement. More sig digs means a more precise
measurement.
For example,
less precise
10.0 cm
10.0365 cm
more precise
Count from left to right, beginning with the first digit that
is not zero.
Do not count zeros that are in front of a value, these are
merely placeholders.
Exact numbers have an infinite number of significant
digits, because they do not involve an estimated
measurement. Exact numbers are:
eg. 1000 m = 1 km
a) numbers that are definitions
1 dozen = 12
b) numbers that result
eg. 40 students
from counting objects
150 books
For each of the following measured values,
indicate the number of significant digits.
1) 12.7 m
these zeros are
placeholders
3
2) 10.03 kg 4
3) 0.0034 s
2
4) 200 min
3
5) 200 students
infinite
6) 2.746 x 1012
4
What happens when we perform
mathematical operations with these
estimated, measured values?
The result contains some significant
figures and some that are not because the
arithmetic was performed with uncertain
numbers. Our answer can NEVER be
more precise than the least precise value
we used in our calculations.
When adding or subtracting, add or subtract, then round
off the answer to the least number of decimal places of
the numbers that you used.
1) 42.3 g + 16.452 g = 58.8 g
2) 924 + 63.2 + 27.54 = 1015
3) 205.65 kg – 60 kg = 146 kg
When multiplying or dividing, multiply or divide, then
round off the answer to the least number of significant
digits of the numbers that you used.
1) 1.32 m × 0.4 m = 0.5 m2
2) 0.00543  8.33 x 10-5
65.2
3) 25.7 × 2403 = 6.18 × 104
4) 0.0028 × 983 ÷ 6.5 × 10-7 = 4.2 x 106
When doing a series of calculations to arrive at an answer,
never round off your sub-steps. Only round your final
answer. If possible, keep the significant digits in your
calculator. A good rule of thumb is to write three more
significant digits than you’ll need to round to at the end.
Sig Digs review sheet