Transcript Significant Figures

Significant Figures
Physical Science
What is a significant figure?
• There are 2 kinds of numbers:
– Exact: the amount of money in your
account. Known with certainty.
– Approximate: weight, height—anything
MEASURED. No measurement is perfect.
– When a measurement is recorded only those
digits that are dependable are written down.
When to use Significant figures
– If you measured the width of a
paper with your ruler you might
record 21.7cm.
To a mathematician 21.70, or 21.700
is the same. 21.700cm
To a scientist 21.7cm and 21.70cm is
NOT the same. It means the
measurement is accurate to within
one thousandth of a cm.
Our instruments are crude and
open to human error.
• If you used an ordinary ruler,
the smallest marking is the mm,
so your measurement has to be
recorded as 21.7cm or to the
nearest 0.1 . If you use the
balances the best measurement
could only be to the nearest 0.01
How do I know how many Sig Figs?
• Rule #1: All digits are
significant starting with
the first non-zero digit
on the left.
12 - has 2 significant digits
367 – has 3 sig. digs
How do I know how many Sig Figs?
Rule # 2: In whole
numbers that end in zero,
the zeros at the end are
not significant. 300 – has 1
sig. fig. 4,500,000 – has 2 sig figs.
How many sig figs?
•7
• 40
• 0.5
• 0.00003
• 7 x 105
• 7,000,000
•1
•1
•1
•1
•1
•1
How do I know how many Sig Figs?
• Rule #3: If zeros are
sandwiched between
non-zero digits, the
zeros become
significant. 201 – has 3 sig
figs 340004 – has 6 sig figs.
How do I know how many Sig Figs?
• Rule # 4: If zeros are at
the end of a number
that has a decimal, the
zeros are significant.
23.00 – has 4 sig. figs 10.0 – has
3 sig. figs.
How do I know how many Sig Figs?
• Rule #4 cont.: These zeros
are showing how accurate
the measurement or
calculation are. The more
place values, the more
precise the number.
How many sig figs here?
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1.2
2100
56.76
4.00
0.0792
7,083,000,000
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•
•
•
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2
2
4
3
3
4
How many sig figs here?
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3401
2000
2100.0
5.00
0.00412
8,000,050,000
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4
1
5
3
3
6
What about calculations with
sig figs?
• Rule # 5: When adding or
subtracting, the answer can only
show as many decimal places as the
measured number having the fewest
decimal places. Significant digits aren’t
considered.
• For example, 0.14 + 1.2243 = 1.3643, but round to 1.36 (two
decimal places because 0.14 has only 2 decimal places.)
Rule # 6” Multiplying and
Dividing Significant Figures
• When multiplying or dividing, the
answer may only show as many
significant digits as the measured number
having the fewest significant digits.
• For example, 0.33 x 325.5 = 107.415, but
round to 110 (two significant digits
because 0.33 has only two significant
digits).
Add/Subtract examples
• 2.45cm + 1.2cm = 3.65cm,
• Round off to
= 3.7cm
• 7.432cm - 2cm = 5.432
round to
 5 cm
A couple of multiplying and
dividing examples
• 56.78 cm x 2.45cm = 139.111
• Round to
 139cm2
2
cm
• 715.8cm / 9.6cm = 74.5625 cm
• Round to ?
• 75 cm
2 sig. figs
The End
Have Fun Measuring and
Happy Calculating!