Transcript Significant Figures - Brookwood High School

Significant Figures
What is a significant figure?
• The precision of measurements are indicated
based on the number of digits reported.
• Significant figures are the digits that are
reported
•Approximate: weight, height—anything
MEASURED; no measurement is perfect.
When to use Significant figures
• When a measurement is recorded only
those digits that are dependable are written
down.
• Example: If you measured the width of a
piece of paper with your ruler you might
record 21.7cm.
-To a mathematician 21.70, or
21.700 is the same.
When To Use Significant Figures
• But, to a scientist 21.7cm and 21.70cm is
NOT the same.
• 21.700 cm to a scientist means the
measurement is accurate to within one
thousandth of a cm.
• If you used an ordinary ruler, the smallest
marking is the mm, so your measurement
has to be recorded as 21.7cm.
How do I know how many Significant
Figures?
Rules:
1. All digits are significant starting with the
first non-zero digit on the left.
(1, 2, 3, 4, 5, 6, 7, 8, 9)
**Exception to rule: In whole numbers that
end in zero, the zeros at the end are not
significant.
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?
Rules continued…
2. If zeros are sandwiched between non- zero digits,
the zeros become significant.
Ex. (103) (12.06)
3. If zeros are at the end of a number that has a
decimal, the zeros are significant.
Ex. (8.20); these zeros are showing how
accurate the measurement or
calculation are.
How many sig figs here?
•
•
•
•
•
•
1.2
2100
56.76
4.00
0.0792
7,083,000,000
•
•
•
•
•
•
2
2
4
3
3
4
How many sig figs here?
•
•
•
•
•
•
3401
2100
2100.0
5.00
0.00412
8,000,050,000
•
•
•
•
•
•
4
2
5
3
3
6
What about calculations with
significant figures?
Rule:
• When adding or subtracting measured numbers,
the answer can have no more places after the
decimal than the LEAST of the measured
numbers. OR, in other words, the smallest number
of sig figs in the problem are how many sig figs
you should record in your answer.
• Exponents MUST be equal before you add or
subtract!
Add/Subtract examples
• 2.45cm + 1.2cm = 3.65cm,
• Round off to
= 3.7cm
• 7.432cm + 2cm = 9.432
round to
 9cm
Multiplication and Division
Rule:
• When multiplying or dividing, the result can
have no more significant figures than the least
reliable measurement. OR, in other words, the
smallest number of sig figs in the problem are
how many sig figs you should record in your
answer.
• When multiplying, add exponents
• When dividing, subtract exponents
A couple of examples
• 56.78 cm x 2.45cm = 139.111
• Round to
 139cm2
• 75.8cm x 9.6cm = ?
2
cm
The End
Happy Calculating!