Transcript Significant Digits - Plymouth High School

Significant Digits
Measuring with Precision
Significant Digits (sd)
• Defn: Those numbers that result from
directly measuring an object. It shows the
precision of the measurement.
• Units must be included (no units no sd)
• The precision of the measurement depends
upon the measuring instrument
• Use the following PRIORITIZED list to
determine the number of sd’s in a
measurement, calculation, or conversion
Rule 1: All nonzero digits are
significant (they were measured)
•
•
•
•
Samples
a. 234 m
b. 1678 cm
c. 0.23 g
•
•
•
•
SD’s and precision
a. 3 sd to the m
b. 4 sd to the cm
c. 2 sd to the cg
Rule 2: All zeros between nonzero
(or significant) digits are significant
•
•
•
•
Samples
a. 202 mm
b. 1003 cm
c. 0.200105 m
•
•
•
•
SD’s and precision
a. 3 sd to the mm
b. 4 sd to the cm
c. 6 sd to the mm
Rule 3: Zeros to the right of a nonzero digit
but to the left of an understood decimal are
NOT significant unless otherwise indicated.
•
•
•
•
•
Samples:
a. 200 cm
b. 109,000 m
c. 1,000,000 mm
d. 200 cm
• e. 200 cm
• SD’s and precision
•
•
•
•
a. 1 sd to the m
b. 3 sd to the km
c. 1 sd to the km
d. 3 sd to the cm
(the bar over the zero
indicates the last
measured zero)
• e. 2 sd to the dm
Rule 4: All zeros to the right of a decimal
point but to the left of a nonzero digit are
NOT significant.
•
•
•
•
Samples
a. 0.0032 m
b. 0.01294 g
c. 0.00000002 L
•
•
•
•
SD’s and precision
a. 2 sd to the .1 mm
b. 4 sd to the .01 mg
c. 1 sd to the .01 mL
Rule 5: All zeros to the right of a decimal
point and following a nonzero digit are
significant
•
•
•
•
•
Samples
a. 20.00 g
b. 0.07080 mm
c. 1.0400 cm
d. 45.00
•
•
•
•
•
SD’s and precision
a. 4 sd to the cg
b. 4 sd to the .01 mm
c. 5 sd to the mm
d. 0 sd
How to use this information when
converting/evaluating measures
• Examine the number & go through rules IN
ORDER
• Rule 1 - underline any nonzero digits
• Rule 2 - underline any zeros between these
• Rule 3 - place an ‘n’ under the zeros right of the
last nonzero and before the understood decimal
• Rule 4 - place an ‘n’ under the zeros to the left of
the last nonzero but right of the decimal
• Rule 5 - underline zeros right of the last nonzero
and right of a decimal
• Count the number of underlined digits = # sd
Sig Figs – The Alternate Method
Pacific
Ocean
Atlantic
Ocean
Finding Sig Figs using the A & P
• “A” stands for Absent
and Atlantic
• “P” stands for Present
and Pacific
• Place the number in the
middle of the U.S.
• Ask – “Is the decimal
point Absent or Present?”
P
20 400 m
A
Numbers Without Decimal Points
• If the decimal point is
NO Decimal Point
Absent think “A” –
– it is Absent
Absent = Atlantic
• Start from the Atlantic
A
20 400 m
coast & move through P
the number
• Count the first nonzero
digit you hit & every
The 2, 0, & 4 are significant
number to the left of it
There are 3 sd with precision
as significant digits
to the 100 m or hm
Numbers With Decimal Points
• If the decimal point is
Decimal Point – it
Present think “P” –
is Present
Present = Pacific
• Start from the Pacific
A
0.00920 dg
coast & move through P
the number
• Count the first nonzero
digit you hit & every
The 9, 2, & 0 are significant
number to the right of it
There are 3 sd with a
as significant digits
precision of .00001 dg or mg
Find how many sd’s & precision
1.040 cm
Ans: 4 sd to the .001 cm
202 mm
Ans: 3 sd to the 1 mm
300 cm
Ans: 2 sd to the 10 cm (dm)
45.006
Ans: 0 sd – no unit
How to use SD rules when
multiplying
1. Find the number of significant digits in
each of the starting numbers and note the
lowest number of significant digits
–
ex. 2.40 cm x 3 cm (lowest # of sd is 1)
2. Multiply the measurements
3. Round the product to the lowest # of sd
found in #1
– 2.40 cm x 3 cm = (7.2 cm2) = 7 cm2