Transcript Significant Digits

Significant Digits
Uncertainty of Measurement
Three Rules
• Non-zero digits are significant
• Zeros between two significant digits
are significant
• Zeros at the right end of a number,
after a decimal point, are significant
Non-zero digits are significant
• Number
455.6
7.98
0.6224
5.2
• Significant Digits
4
3
4
2
Zero to left of decimal point
• 0.78895
5 significant digits
• The zero to the left of the decimal point
is there to communicate that the
decimal point is a decimal point convention
Problems!
• Numbers like
308.5
0.000811
5000
Zeros between non-zero digits are
significant
• Number
28.09
1008.91
3.005
2.03
• Significant Digits
4
6
4
3
Space Holding zeros on numbers
less than one
• 0.00678
• 0.030086
3 significant digits
5 significant digits
Trailing Zeros
• 200 is considered to have only one
significant digit
• 38,000 has two significant digits
Problem area
• 5000 might really have four
significant digits - an exact count or
measurement
• write number as 5000.
• Scientific notation used to indicate
significant digits
Review
•
•
•
•
•
78002.1
0.00006003
34.61
8.81
42,300
•
•
•
•
•
6
4
4
3
3
Multiplication & Division
• An answer cannot have more significant
digits than the measurement with the
least number of significant digits used
in the operation.
(3.006) X (0.0067) = 0.0201402
= 0.020
only 2 sig. Digits
Addition & Subtraction
• The answer is rounded to the least
number of places in the decimal portion
of any number in the operation
134.008
89.70
57.9
281.608 = 281.6