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
• Numbers like 308.5
0.000811
5000
Problems!
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 • •
0.00
678
0.0
30086 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
• 78002.1
• 0.00006003
• 34.61
• 8.81
• 42,300 Review • 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