Transcript The following are NEVER significant

Significant Figure Rules
Rules
The following are always
significant
•Non zero digits
•Zeros between non zero
digits
•Zero to the right of a non
zero digit and to the left of
a written decimal
•Finishing zeros to the
right of a decimal place
Examples
673 has 3
506 has 3
1.009 has 4
57.00 has 4
The following are NEVER
significant
•Zeros to the left of the
first non zero digit
0.67 has 2
0.004 has 1
EXCEPTIONS
•Counting numbers
•Exact conversion factors
30 days in June
100 cm in 1 m
Math in Significant Figures
• Multiplication and Division
– The # of significant figures in the
result is the same as the # in the
least precise measurement used
in the calculation
– 0.024 x 1244= (two significant
figures )
•
Sample Problem: Find the area of a
rectangle 2.1 cm by 3.24 cm.
– Solution: Area = 2.1 cm x 3.24 cm = 6.8cm2
Math in Significant Figures
• Addition and Subtraction
•
– The # of significant figures in the result has the same
number of decimal places as the least precise
measurement
– Round to the least # of decimal places
Sample Problem: Add 42.56 g + 39.460 g + 4.1g
Solution:
42.56 g
39.460 g
4.1 g
Sum = 86.1 g
Rules for Rounding
• In a series of calculations,
carry the extra digits through
to the final result, then round
• If the digit to be removed
– Is less than 5, the preceding digit
stays the same
– Is equal to or greater than 5, the
preceding digit is increased by 1
Scientific Notation
Why use Scientific
Notation?
M x 10n
• M is a number between 1 and
10
• n is an integer
• all digits in M are significant
– if n = (+)#, then move the
decimal to the right
• 1.0 x 105 = 100000
– If n = (-)#, then move the decimal
to the left
• 1.0 x 10-5 = .00005
Sample Problems
• Express these numbers in
decimal notation.
1. 8.32 x 10-2 _____________
2. 5.4 x 104 ______________
3. 9.67 x 103 _____________
4. 1.457 x 102_____________
5. 3.00 x 10-1 _____________
6. 2.22 x 10-6 _____________
Reducing to Scientific
Notation
1. Move decimal so that M is
between 1 and 10
2. Determine n by counting the
number of places the
decimal point was moved
a. Moved to the left, n is
positive
b. Moved to the right, n is
Sample Problems
•
47,000
_____________________
•
0.00047
____________________
•
0.4100
_____________________
•
421
_______________________
Mathematical Problems
•
Addition and subtraction
–
•
Multiplication
–
–
•
Operations can only be performed if
the exponent on each number is the
same
M factors are multiplied
Exponents are added
Division
–
–
M factors are divided
Exponents are subtracted (numerator
- denominator)
Sample Problems
1. (2.8 x 10 5) +(7.53 x 10 5)
________________________
2. (3.1 x 10 -2) (4.380 x 10 3)
________________________
3. (4.20 x 10 2) (0.040 x 10 -1)
________________________
4. 3.0 x 10 3 ÷ 1.2 x 10 4
________________________
5. 4.95 x 10 6 ÷ 2.33 x 10 -2
________________________