Section 4 Approximate Numbers and Significant Digits

1
Chapter 2

• Section 4 Approximate Numbers and Significant
  Digits

2
Approximate Numbers

• Measurements are approximations
• Some fractions represented by decimals
• Irrational numbers represented by decimals

3
Exact Numbers

• Numbers from counting.
• Number of people in this room.
• Number of cars in the Bldg 100 lot
• Definitions
• 1 inch 2.54 cm

4
Significant Digits

• Format computation results.
• Understand the quality of a measurement.
• All non-zero numbers are significant.
• 23.5 125 1.1 1428.55
• Zeros located between non-zero digits are
  significant.
• 205 10.4 1007
• Zeros used as placeholders are not significant.
• 5,000 14,000 0.065 0.002
• Zeros to right of a significant digit in a
  decimal number are significant.
• 2.30 1.500 34.50

5
Examples

• Determine the number of significant digits for
  each approximate number
• 87,000
• 408,000
• 4.0005
• 0.04
• 4.000
• 0.000503

2 significant digits
3 significant digits
5 significant digits
1 significant digit
4 significant digits
3 significant digits
6
Accuracy Precision

• Accuracy of a Decimal Number
• Determined by the number of significant digits
• 23.5 1.055 0.02
• Precision of a Decimal Number
• Determined by the location of rightmost
  significant digit.
• 23.5 1.055 0.02

7
Examples

• State the precision and accuracy of each
  approximate number
• 1.25
• 0.008
• 12,000

P hundredths A 3 sig. digits
P thousandths A 1 sig. digit
P thousands A 2 sig. digits
8
Rounding

• Round each of the following approximate numbers
  to three significant digits
• 5.713
• 4096
• 501.46
• Round each of the following approximate numbers
  to two significant digits
• 0.21505
• 53.72
• 287.4

5.71
4100
501
0.22
54
290
9
Adding/Subtracting Measurements

• Base your finished result upon the precision of
  the least precise number.
• Precision is based on the rightmost significant
  digit.
• 35.5 cm 16.485 cm 51.985 cm
• 52.0 cm

10
Multiplying and Dividing Measurements

• When multiplying or dividing approximate numbers
  (measurement numbers)
• Answer based on number with the fewest
  significant digits.
• 12.1 x 15.6
• 123.56 x 2.21
• 18.21 ? 5.6
• 123.56 ? 2.21

11
Roots

• When the root of an approximate number is found,
  the accuracy of the result is the same as the
  accuracy ( of significant digits) of the
  original number.

1.58113883
1.6
4.101219331
4.101
12
Practice

• MathXL Ch 2 Section 4 Homework
• Ch 2 Practice Test
• Ch 2 Graded Test