Chapter 4: Measurements and Significant Figures

A significant figure is a digit that is a reliable indicator of value.

Significant figure conventions guide us when we report the results of measurements so that what we report indicates the exactness of the measuring device.

Chapter 4: Measurements and Significant Figures

Chapter 4, Box 1 (p.53)1. The number of significant

figures is related to the certainty of a measurement or a count of great magnitude.

(number of microscopes in lab vs. number of sand grains on

beach)

Chapter 4, Box 1 (p.53)2. When reporting a measurement, record as many digits as are certain plus one digit that is estimated.

(with meter or ruler, estimate last place…..on digital display, assume instrument estimated last place)

Chapter 4, Box 1 (p.53)3. All non-zero digits in a number are significant.

(98.34 has four significant figures)

Chapter 4, Box 1 (p.53)4. All zeros between two non-zero digits are significant

(100.4 has four significant figures)

Chapter 4, Box 1 (p.53)5. Zero digits to the right of a non-zero digit but to the left of an assumed decimal point may or may not be significant.

$156,400,000

place holders,but not significantfigures

Chapter 4, Box 1 (p.53)6. All zeros to the right of a decimal point and to the right of a non-zero digit before a decimal place are significant.

340.000.340003.4000

all have five significant figures

Chapter 4, Box 1 (p.53)7. All digits to the left of a non-zero digit and to the right of a decimal point are not significant unless there is a significant digit to their left.

0.0098 two significant figures

0.4098 four significant figures

Chapter 4, Box 2 (p.55)1. It is assumed that the last digit of a result from a calculation is rounded.

2. When rounding:a. If the digit to be dropped is less than 5, the preceding digit remains the same.

Ex. 54.83 is rounded to 54.8

Chapter 4, Box 2 (p.55)2. When rounding:

b. If the digit to be dropped is 5 or more, the preceding digit increases by one.

Ex. 54.78 is rounded to 54.8

Ex. 54.65 is rounded to 54.7

Chapter 4, Box 2 (p.55)3. Round after performing a calculation.

4. Rule for addition or subtractionis different than for multiplication or division.

Depends on number of places to the right of the decimal point

Chapter 4, Box 2 (p.55)4. Rule for addition or subtractionis different than for multiplication or division.

Depends on number of places to the right of the decimal point (least)

98.0008 7.9878+56.2162.1886 round to 162.2

Chapter 4, Box 2 (p.55)5. In multiplication and division, keep as many significant figuresas are found in the number with the least significant digits.

0.54678 X 0.980 X 7.899 =

3 significant figures

4.23

Significant DigitsThe “Pacific-Atlantic” Rule for Significant Digits:

If a decimal is Present, start counting from the Pacific side

0.006501 2 3 3 significant

digits

first non-zero digit

Significant DigitsThe “Pacific-Atlantic” Rule for Significant Digits:

If a decimal is Absent, start counting from the Atlantic side

123030001235 significant

digits

first non-zero digit45