Significant (Measured) Digits

Measuring with Precision

Defn: Those numbers that result from directly measuring an object. It shows the precision of the measurement.

Units must be included (no units no sd) The precision of the measurement depends

upon the measuring instrument Use the following PRIORITIZED list to determine

the number of sd’s in a measurement, calculation, or conversion

Significant Digits (sd)

Rule 1: All nonzero digits are significant (they were measured)

Samples a. 234 m b. 1678 cm c. 0.23 g

SD’s and precision

a. 3 sd to the m

b. 4 sd to the cm

c. 2 sd to the cg

Rule 2: All zeros between nonzero (or significant) digits are significant

Samples a. 202 mm b. 1003 cm c. 0.200105 m

SD’s and precision

a. 3 sd to the mm

b. 4 sd to the cm

c. 6 sd to the mm

Translation: In between 0s must be measured

Rule 3: Zeros to the right of a nonzero digit but to the left of an understood decimal are NOT significant unless otherwise indicated.

a. 200 cm b. 109,000 m c. 1,000,000 mm d. 200 cm e. 200 cm

a. 1 sd to the m b. 3 sd to the km c. 1 sd to the km d. 3 sd to the cm e. 2 sd to the dm

Translation: 0s at the end of a whole number are NOT measured unless marked.

(a bar over a zero indicates the last measured zero)

Rule 4: All zeros to the right of a decimal point but to the left of a nonzero digit are NOT significant.

Samples a. 0.0032 m b. 0.01294 g c. 0.00000002 L

SD’s and precision

a. 2 sd to the .1 mm

b. 4 sd to the .01 mg

c. 1 sd to the .01 mL

Translation: 0s in front of a number less than 1 are NOT measured.

Rule 5: All zeros to the right of a decimal point and following a nonzero digit are significant

Samples a. 20.00 g b. 0.07080 mm c. 1.0400 cm d. 45.00

SD’s and precision a. 4 sd to the cg b. 4 sd to the .01

mm c. 5 sd to the mm d. 0 sd

Translation: 0s at the end of a decimal number are measured.

Examine the number & go through rules IN ORDER

Rule 1 - underline any nonzero digits Rule 2 - underline any zeros between these Rule 3 - place an ‘n’ under the zeros at the

end of a whole number (after any overlined 0s)

Rule 4 - place an ‘n’ under zeros in front of a number less than one

Rule 5 - underline zeros at the end of a decimal number

Count the number of underlined digits = # sd

How to use this information when converting/evaluating measures

Rule: Your calculation (answer) must have the same precision as the LEAST precise original measurement

Find the number of significant digits in each of the starting numbers and note the lowest number of significant digits ex. 2.40 cm x 3 cm (lowest # of sd is 1)

Calculate your answer Round the answer to the lowest # of sd

found in #1 2.40 cm x 3 cm = (7.2 cm2) = 7 cm2

How to use SD rules when multiplying/dividing

Significant Figures

Significant Figures

All measurements are inaccurate Precision of measuring device Human error Faulty technique

Significant Figures

Measurements need to convey precision Must include degree of uncertainty Sig Figs tell us

Significant Figures

Significant Figures

1. Significant figures in a measurement include

all of the digits that are known precisely plus one last digit that is estimated.

Significant Figures

2. Non-zero digits are always significant.

103.230002

Significant Figures

3. All final zeros after the decimal point are significant.

12.740

0.0420

Significant Figures

4. Zeros between two other significant digits are always significant.

10.0

2004

6.000

Significant Figures

5. Zeros used only for spacing the decimal point are not significant.

100

0.00000233

Killing Babies

Always put a 0 in front of a decimal point 0.247 0.0042 .873

Significant Figures

Significant Figures

1)   400   2)    200.0

3)    0.0001 4)    218

5)  320   6)    0.00530

7)    22 568 8) 4755.50 

Significant Figures1)   4.0 x 103       2)    1.67 x 10-8

3)    5 x 1012    4)    2.00 x 104

5)  635.000 6)   22 000

7)    5201 8)    81 

Significant Figures

6. If you add or subtract, the answer is rounded to the same number of decimal places as the measurement with the least number of decimal places.

Significant Figures

7. If you multiply or divide two numbers, the answer is rounded off to the number of significant figures in the least precise term used in the calculation (i.e. the number with the fewest sig figs).

Calculations

Calculations