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 cm  c 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 cm  c m  SD’s and precision  a. 3 sd to the mm  b. 4 sd to the cm  c. 6 sd to the  m Translation: In between 0s must be measured

NOT 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)

NOT Rule 4: All zeros to the right of a decimal point but to the left of a nonzero digit are NOT significant.  Samples  a m  b g  c 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  L 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 g  b mm  c cm  d  SD’s and precision  a. 4 sd to the cg  b. 4 sd to the.01  m  c. 5 sd to the  m  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 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 cm 2 ) = 7 cm 2 How to use SD rules when multiplying/dividing

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

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

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

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

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

Killing Babies  Always put a 0 in front of a decimal point   .873 

Significant Figures

1) 400 2) ) ) 218 5) 320 6) ) )

Significant Figures 1) 4.0 x ) 1.67 x ) 5 x ) 2.00 x ) ) ) 52018) 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