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# Significant digits

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### Significant digits

1. 1. Significant (Measured) Digits Measuring with Precision
2. 2. Significant Digits (sd) <ul><li>Defn: Those numbers that result from directly measuring an object. It shows the precision of the measurement. </li></ul><ul><li>Units must be included (no units no sd) </li></ul><ul><li>The precision of the measurement depends upon the measuring instrument </li></ul><ul><li>Use the following PRIORITIZED list to determine the number of sd’s in a measurement, calculation, or conversion </li></ul>
3. 3. Rule 1: All nonzero digits are significant (they were measured) <ul><li>Samples </li></ul><ul><li>a. 234 m </li></ul><ul><li>b. 1678 cm </li></ul><ul><li>c. 0.23 g </li></ul><ul><li>SD’s and precision </li></ul><ul><li>a. 3 sd to the m </li></ul><ul><li>b. 4 sd to the cm </li></ul><ul><li>c. 2 sd to the cg </li></ul>
4. 4. Rule 2: All zeros between nonzero (or significant) digits are significant <ul><li>Samples </li></ul><ul><li>a. 202 mm </li></ul><ul><li>b. 1003 cm </li></ul><ul><li>c. 0.200105 m </li></ul><ul><li>SD’s and precision </li></ul><ul><li>a. 3 sd to the mm </li></ul><ul><li>b. 4 sd to the cm </li></ul><ul><li>c. 6 sd to the  m </li></ul>Translation: In between 0s must be measured
5. 5. Rule 3: Zeros to the right of a nonzero digit but to the left of an understood decimal are NOT significant unless otherwise indicated. <ul><li>a. 200 cm </li></ul><ul><li>b. 109,000 m </li></ul><ul><li>c. 1,000,000 mm </li></ul><ul><li>d. 200 cm </li></ul><ul><li>e. 200 cm </li></ul><ul><li>a. 1 sd to the m </li></ul><ul><li>b. 3 sd to the km </li></ul><ul><li>c. 1 sd to the km </li></ul><ul><li>d. 3 sd to the cm </li></ul><ul><li>e. 2 sd to the dm </li></ul>Translation: 0s at the end of a whole number are NOT measured unless marked. (a bar over a zero indicates the last measured zero)
6. 6. Rule 4: All zeros to the right of a decimal point but to the left of a nonzero digit are NOT significant. <ul><li>Samples </li></ul><ul><li>a. 0.0032 m </li></ul><ul><li>b. 0.01294 g </li></ul><ul><li>c. 0.00000002 L </li></ul><ul><li>SD’s and precision </li></ul><ul><li>a. 2 sd to the .1 mm </li></ul><ul><li>b. 4 sd to the .01 mg </li></ul><ul><li>c. 1 sd to the .01  L </li></ul>Translation: 0s in front of a number less than 1 are NOT measured.
7. 7. Rule 5: All zeros to the right of a decimal point and following a nonzero digit are significant <ul><li>Samples </li></ul><ul><li>a. 20.00 g </li></ul><ul><li>b. 0.07080 mm </li></ul><ul><li>c. 1.0400 cm </li></ul><ul><li>d. 45.00 </li></ul><ul><li>SD’s and precision </li></ul><ul><li>a. 4 sd to the cg </li></ul><ul><li>b. 4 sd to the .01  m </li></ul><ul><li>c. 5 sd to the  m </li></ul><ul><li>d. 0 sd </li></ul>Translation: 0s at the end of a decimal number are measured.
8. 8. How to use this information when converting/evaluating measures <ul><li>Examine the number & go through rules IN ORDER </li></ul><ul><li>Rule 1 - underline any nonzero digits </li></ul><ul><li>Rule 2 - underline any zeros between these </li></ul><ul><li>Rule 3 - place an ‘n’ under the zeros at the end of a whole number (after any overlined 0s) </li></ul><ul><li>Rule 4 - place an ‘n’ under zeros in front of a number less than one </li></ul><ul><li>Rule 5 - underline zeros at the end of a decimal number </li></ul><ul><li>Count the number of underlined digits = # sd </li></ul>
9. 9. When converting measurements <ul><li>Rule: The converted measurement must have exactly the same precision as the original measurement. </li></ul><ul><li>Ex. When converting 6.0 cg to dag is the conversion .006 dag or .0060 dag? </li></ul><ul><ul><li>6.0 cg has 2 sd so the conversion must have 2 sd. Which conversion has 2 sd? </li></ul></ul><ul><ul><li>Answer: .0060 dag </li></ul></ul>
10. 10. How to use SD rules when multiplying/dividing <ul><li>Rule: Your calculation (answer) must have the same precision as the LEAST precise original measurement </li></ul><ul><li>Find the number of significant digits in each of the starting numbers and note the lowest number of significant digits </li></ul><ul><ul><li>ex. 2.40 cm x 3 cm (lowest # of sd is 1) </li></ul></ul><ul><li>Calculate your answer </li></ul><ul><li>Round the answer to the lowest # of sd found in #1 </li></ul><ul><ul><li>2.40 cm x 3 cm = (7.2 cm 2 ) = 7 cm 2 </li></ul></ul>