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Significant (Measured) Digits

Significant (Measured) Digits. Measuring with Precision. Significant Digits (sd). 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)

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Significant (Measured) Digits

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  1. Significant (Measured) Digits Measuring with Precision

  2. Significant Digits (sd) • 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

  3. 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 1: All nonzero digits are significant (they were measured)

  4. 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 Rule 2: All zeros between nonzero (or significant) digits are significant Translation: In between 0s must be measured

  5. 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 Rule 3: Zeros to the right of a nonzero digit but to the left of an understood decimal are NOT significant unless otherwise indicated. 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. 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 Rule 4: All zeros to the right of a decimal point but to the left of a nonzero digit are NOT significant. Translation: 0s in front of a number less than 1 are NOT measured.

  7. 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 Rule 5: All zeros to the right of a decimal point and following a nonzero digit are significant Translation: 0s at the end of a decimal number are measured.

  8. How to use this information when converting/evaluating measures • 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

  9. When converting measurements • Rule: The converted measurement must have exactly the same precision as the original measurement. • Ex. When converting 6.0 cg to dag is the conversion .006 dag or .0060 dag? • 6.0 cg has 2 sd so the conversion must have 2 sd. Which conversion has 2 sd? • Answer: .0060 dag

  10. How to use SD rules when multiplying/dividing • 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

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