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Significant Digits

Significant 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) The precision of the measurement depends upon the measuring instrument

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Significant Digits

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  1. Significant 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

  5. Samples: a. 200 cm b. 109,000 m c. 1,000,000 mm d. 200 cm e. 200 cm SD’s and precision a. 1 sd to the m b. 3 sd to the km c. 1 sd to the km d. 3 sd to the cm (the bar over the zero indicates the last measured zero) 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.

  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.

  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

  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 right of the last nonzero and before the understood decimal • Rule 4 - place an ‘n’ under the zeros to the left of the last nonzero but right of the decimal • Rule 5 - underline zeros right of the last nonzero and right of a decimal • Count the number of underlined digits = # sd

  9. Atlantic Ocean Pacific Ocean Sig Figs – The Alternate Method

  10. Finding Sig Figs using the A & P • “A” stands for Absent and Atlantic • “P” stands for Present and Pacific P 20 400 m A • Place the number in the middle of the U.S. • Ask – “Is the decimal point Absent or Present?”

  11. NO Decimal Point – it is Absent A P Numbers Without Decimal Points • If the decimal point is Absent think “A” – Absent = Atlantic • Start from the Atlantic coast & move through the number 20 400 m • Count the first nonzero digit you hit & every number to the left of it as significant digits The 2, 0, & 4 are significant There are 3 sd with precision to the 100 m or hm

  12. Decimal Point – it is Present A P Numbers With Decimal Points • If the decimal point is Present think “P” – Present = Pacific • Start from the Pacific coast & move through the number 0.00920 dg • Count the first nonzero digit you hit & every number to the right of it as significant digits The 9, 2, & 0 are significant There are 3 sd with a precision of .00001 dg or mg

  13. 1.040 cm 300 cm Find how many sd’s & precision Ans: 4 sd to the .001 cm Ans: 2 sd to the 10 cm (dm) 202 mm 45.006 Ans: 3 sd to the 1 mm Ans: 0 sd – no unit

  14. How to use SD rules when multiplying • 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) • Multiply the measurements • Round the product to the lowest # of sd found in #1 • 2.40 cm x 3 cm = (7.2 cm2) = 7 cm2

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