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 Use the following PRIORITIZED list to determine the number of sd’s in a measurement, calculation, or conversion

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

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. 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

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

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

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

Sig Figs – The Alternate Method A tlantic Ocean P acific Ocean

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

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

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

Find how many sd’s & precision cm300 cm 202 mm Ans: 4 sd to the.001 cmAns: 2 sd to the 10 cm (dm) Ans: 3 sd to the 1 mmAns: 0 sd – no unit

How to use SD rules when multiplying 1.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) 2.Multiply the measurements 3.Round the product to the lowest # of sd found in #1 –2.40 cm x 3 cm = (7.2 cm 2 ) = 7 cm 2