DETERMINING SIGNIFICANT FIGURES Crunching numbers with accuracy and precision

BEFORE YOU CAN CRUNCH You must know which digits are significant Because they are going to control the number of digits in a calculated figure 11/27/2018

WHAT IS A SIGNIFICANT FIGURE? Significant figures are all the digits in a measurement that are known with certainty plus a last digit that must be estimated. 11/27/2018

WHICH NUMBERS ARE SIGNIFICANT? For the purposes of significant figures there are two major categories Nonzero digits: 1,2,3,4,5,6,7,8,9 Zero digits: 11/27/2018

NONZERO DIGITS All nonzero digits are significant 3269 cm – 4 significant figures 257 L – 3 significant figures 1.234567 mm – 7 significant figures 11/27/2018

ZEROES Zeroes take three forms Leading zeroes Trapped zeroes Trailing zeroes 11/27/2018

LEADING ZEROES Leading zeroes are zeroes that come before the nonzero digits in a number. They are place holders only and are never considered significant. 0.123 L – 3 significant digits 0.000012 m – 2 significant digits 0.003578 mL – 4 significant digits 11/27/2018

TRAPPED ZEROES Trapped zeroes are zeroes between two nonzero digits. Trapped zeroes are always significant. 101 s – 3 significant figures 20013 m – 5 significant figures 0.3006 cm – 4 significant figures (the leading zero is not significant) 11/27/2018

TRAILING ZEROES Trailing zeroes are zeroes that follow nonzero digits. They are only significant if there is a decimal point in the number. 0.1200 mm – 4 significant figures 3000 s – 1 significant figure 250. mL – 3 significant figures 50.000 g – 5 significant figures 11/27/2018

Exact Numbers Numbers that were not obtained using measuring devices but by counting. They can also arise from definitions. They can be assumed to have an infinite number of significant figures. 11/27/2018

Examples of Exact Numbers 2 in 2r 3 and 4 in ¾ r3 Avogadro’s number is exactly 6.02 x 1023 One inch is exactly 2.54 cm 11/27/2018

Now you try How many significant digits in each of the following: 12 apples 3000 m 69 people 11/27/2018

Answers 1.034 s - 4 significant figures 0.0067 g - 2 significant figures 12 apples - exact number 3000 m - 1 significant figure 69 people - exact number 11/27/2018

Process for Addition/Subtraction Step #1: Determine the number of decimal places in each number to be added/subtracted. Step #2: Calculate the answer, and then round the final number to the least number of decimal places from Step #1.

Addition/Subtraction Examples Round to tenths place. Example #2: Round to hundredths place. Example #3: Round to ones place. 23.456 + 1.2 + 0.05 -------------- 24.706 Rounds to: 24.7 3.56 - 0.14 - 1.3501 --------------- 2.0699 2.07 14 + 0.735 + 12.0 26.735 27

Process for Multiplication/Division Step #1: Determine the number of sig figs in each number to be multiplied/divided. Step #2: Calculate the answer, and then round the final number to the least number of sig figs from Step #1.

Multiplication/Division Examples Round to 1 sig fig. Example #2: 2 sig figs. Example #3: 3 sig figs. 23.456 x 1.2 x 0.05 -------------- 1.40736 Rounds to: 1 3.56 x 0.14 x 1.3501 --------------- 0.67288984 0.67 14.0/ 11.73 1.193520887 1.19

Practice Example #1: Example #2: Example #3: . 23.456 x 4.20 x 0.010 -------------- Rounds to: ? 0.001 + 1.1 + 0.350 --------------- 17/ 22.73