Calculating and using significant figures What’s the point why do scientist need to know them?

 There are 2 different types of numbers  Exact  Measured  Exact numbers are infinitely important 2

5 bucks $5.23

4 An exact number is obtained when you count objects or use a defined relationship. Counting objects are always exact 2 soccer balls 4 pizzas Exact relationships, predefined values, not measured 1 foot = 12 inches 1 meter = 100 cm

 Observed values of experimental quantities have inherent uncertainties.  These uncertainties should always be kept in mind when performing calculations with those values.

In this example the measurements were only made to one decimal

In reality If there is a decimal then count all digits, because nobody ever writes: With a decimal, arrow from left to right to first non zero and count digits = 4 sig figs = 7 sig figs = 11 sig figs

100 = 1 sig fig 321,000,000 = 3 sig figs 21,956 = 5 sig figs

Sig Fig Questions  For each of the numbers below, work out the correct number of sig fig.    100   

 The number of sig figs after multiplication or division is equal to the number of sig figs in the least accurately known quantity  The number of decimals places after addition or subtraction is equal to the smallest number of decimal places in any of the individual terms

The number of sig figs after multiplication or division is equal to the number of sig figs in the least accurately known quantity Two sig figs

The number of sig figs after multiplication or division is equal to the number of sig figs in the least accurately known quantity One sig fig

The number of sig figs after multiplication or division is equal to the number of sig figs in the least accurately known quantity Three sig figs

The number of decimals places after addition or subtraction is equal to the smallest number of decimal places in any of the individual terms (or number of place values between first and last none zero if no decimal) Since each given number is to one decimal place the answer should be to 1 decimal place Correct answer would be 13.0

The number of decimals places after addition or subtraction is equal to the smallest number of decimal places in any of the individual terms Since each given number is to one decimal place the answer should be to 1 decimal place Correct answer would be 10 Weird I know but the level of accuracy in the first number is the 10’s so our answer can’t be more accurate than that!

The number of decimals places after addition or subtraction is equal to the smallest number of decimal places in any of the individual terms Since each given number is to one decimal place the answer should be to 1 decimal place Correct answer would be 10 HundredsTensUnits1/10ths 100

The number of decimals places after addition or subtraction is equal to the smallest number of decimal places in any of the individual terms (or number of place values between first and last none zero if no decimal) HundredsTensUnits1/10ths Would be considered to have three place values

The number of decimals places after addition or subtraction is equal to the smallest number of decimal places in any of the individual terms Since each given number is to one decimal place the answer should be to 1 decimal place Correct answer would be 20 Since the answer is 18 we would round up to get 20

 ADDITION AND SUBTRACTION:  Limiting factor:  NUMBER OF DECIMAL PLACES*  MULTIPLICATION AND DIVISION:  Limiting factor:  NUMBER OF SIGNIFICANT FIGURES.