significant digits ch 1 notes. significant digits used to round measured values when involved in...
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Significant DigitsSignificant Digits
Ch 1 NotesCh 1 Notes
Significant DigitsSignificant Digits
Used to round measured values Used to round measured values when involved in calculations when involved in calculations
When in scientific notation, all When in scientific notation, all numbers on left side of number are numbers on left side of number are significantsignificant
Significant DigitsSignificant Digits
Nonzero #’s are always significantNonzero #’s are always significant
349349 3 sig figs3 sig figs
16391639 4 sig figs4 sig figs
Significant DigitsSignificant Digits
Leading Zeros are Leading Zeros are nevernever significant significant
0.00550.0055 2 sig figs2 sig figs
0.00000003930.0000000393 3 sig figs3 sig figs
Captive Zeros are Captive Zeros are alwaysalways significant significant59085908 4 sig figs4 sig figs
21000042100004 7 sig figs7 sig figs
Significant DigitsSignificant Digits
Trailing Zeros are significant Trailing Zeros are significant IFIF
there is a decimal point in the #there is a decimal point in the #
800800 1 sig fig1 sig fig
29002900 2 sig figs2 sig figs
800.0800.0 4 sig figs4 sig figs
2900.2900. 4 sig figs4 sig figs
Operations with Sig FigsOperations with Sig Figs
Multiplication/Division rule:Multiplication/Division rule:
Retain the same number of sig Retain the same number of sig figs in the answer as the factor figs in the answer as the factor containing the least number of sig containing the least number of sig figs.figs.
4.5 x 2 = 9.0 4.5 x 2 = 9.0 rounds to 9rounds to 9
2000 x 21 = 420002000 x 21 = 42000 rounds to 40000rounds to 40000
11 x 3 x 212 = 6996 11 x 3 x 212 = 6996 rounds to 7000rounds to 7000
Operations with Sig FigsOperations with Sig FigsAddition/Subtraction RuleAddition/Subtraction Rule
leave the answer rounded to the leave the answer rounded to the same precision (same decimal place) same precision (same decimal place) as the least precise number involved as the least precise number involved in the operation.in the operation.
2 + 2.3 = 4.3 2 + 2.3 = 4.3 rounds to 4rounds to 4120 + 11 = 131120 + 11 = 131 rounds to rounds to
1301301.65 + 3 – 2.90 = 1.75 1.65 + 3 – 2.90 = 1.75 rounds to 2rounds to 2
Sig Fig ExamplesSig Fig Examples
#1: 23.0#1: 23.0
4.254.25
+ 25,620+ 25,620
#2:#2: 2.3 x 102.3 x 10-4-4
316316
Examples SolutionsExamples Solutions#1: 23.#1: 23.00
4.74.755
+ 25,6+ 25,62200
25,625,6447.757.75
rounds torounds to 25,65025,650
#2:#2: 2.3 x 102.3 x 10-4-4 2sf2sf
316316 3sf3sf
== 7.27.27 x 107 x 10-7-7
rounds to 7.3 x 10rounds to 7.3 x 10-7-7
Sig Fig Situation #1: Let’s Not But Sig Fig Situation #1: Let’s Not But Say We DidSay We Did
Don’t worry about rounding combo Don’t worry about rounding combo problems until all the work in the problems until all the work in the calculator is done, but heed the rules calculator is done, but heed the rules as if you did to find out # of digits as if you did to find out # of digits needed in the end:needed in the end:(3.5 + 2.9454) / 357 = (6.4454)/357(3.5 + 2.9454) / 357 = (6.4454)/357= 0.018054341= 0.018054341Rounding: addition to tenths digit, which Rounding: addition to tenths digit, which
would leave 2 sig figs. 2 sig figs divided would leave 2 sig figs. 2 sig figs divided by 3 sig figs leaves 2 in answer: by 3 sig figs leaves 2 in answer: 0.0180.018
Sig Fig Situation #2: Less than Sig Fig Situation #2: Less than ZeroZero
2000 (1 sig fig) vs. 2001 (4 sig figs)2000 (1 sig fig) vs. 2001 (4 sig figs)
What if you want 2000 to have 4 sig What if you want 2000 to have 4 sig figs like 2001?figs like 2001?
2.000 x 102.000 x 103 3 for 4 sig figsfor 4 sig figs
2.00 x 102.00 x 1033 for 3 sig figs for 3 sig figs
2.0 x 102.0 x 1033 for 2 sig figs for 2 sig figs
2 x 102 x 1033 for 1 sig fig for 1 sig fig
Sig Figs Situation #3: Exact #’sSig Figs Situation #3: Exact #’sWhenever a quantity has no Whenever a quantity has no uncertainty, it does not affect the # uncertainty, it does not affect the # of sig figs in answer if x/÷/+/-of sig figs in answer if x/÷/+/-
Ex: four sides of a square…if one Ex: four sides of a square…if one side has a length of 2.0 m, then side has a length of 2.0 m, then 4 (exact #) x 2.0 m = 8.4 (exact #) x 2.0 m = 8.00 m (retain m (retain two sig figs cause exact # doesn’t two sig figs cause exact # doesn’t matter to sig fig roundingmatter to sig fig rounding
Sig Figs Situation #4: Units!Sig Figs Situation #4: Units!
Units are to be treated in the same Units are to be treated in the same algebraic sense as variablesalgebraic sense as variables
Units do not affect sig figs but must be Units do not affect sig figs but must be common to add/subtract valuescommon to add/subtract values23 g + 32.00 g = 55.00 rounds to 23 g + 32.00 g = 55.00 rounds to 5555 gg
23 g x 32.00 g = 736.0000 rounds to 23 g x 32.00 g = 736.0000 rounds to 740740 gg22
23 kg + 27 ml 23 kg + 27 ml cannot be simplified cannot be simplified