Significant Digits Ch 1 Notes. Significant Digits Used to round measured values when involved in calculations When in scientific notation, all numbers.

Significant DigitsSignificant Digits

Ch 1 NotesCh 1 Notes


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


Nonzero #’s are always significantNonzero #’s are always significant

349349 3 sig figs3 sig figs



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



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


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

Significant Digits Ch 1 Notes. Significant Digits Used to round measured values when involved in calculations When in scientific notation, all numbers.

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