Significant Figures & Measurement. How do you know where to round? In math, teachers tell you In math, teachers tell you In science, we use significant.

Significant Figures & Significant Figures & MeasurementMeasurement

How do you know where to How do you know where to round?round?

• In math, teachers tell youIn math, teachers tell you• In science, we use significant In science, we use significant

figure rulesfigure rules

Figuring Out the RulesFiguring Out the Rules

• ““47.6 cm” has 3 sigfigs47.6 cm” has 3 sigfigs• ““3.981 cm” has 4 sigfigs3.981 cm” has 4 sigfigs• ““25 cm” has 2 sigfigs25 cm” has 2 sigfigs• So… what can we say about So… what can we say about

that?that?

RuleRule #1#1

All non zero digits All non zero digits are significant.are significant.

PracticePractice

• ““163.4 cm” has ____ sigfigs.163.4 cm” has ____ sigfigs.• ““28” has ____ sigfigs.28” has ____ sigfigs.• 893.27 has ____sigfigs.893.27 has ____sigfigs.

4

2

5

Figuring Out the RulesFiguring Out the Rules

• ““203 cm” has 3 sigfigs203 cm” has 3 sigfigs• ““6.004 cm” has 4 sigfigs6.004 cm” has 4 sigfigs• ““50.093 cm” has 5 sigfigs50.093 cm” has 5 sigfigs• So… what can we say about So… what can we say about

that?that?

RuleRule #2#2

Sandwiched zeros Sandwiched zeros are always are always significant.significant.

PracticePractice

• ““20.05 cm” has ____ sigfigs.20.05 cm” has ____ sigfigs.• ““201” has ____ sigfigs.201” has ____ sigfigs.• ““803.27” has ____sigfigs.803.27” has ____sigfigs.

43

5

Figuring Out the RulesFiguring Out the Rules

• ““0.004 cm” has 1 sigfig0.004 cm” has 1 sigfig• ““0.0203 cm” has 3 sigfigs0.0203 cm” has 3 sigfigs• ““0.16 cm” has 2 sigfigs0.16 cm” has 2 sigfigs• So… what can we say about So… what can we say about

that?that?

RuleRule #3#3

Leading zeros are Leading zeros are never significant.never significant.

PracticePractice

• ““0.0065 cm” has ____ sigfigs.0.0065 cm” has ____ sigfigs.• ““0.02003” has ____ sigfigs.0.02003” has ____ sigfigs.• ““0.837” has ____sigfigs.0.837” has ____sigfigs.

24

3

Figuring Out the RulesFiguring Out the Rules

• ““20 cm” has 1 sigfig20 cm” has 1 sigfig• ““20. cm” has 2 sigfigs20. cm” has 2 sigfigs• ““340 cm” has 2 sigfigs340 cm” has 2 sigfigs• ““340.0 cm” has 4 sigfigs340.0 cm” has 4 sigfigs• So… what can we say about So… what can we say about

that?that?

RuleRule #4#4

Zeros at the end Zeros at the end (trailing zeros) are only (trailing zeros) are only significant when there significant when there

is a decimal point is a decimal point somewhere in the somewhere in the

number.number.

PracticePractice

• ““25,000 cm” has ____ sigfigs.25,000 cm” has ____ sigfigs.• ““320.00 cm” has ____ sigfigs.320.00 cm” has ____ sigfigs.• ““430. cm” has ____ sigfigs.430. cm” has ____ sigfigs.

2

5

3

Significant Figure RulesSignificant Figure Rules

1.1. All nonzero digits are significant.All nonzero digits are significant.

2.2. Sandwich zeros are always Sandwich zeros are always significant.significant.

3.3. Leading zeros are never significant.Leading zeros are never significant.

4.4. Trailing zeros are only significant Trailing zeros are only significant when there is a decimal point when there is a decimal point somewhere in the number.somewhere in the number.

Rounding to a # of Sig FigsRounding to a # of Sig Figs

• At the end of your calculation, the At the end of your calculation, the calculator says “6848.5973”calculator says “6848.5973”– To 1 sig fig:To 1 sig fig:– To 2 sig figs:To 2 sig figs:– To 3 sig figs:To 3 sig figs:– To 4 sig figs:To 4 sig figs:– To 5 sig figs:To 5 sig figs:

700068006850

6849

6848.6

So, what about rounding?So, what about rounding?

• When doing calculations, the final When doing calculations, the final answer must contain the answer must contain the leastleast number of sigfigs.number of sigfigs.

• Example: (2.07 cm)(0.045 cm) = ?Example: (2.07 cm)(0.045 cm) = ?• Calculator says: 0.09315 cmCalculator says: 0.09315 cm22

• 2.07 has 3 sigfigs, 0.045 has 2 sigfigs2.07 has 3 sigfigs, 0.045 has 2 sigfigs• We use 2 sigfigs in our answer (least!)We use 2 sigfigs in our answer (least!)• So, 0.093 cmSo, 0.093 cm22 is correct! is correct!

More PracticeMore Practice

1.1. (0.20 cm)(5.66 cm) = ?(0.20 cm)(5.66 cm) = ?

2.2. (35.01 cm)(0.2 cm) = ?(35.01 cm)(0.2 cm) = ?

3.3. (0.0071 cm)(95,000 cm) = ?(0.0071 cm)(95,000 cm) = ?

1.1 cm1.1 cm22

7 cm7 cm22

670 670 cmcm22

More on roundingMore on rounding

• Round 150.093 to two significant figuresRound 150.093 to two significant figures• Start from left, count two figuresStart from left, count two figures• Look to the right of the second,Look to the right of the second,• Is it 5 or more, round upIs it 5 or more, round up• Make sure you leave zeros to place the Make sure you leave zeros to place the

decimal! (don’t truncate)decimal! (don’t truncate)• 15 does NOT = 150.093, it’s not even 15 does NOT = 150.093, it’s not even

close…150.093=150!close…150.093=150!

Any questions?Any questions?

I got one:I got one:What about What about

adding/subracting?adding/subracting?

Joke, get it?

Figuring Out the RulesFiguring Out the Rules

• 47.6 cm47.6 cm 13.348 cm 13.348 cm• ++3.981 cm3.981 cm -11.3 cm-11.3 cm• =51.6 cm=51.6 cm = 2.0 cm = 2.0 cm• So… what can we say about So… what can we say about

that?that?

Adding & Adding & subtractingsubtractingUse the least Use the least

amount of decimal amount of decimal places.places.

Don’t round until Don’t round until you are done you are done calculating!calculating!

PracticePractice

• 12.345+13.6512.345+13.65• =26.00=26.00• 2.3 - 1.212.3 - 1.21• Calculator says 1.0900..Calculator says 1.0900..• =1.1=1.1

Point to ponderPoint to ponder

• 2.5 x 102.5 x 1099 +2.300 x 10 +2.300 x 1033

• =2.5 x 10=2.5 x 1099 • AnotherAnother• 3.0 x 103.0 x 1088 – 23,0000 – 23,0000• = 3.0 x 10= 3.0 x 1088

It’s what significant means.It’s what significant means.2.5 x 109 is way bigger than

2.345 x 103

2.345 x 103 is insignificant compared to 2.5 x 109, it is smaller than the uncertainty in 2.5 x 109

2,500,000,000 (uncertainty is +/-50,000,000!)

+2,3452,500,002,345

2.5 x 109

Last oneLast one

• 1.50 x 101.50 x 1066 +2.345 x 10 +2.345 x 1055

• 1.50 x 101.50 x 1066

• +0.2345 x 10+0.2345 x 1066

• =1.73 x 10=1.73 x 1066

Make the exponents the same, youll need to move the decimal!

What’s the ruleWhat’s the rule

• Line up the decimalsLine up the decimals• In scientific, that means make them In scientific, that means make them

both have the same exponent (the both have the same exponent (the bigger one)bigger one)

• DoneDone