• College – slightly more sophisticated rule for rounding at 5’s. – Your book covers this in Appendix B.

• If you always round up at 5’s, you will introduce statistical error into your data.

• For now, use the rules you learned in elementary school.

KNOW PLACE VALUE!KNOW PLACE VALUE!

7492.6381507492.638150• Identify the place value of each digit.

• Round to the 10’s place: 74907490

• Round to the thousandthth’s place: 7492.6387492.638

So, the general rules So, the general rules for rounding to the for rounding to the ________ place are…________ place are…nnthth

Rounding to the ________ place.

LOOK TO THE RIGHT!LOOK TO THE RIGHT!• Five or more, round up.• Four or less, ignore.

– Rounding in front ofin front of the decimal, ignore ignore means ‘replace with zeromeans ‘replace with zero.’ YOU YOU CANNOT CHANGE THE PLACE CANNOT CHANGE THE PLACE VALUE!VALUE!

– Rounding afterafter the decimal, ignore means ignore means dropdrop.

nnthth

Let’s Practice!Let’s Practice!

7492.6381507492.638150One’s place: 74937493

Tenth’s place: 7492.67492.6

Hundred’s place: 75007500

Hundredth’s place: 7492.647492.64

Thousand’s place: 70007000

Significant Figures

• New Vocabulary

• Chemist’s use the number of sig figs to round to instead of place value.

Significant Figures

• All measurementsmeasurements involve significant figures.

• Exact numbers (counts and definitions) have an infinite number of sig figs.

How Many Sig Figs in a Measurement?

7492.638150 m7492.638150 m• Start counting from the Start counting from the leftleft at the first at the first

non-zeronon-zero integer. integer.

This number has 10 sig figs!

How Many Sig Figs in a Measurement?

0.0073846152 m0.0073846152 m

This number has 8 sig figs!

How Many Sig Figs in a Measurement?

0.00492000 g0.00492000 g

This number has 6 sig figs!

How Many Sig Figs in a Number?

544000544000

But this number has only 3 sig figs!

So what are the rules for So what are the rules for significant figures?significant figures?

Rules for counting sig figs

• Non-zero digits are always significant.• Captive zeros are always significant.(Captive means a zero between 2 other sig figs.)• Leading zeros are never significant.• Trailing zeros areare significant when a

decimal point is presentpresent.– Trailing zeros are notnot significant when

a decimal point is absentabsent.

Once in a blue moon …Once in a blue moon …

•5300 cm•Ordinarily for decimal point absent, there would be 2 sig figs, but the bar over the zero makes it a sig fig! Now there are 3.

_

Rounding by sig figs

Round 7492.6381507492.638150 to to

2 sig figs: 75007500

3 sig figs: 74907490

4 sig figs: 74937493

5 sig figs: 7492.67492.6

6 sig figs:

7492.647492.64