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.

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Presentation transcript:

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! Identify the place value of each digit. Round to the 10’s place:7490 thRound to the thousandth’s place:

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

Rounding to the ________ place. LOOK TO THE RIGHT! Five or more, round up. Four or less, ignore. in front ofignore means ‘replace with zeroYOU CANNOT CHANGE THE PLACE VALUE! –Rounding in front of the decimal, ignore means ‘replace with zero.’ YOU CANNOT CHANGE THE PLACE VALUE! afterignore means drop –Rounding after the decimal, ignore means drop. n th

Let’s Practice!

One’s place:7493 Tenth’s place: Hundred’s place: 7500 Hundredth’s place: Thousand’s place:7000

Significant Figures New Vocabulary Chemist’s use the number of sig figs to round to instead of place value.

Significant Figures measurementsAll measurements involve significant figures. Exact numbers (counts and definitions) have an infinite number of sig figs.

How Many Sig Figs in a Measurement? m Start counting from the left at the first non-zero integer.Start counting from the left at the first non-zero integer. This number has 10 sig figs!

How Many Sig Figs in a Measurement? m This number has 8 sig figs!

How Many Sig Figs in a Measurement? g This number has 6 sig figs!

How Many Sig Figs in a Number? But this number has only 3 sig figs!

So what are the rules for 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. are presentTrailing zeros are significant when a decimal point is present. not absent –Trailing zeros are not significant when a decimal point is absent.

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 to Round to 2 sig figs: sig figs: sig figs: sig figs: sig figs: