Rounding

1
Rounding
2

• College slightly more sophisticated rule for
  rounding at 5s.
• Your book covers this in Appendix B.
• If you always round up at 5s, you will introduce
  statistical error into your data.
• For now, use the rules you learned in elementary
  school.

3
KNOW PLACE VALUE!

• 7492.638150
• Identify the place value of each digit.

• Round to the 10s place

7490

• Round to the thousandths place

7492.638
4
So, the general rules for rounding to the
________ place are
nth
5
Rounding to the ________ place.
nth

• LOOK TO THE RIGHT!
• Five or more, round up.
• Four or less, ignore.
• Rounding in front of the decimal, ignore means
  replace with zero. YOU CANNOT CHANGE THE PLACE
  VALUE!
• Rounding after the decimal, ignore means drop.

6
Lets Practice!
7
7492.638150

• Ones place

7493
Tenths place
7492.6
Round to the
7500
Hundreds place
Hundredths place
7492.64
Thousands place
7000
8
Significant Figures

• New Vocabulary
• Chemists use the number of sig figs to round to
  instead of place value.

9
Significant Figures

• All measurements involve significant figures.
• Exact numbers (counts and definitions) have an
  infinite number of sig figs.

10
How Many Sig Figs in a Measurement?

• 7492.638150 m
• Start counting from the left at the first
  non-zero integer.

This number has 10 sig figs!
11
How Many Sig Figs in a Measurement?

• 0.0073846152 m

This number has 8 sig figs!
12
How Many Sig Figs in a Measurement?

• 0.00492000 g

This number has 6 sig figs!
13
How Many Sig Figs in a Number?

• 544000

But this number has only 3 sig figs!
14
So what are the rules for significant figures?
15
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 are significant when a decimal
  point is present.
• Trailing zeros are not significant when a decimal
  point is absent.

16
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.

17
Rounding by sig figs

• Round 7492.638150 to

2 sig figs
7500
3 sig figs
7490
4 sig figs
7493
5 sig figs
7492.6
6 sig figs
7492.64