Significant Figures But their friends call them sig figs…

“Only those who have the patience to do simple things perfectly will acquire the skill to do difficult things easily.” Johann von ShillerJohann von Shiller

Measurements Numbers in science class are measurements, and have a meaning. Numbers in science class are measurements, and have a meaning. In the measurement,.0045 cm, the zeros are just place holders for the measurement digits of 4 and 5. In the measurement,.0045 cm, the zeros are just place holders for the measurement digits of 4 and 5. We could rewrite this as 4.5x10 -3 without losing any accuracy, so these zeros don’t matter as much as the 4 and five. We could rewrite this as 4.5x10 -3 without losing any accuracy, so these zeros don’t matter as much as the 4 and five.

Sig Figs Numbers that are important in a measurement are called significant figures. Numbers that are important in a measurement are called significant figures. There are four simple rules we can follow to determine which numbers are sig figs in a measurement. There are four simple rules we can follow to determine which numbers are sig figs in a measurement.

Rule 1 Every nonzero number is a sig fig. Every nonzero number is a sig fig has two sig figs, the 2 and the has two sig figs, the 2 and the has four sig figs12.43 has four sig figs How about ?How about ? Three sig figs!Three sig figs!

Rule 2 Zeroes trapped are sig figs. Zeroes trapped are sig figs. 203 has three sig figs203 has three sig figs The two and three because of rule 1 The two and three because of rule 1 The zero is trapped, so it’s a sig fig The zero is trapped, so it’s a sig fig has four sig figs1.024 has four sig figs How many sig figs are in 609,000?How many sig figs are in 609,000? Three!Three!

Rule 3 Zeros on the left are not sig figs. Zeros on the left are not sig figs has two sig figs.0045 has two sig figs.0203 has three sig figs.0203 has three sig figs How many sig figs are in ?How many sig figs are in ? Four sig figs!Four sig figs!

Rule 4 Final zeros to the right of the decimal are sig figs. Final zeros to the right of the decimal are sig figs has four sig figs has four sig figs has five sig figs has five sig figs How many sig figs are in 3.00?How many sig figs are in 3.00? 3 sig figs!3 sig figs!

How many sig figs are in each measurement? x x (the 10 factor doesn’t count)

Why does this matter? When we use measurements to do math, we often end up with more digits than we started with. When we use measurements to do math, we often end up with more digits than we started with. Ex. Ex. Find the area of a triangle with a base of.3 cm and height of 1.5 cm.Find the area of a triangle with a base of.3 cm and height of 1.5 cm. Area =.225 cm 2Area =.225 cm 2 Problem, we have an answer that is accurate to the thousandths place, but the measurements were only accurate to the tenth.Problem, we have an answer that is accurate to the thousandths place, but the measurements were only accurate to the tenth.

Old Man! I’m Confused! I will show you a trick. I will show you a trick. Remember: tricks are useful, but don’t confuse them with understanding… Remember: tricks are useful, but don’t confuse them with understanding…

If there is a decimal… If there is a decimal, we bring an arrow from the left… If there is a decimal, we bring an arrow from the left… The arrow goes through any zeros. The arrow goes through any zeros. It stops when it hits a number. It stops when it hits a number. Everything left is a sig fig… Everything left is a sig fig…

If there is no decimal… If there is no decimal, we bring an arrow from the right… If there is no decimal, we bring an arrow from the right… The arrow goes through any zeros. The arrow goes through any zeros. It stops when it hits a number. It stops when it hits a number. Everything left is a sig fig… Everything left is a sig fig…

Assignment Page 51 Page and 8483 and 84 Add this to previous book work Add this to previous book work Need help? More info on sig figs can be found on pages 38-39, including some samples. Need help? More info on sig figs can be found on pages 38-39, including some samples.