Chem-To-Go Lesson 2Unit 1

SIGNIFICANT FIGURES

1) Determine the units used on the ruler.2) Look closely to determine the smallest marking on the ruler.3) Record your measurement, including all markings PLUS ONE

ESTIMATED DIGIT.

HOW TO USE A RULER

Example: Measure the black line.1)Units: 2)Smallest marking:3)All markings PLUS ONE ESTIMATED DIGIT:

Using this ruler, we decided that our line is 5.70 cm long.

Let’s evaluate the importance of each digit in the measurement:

5.70 cm

SIGNIFICANT FIGURES

• The 5 communicates that the line is at least 5 cm long…not 4 or 6.• The 7 communicates that the line is over 5 cm long, and our eyes

can look closely to see that the line is 7/10 passed the 5 cm mark.• The 0 communicates that MY EYES see the line ends EXACTLY at the

7/10 mark.

All 3 digits report

information.

Situation: Your lab partner is using the ruler, and you are recording the measurements. She calls out:

Length = 14.52 cmWidth = 10.45 cmHeight = 5.31 cm

Which digits do you know that she is estimating?

If four sets of lab partners measured the same object, do you expect them to get the same measurements?

What if the lab groups were asked to calculate the volume of the object? Would their answers be the same?

RECOGNIZING SIG FIGS

Estimated digits give information, BUT they can lead to disagreements

in data.

Between a rock and a hard place: The estimated digit gives important info BUT it creates a problem with reliability.

Special rules for calculating measurements exist to ease the problem.

AGREEMENT IN CALCULATIONS

RULES FOR ADDITION & SUBTRACTION

1) Line up the decimals. If the measurements were made by the same instrument, then they should go to the same decimal place.

2) Identify the “shortest” number. (Least number of decimal places)

3) Imagine (or draw) a vertical line at the end of the shortest number.

4) Add or subtract.5) Round your answer at the line.

13.510 g + 2.522 g + 1.78 g

13.510 g 2.522 g

+1.78 g 17.812 g

FINAL ANSWER: 17.81 g

Multiplication and division rules require you to assess the numbers that you’ll be multiplying or dividing.

You’ll need to count how many digits in each number are significant. Zeros complicate our counting. We’ll learn to deal with them in class tomorrow.

AGREEMENT IN CALCULATIONS

RULES FOR MULTIPLICATION & DIVISION

1) Count the significant figures in each number.

2) Multiply or divide as usual.3) Round to the least number of

significant figures. Your answer cannot be more specific than your least specific answer.

Length = 14.52 cmWidth = 10.45 cmHeight = 5.31 cm

4 sig figs4 sig figs3 sig figsLeast # of sig figs is 3,

so my answer can only have 3 digits.

FINAL ANSWER: 806 cm3

Volume = 805.70754 cm3