UNIT: Chemistry and Measurement

Objectives: Lesson 2 of 4• You will learn how to convert extremely large or small numbers into

scientific notation• You will learn the difference between the terms Accuracy and

Precision• You will be able to solve problems with Significant Figures

TOPIC: Measurement

QuickwriteIn 1-2 sentences answer one of the questions below:• What are some measurements you might take in a

Chemistry lab?• Why do you think it is important to make accurate and

precise measurements?• Finally, in your own words, try to define the term accurate:

Scientific Notation• To make large number seem small, scientist use something call

scientific notation• Lets look at the speed of light• Light travels 9,500,000,000,000,000 kilometers in one year• 9,500,000,000,000,000 written in scientific notation is -- 9.5 x 1015

• How did I get 9.5 x 1015?• By moving the decimal over 15 places between the 9 and the 5

9,500,000,000,000,000x 1015

Scientific Notation• You have about

50,000,000,000,000,000 cells in your body!

• Let’s write this in scientific notation

x 1016

Scientific Notation• Scientific notation is a useful way to represent

numbers that are very large or very small • All numbers are written in a form of exponents

of ten such as 9.5 x 1015

What is Scientific Notation?• A way to represent numbers that are very large

or small • Numbers are written in a form of exponents of

ten such as 9.5 x 1015

Practice:• Try to write 602,300,000,000,000,000,000,000 in

scientific notation:

602,300,000,000,000,000,000,000x 1023

Accuracy and Precision• It is important to make measurements that

are both accurate and precise • Accuracy is how close a measurement is to

the correct or accepted value• Precision is how close a measurement

agrees with other measurements of similar value

• Lets apply these terms to a dart board, and our bull's-eye is our “Accepted Value” then we can begin to understand the difference between Accuracy and Precision

Not Precise or Accurate

Precise, Not Accurate

Precise and Accurate

What is the difference between Accuracy and Precision?

• Accuracy is how close a measurement is to the correct or accepted value

• Precision is how close a measurement agrees with other measurements of similar value

Significant Figures• Whenever a measurement is made with a device such as a ruler or Graduated

Cylinder, a certain degree of estimate is required• For example, lets say we want to measure the length of this nail• We can see the that the length of the nail is between 1.5 and 1.6 centimeters• Because no scale exist between 1.5 and 1.6, we must estimate the nails length• Using a visual estimate, we could estimate the nails length as either 1.54 or

1.56 centimeters 1.54 cm 1.56 cm?

• So, which on is it? Is it 1.54 or 1.56 centimeters?• It is important to realize that the first two numbers are the same and are therefore

certain; however, the third estimate (hundredths place) can vary and is therefore uncertain

• Measurement always has some level of uncertainty• Significant Figures are numbers recorded in a measurement that include all certain

numbers plus the first uncertain numbercertain uncertain

What are Significant Figures?• The numbers recorded in a measurement that

include all certain numbers plus the first uncertain number

Significant Figure Rules• Chemistry requires many types of calculations and measurements• To help us obtain accurate and precise results, me must use a set rules known as

the Significant Figure Rules; these rules are as follows: All Nonzero integers or numbers count as significant

For example, in the number below this includes integers 7, 5, and 8

0.0070580

Zeros in front of nonzero numbers or integers are NOT significant For example, in the number below this includes the first three zeros

Zeros between nonzero integers or numbers are significantFor example, in the number below this includes the zero between 7 and 5

significant

NOT significant significant significant

Trailing zeros at the end of a number are only significant if the number contains a decimalFor example, in the number below this includes the zero after 8 because a decimal is present

5 significant figures TOTAL

Practice:• Determine the number of significant figures in

each measurement below:– A piece of magnesium metal weighs 0.0340 gramsAnswer: the number contains 3 significant figures– A piece of hair from a crime lab weighs 0.0050060 gramsAnswer: The number contains 5 significant figures

Rules for Rounding Off• Sometimes our calculators give us answers with a very large number of digits, therefore it

is important we learn how to round off• Consider the number below, it is made up certain place names• For example, the 8 is located in the thousands place• The 4 is located in the hundreds place• The 5 is located in the tens place• The 6 is located in the tenths place• The 5 is located in the hundredths place• The 3 is located in the thousandths place

845.653

thousands place

hundreds place tens place te

nths

plac

e

hund

redt

hs pl

ace

thou

sand

ths p

lace

• Lets say we want to round the number below to nearest hundredths place• Because the last digit, 3 is less than 5, our answer would be 845.65 • Now lets say we want to round the number below to the nearest tenths place• Remember, any number greater than or equal to 5, we round up, which gives us

an answer of 845.7 • It is important to realize that when you are performing calculations on a

calculator, only round off until you have arrived at your final answer

Practice:• Round each number below to the nearest “tenths”

place:– A piece of magnesium metal weighs 1.58 gramsAnswer: Because 8 is greater than or equal to 5, the answer is 1.6 grams

– A sample of water has a mass of 150.11 gramsAnswer: Because 1 is less than 5, the answer is 150.1

Significant Figure Rules in Calculations• You will often be performing calculations that involve multiplication, division, addition

and subtraction• When using significant figures in calculations, there are rules we must consider, these

rules are as follows:For multiplication or division, the number of significant figures in your answer will be the

same as the number with the smallest number of significant figuresFor example, let’s say you perform the following calculation below:

4.56 x 1.4 = 6.384, the smallest number 1.4, contains 2 significant figures, so our answer must contain two significant figures

Therefore our answer will be 6.43 significant

figures2 significant

figures

For addition and subtraction, the number of significant figures in your answer will be the same as the number with the smallest number of decimal placesFor example, let’s say you perform the following calculation below:

12.08 + 6.2 = 18.28, the number with the smallest number of decimal places is 6.2, so our answer must contain only one decimal place

Therefore our answer will be 18.32 decimal

places1 decimal

place

What are the Significant Figures Rules?Rules:

1. All Nonzero numbers count as significant 2. Zero's in front of nonzero numbers are NOT significant3. Zero's between nonzero numbers are significant4. Trailing zero's at the end of a number are only significant if the number

contains a decimal

Calculation Rules:5. For multiplication/division, the number of significant figures in your

answer will be the same as the number with the smallest number of significant figures

6. For addition/subtraction, the number of significant figures in your answer will be the same as the number with the smallest number of decimal places

Practice:• Solve each problem below, make sure your answer contains

the correct number of significant figures: (remember to round)5.18 x 2.23 x 1.1 = ??????Answer: 12 Because 1.1 has 2 significant figures, therefore our answer must contain only 2 significant figures

7.266 – 4.6= ??????Answer: 2.7 Because 4.6 has only one decimal place therefore our answer must contain only one decimal place (don’t forget to round up)

(1.33 x 2.8) + 8.41 = ??????Answer: 12.1 Because 1.33 x 2.8 = 3.724 = 3.7, 3.7 + 8.41 = 12.11, notice 3.7 has only one decimal place therefore our answer must contain only one decimal place

12

2.7

12.1

Summary (you can always write your own summary)

• In the expression (1.33 x 2.8) + 8.41 = 12.1, describe how you were able to determine the answer using significant figures

• Imagine you are measuring an object with a ruler, explain the difference between a certain and an uncertain measurement

• How many significant figures does 0.8060 contain?• How many significant figures does 22.1 contain?• Summarize the significant figure rules: