introduction to scientific notation & significant figures

Introduction to Scientific Notation & Significant

FiguresPacket #6

IntroductionA measurement is a

quantity that has both a unit and number

Measurements are fundamental to the experimental sciences.

Measurements, in science, utilize the International System of Measurements (SI).

Scientific Notation

Scientific NotationA given number is

written as the product of two numbersA coefficient and 10

raised to a power.

Converting to Scientific NotationPositive

Decimal point goes left

NegativeDecimal point goes

right

Addition & Subtraction

Multiplication & Division

Multiplication Table

Accuracy, Precision & Error

Accuracy, Precision & ErrorAccuracy

Measure of how close a measurement comes to the actual or true value of what ever is being measured.

Measure value is compared to correct value.

PrecisionIs a measure of how close

a series of measurements are to one another.

Two or more measurements are compared.

Accuracy, Precision & ErrorError

Experimental value – accepted value Experimental value

Value measure inside laboratory

Accepted Value Correct value based on

reliable references

Percent ErrorAbsolute value of the

error divided by accepted value, multiplied by 100 Percent Error = |Error|/Accepted Value * 100

Significant Figures

Significant FiguresEach of the digits of a

number that are used to express it to the required degree of accuracy, starting from the first nonzero digit.The significant figures

in a measurement include all of the digits that are known , plus a last digit that is estimated.

Significant FiguresRule #1Every nonzero digit in a reported

measurement is assumed to be significant.24.7 m0.743 m714 m

All three have three significant figures

Significant FiguresRule #2Zeros appearing between nonzero digits are

significant.7003 m40.79 m1.503 m

All have four significant figures

Significant FiguresRule #3Leftmost zeros appearing in front of nonzero

digits are not significant.0.0071 m0.42 m0.000099 m

All have two significant figures This issue is eliminated when writing in scientific

notation. 0.0071 = 7.1 * 10-3

0.000099 = 9.9 * 10-5

Significant FiguresRule #4Zeros at the end of a number and to the right

of a decimal point are always significant.43.00 m1.101 m9.000 m

All have four significant figures

Significant FiguresRule #5Zeros are the rightmost end of a measurement that lie to the

left of an understood decimal point are not significant if they serve as place holders to show the magnitude of the number.300 m7000 m27210 m

The zeros in these numbers are NOT significant One significant figure One significant figure Four significant figures

If the zeros were KNOWN MEASURED VALUES, then they would be significant.

Writing 300 m in scientific notation, 3.00*102 makes it clear that the zeros are significant.

Significant FiguresRule #6There are two situations in which numbers have an

unlimited number of significant figures.Counting

If one counts 23 students in a classroom, then there are EXACTLY 23 students. This value has an unlimited number of significant figures

Defined quantities within a system of measurement 60 mins = 1 hr 100 cm = 1 m

Each of these numbers has an unlimited number of significant figures.

However, exact quantities do not affect the process of rounding an answer to the correct number of significant numbers.

Significant FiguresProblemsHow many significant figures are in each

measurement and what ultimate rule applies?123 m40506 mm9.8000*104

22 meter sticks0.07080 m98000 m

Significant FiguresProblems II314.721 meters (four)0.001775 meters (two)8792 meters (two)

Addition & SubtractionSignificant Figures

Addition & Subtraction RuleThe answer to an addition or subtraction

calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.

Addition & SubtractionCalculate the sum of the three

measurements. Give the answer to the correct number of significant figures.12.52 meters + 349.0 meters + 8.24 meters

Solving the problemCalculate the sum and then analyze each

measurement to determine the number of decimal places required in the answer.

Addition & Subtraction IIAlign the numbers based upon what is

provided.Final answer should be 369.76 meters.The second measurement, 349.0 meters, has

the least number of digits after the decimal point.

The answer is rounded to 369.8 meters or 3.698 * 102 meters.

Multiplication & Division Significant Figures

Multiplication & Division RuleIn calculations involving multiplication and

division, one needs to round the answer to the same number of significant figures as the measurement with the least number of significant figures.

Examples7.55 meters * 0.34 meters2.10 meters * 0.70 meters2.4526 meters ÷ 8.4

Review