Words to Know Qualitative measurements – results

are in a descriptive, nonnumeric form

(Forehead feels hot)

Quantitative – results are in a definite form, usually as numbers or units (Temperature is 1020 F)

Objectives

Distinguish among the accuracy, precision, and error of a measurement

Identify the number of significant figures in a measurement and in the result of a calculation

Words to Know Accuracy – a measure

of how close a measurement comes to the actual or true value of whatever is measured

(Closeness of a dart to the bull’s-eye)

Precision – a measure of how close a series of measurements are to one another; depends on more than one measurement (The closeness of several

darts to one another-reproducibility)

Accepted value – correct value based on reliable references (Example: Boiling point of pure water is 1000C at standard atmospheric pressure)

Experimental value – value measured in the lab

Error = experimental value minus accepted value

Error can be positive or negative number

Practice A thermometer measures the boiling

point of pure water at standard atmospheric pressure. It reads 99.10C.

What is the accepted value? What is the experimental value? What is the error? Ans. – Acc (1000C) Exp (99.10C) Error is 99.10C – 1000C, or -0.90C

Percent Error (Relative Error)

Percent error is the absolute value of the error divided by the accepted value, multiplied by 100%

Using absolute value means that the percent error will always be a positive value

Calculate the percent error for the boiling pure water

Answer

Percent error = (absolute value of the error ÷ accepted value) x 100%

.90C ÷ 100.00C = 0.009 0.009 x 100% Move decimal point two places to the

right Answer is 0.9%

Significant Figures All the digits that are known, plus a last digit

that is estimated Every non-zero digit is significant. Examples: There are three significant

figures in 24.7 meters, 0.743 meters, and 714 meters.

Zeros appearing between non-zero digits are significant.

Examples: There are four significant digits in 7003 meters, 40.79 meters, and 1.503 meters.

Leftmost zeros appearing in front of non-zero digits are not significant. They act as placeholders.

Examples: 0.0071 meter, 0.42 meter, and 0.000099 meter each have only two significant figures.

Write these numbers in scientific notation to get rid of placeholding zeros.

Answers

Decimal point moves to the right, so all exponents will be negative numbers

7.1 x 10-3 meter 4.2 x 10-1 meter 9.9 x 10-5 meter

Zeros at the end of a number and to the right of a decimal point are always significant.

Examples: 43.00 meters, 1.010 meters, and 9.000 meters each have four significant figures

In a number that has no decimal point, zeros at the rightmost end of the measurement are not significant if they serve as placeholders to show the magnitude of the number.

Examples: 2500 meters 460,000 meters, and 16,000 meters each have 2 significant figures

If such zeros were known measured values, however, then they would be significant and should be written in scientific notation.

Examples: 300 meters and 7000 meters each have one significant figure

If the zeros are known measured values, record them as 3.00 x 102

meters and 7.00 x 103 meters The measurement 27210 has four

significant figures.

Atlantic/Pacific Rule If a decimal

point is present, count from this side starting with the first non-zero digit and keep counting until there are no remaining digits.

If a decimal point is absent, count from this side starting with the first non-zero digit and keep counting until there are no remaining digits.

Measurements with an Unlimited Number of Significant Digits

1. Counting Example: 23 people in the classroom

(Not 22.9 or 23.1) 23.00000000…………………………..

2. Exactly defined quantities Example: 60 minutes = 1 hour

60.00000000…………………………..

Identify the Number of Significant Figures

4.0 x 103

1.67 x 10-8

5201 635.000 22 000 0.00530 200.0 400 218 4755.50

Significant Figures in Calculations

Calculation cannot be more exact than the measured values used to obtain it

Example: Find the area of a floor measures 7.7 meters by 5.4 meters

Each measurement has only two significant figures

Calculator reads 41.58 square meters

If the digit immediately to the right of the last significant digit is less than 5, it is dropped

If it is 5 or greater, the value of the last significant digit is increased by 1

41.58 square meters becomes 42 square meters

Practice Problems Round each measurement to two

significant figures. Write your answers in scientific notation.

A. 94.592 grams B. 2.4232 x 103 grams C. 0.007 438 grams D. 54 752 grams E. 6.0289 x 10-3 grams F. 405.11 grams

Answers

A. 9.5 x 101 grams B. 2.4 x 103 grams C. 7.4 x 10-3 grams D. 5.5 x 104 grams E. 6.0 x 10-3 grams F. 4.1 x 102 grams

Calculation Rules Multiplication and Division – round the

answer to the same number of significant figures as the measurement with the least number of significant figures

Addition and Subtraction – the answer should be rounded to the same number of decimal places as the measurement with the least number of decimal places