Chem 160- Ch # 2l. Numbers from measurements.

Measurements Experiments are performed. Numerical values or data are obtained from these measurements.

12 inches = 1 foot100 centimeters = 1 meter Exact numbers have an infinite number of significant figures. Exact numbers occur in simple counting operations Exact Numbers Defined numbers are exact

Form of a Measurement 70.0 kilograms = 154 pounds numerical value unit

Significant Figures The number of digits that are known plus one estimated digit are considered significant in a measured quantity estimated known

Significant Figures on Reading a Thermometer

Temperature is estimated to be 21.2 o C. The last 2 is uncertain. The temperature 21.2 o C is expressed to 3 significant figures.

Temperature is estimated to be 22.0 o C. The last 0 is uncertain. The temperature 22.0 o C is expressed to 3 significant figures.

Temperature is estimated to be o C. The last 1 is uncertain. The temperature o C is expressed to 4 significant figures.

461 All nonzero numbers are significant. Significant Figures

461 All nonzero numbers are significant. Significant Figures

461 3 Significant Figures All nonzero numbers are significant. Significant Figures

401 3 Significant Figures A zero is significant when it is between nonzero digits. Significant Figures

A zero is significant when it is between nonzero digits. 5 Significant Figures Significant Figures

A zero is significant at the end of a number that includes a decimal point. 5 Significant Figures Significant Figures

A zero is significant at the end of a number that includes a decimal point. 5 Significant Figures Significant Figures

A zero is not significant when it is before the first nonzero digit. 1 Significant Figure Significant Figures

A zero is not significant when it is before the first nonzero digit. 3 Significant Figures Significant Figures

A zero is not significant when it is at the end of a number without a decimal point. 1 Significant Figure Significant Figures

Rounding off Numbers

Rounding Off Numbers Often when calculations are performed extra digits are present in the results. It is necessary to drop these extra digits so as to express the answer to the correct number of significant figures. When digits are dropped the value of the last digit retained is determined by a process known as rounding off numbers.

Rule 1. When the first digit after those you want to retain is 4 or less, that digit and all others to its right are dropped. The last digit retained is not changed. 4 or less Rounding Off Numbers

5 or greater Rule 2. When the first digit after those you want to retain is 5 or greater, that digit and all others to its right are dropped. The last digit retained is increased by 1. drop these figures increase by 1 6 Rounding Off Numbers

Significant Figures in Calculations

Multiplication or Division

In multiplication or division, the answer must contain the same number of significant figures as in the measurement that has the least number of significant figures.

(190.6)(2.3) = Answer given by calculator. 2.3 has two significant figures has four significant figures. The answer should have two significant figures because 2.3 is the number with the fewest significant figures. Drop these three digits. Round off this digit to four. The correct answer is 440 or 4.4 x 10 2

Addition or Subtraction

The results of an addition or a subtraction must be expressed to the same precision as the least precise measurement.

The result must be rounded to the same number of decimal places as the value with the fewest decimal places.

Add , 129 and Answer given by calculator. Least precise number. Round off to the nearest unit Correct answer.

Scientific Notation of Numbers

Very large and very small numbers like these are awkward and difficult to work with. Very large and very small numbers are often encountered in science.

A method for representing these numbers in a simpler form is called scientific notation x x

Scientific Notation Write a number as a power of 10 Move the decimal point in the original number so that it is located after the first nonzero digit. Follow the new number by a multiplication sign and 10 with an exponent (power). The exponent is equal to the number of places that the decimal point was shifted.

Write 6419 in scientific notation x x x 10 3 decimal after first nonzero digit power of 10

Write in scientific notation x x x x decimal after first nonzero digit power of 10