Lesson 3 - Measurements in Chemistry

AMA Computer Learning Center College of Butuan Inc.

General Chemistry

Lesson 3 – Measurements in Chemistry

December 5, 2011 – ER5

Part A: The Number Used In Chemistry

A.1 The Numerical Value of Measurement

A.2 Significant Figures and Mathematical Operations

A.3 Expressing Large and Small Numbers: Scientific Notation

Objectives:

A.1.1 Describe the difference between accuracy and precision

A.1.1 Determine the number of significant figures in a measurement.

A.2.1 Perform arithmetic operations, rounding the answer to the appropriate number of significant figures

A.3.1 Write very large or small measurements in scientific notation.

A.3.2 Perform arithmetic operations involving scientific notation.

A.1 The Numerical Value of a Measurements

The Qualities of a Number

Measurements       - determines the quality, dimensions, or extent of something, usually in comparison to a specific unit.

Unit                         – is a definite adopted as a standard of measurements.

Thus a measurement (e.g., 1.23 meters) consists of two parts: numerical quantity (1.23) followed by a specific unit (meters).

Significant Figure   – is a digital that is either reliably unknown or closely estimated.

Example: What is the significant figure of 12,000?

Answer -  There are two significant figures – 1 and 2.

(We can assume that 1 is reliable and reproducible from any number of estimates, but the 2 is estimated. The zeros are not significant figure since they actually have no specific numerical meaning.)

The number of significant figures or digits in a measurement is simply the number of measured digits and refers to the precision of measurements.

Precision                 - relates to the degree of reproducibility or uncertainty of measurement. Indeed, all measured values have an uncertainty that is expressed in the last significant figure to right.

Example: A crowd at the concert is seated in the bleachers of a stadium instead of milling about. In this case, a more precise estimate is possible since the exact capacity of the stadium is know. The crowd can now be estimated between 12,400 and 12,600, or an average of 12,500.

Answer – This is a measurement with three significant figures. The 1 and 2 are now reliable, but the third significant figure, the 5, is estimated.

The more significant figures in a measurement, the more precise it is.

Accuracy                 -  accuracy in a measurement refers to how close the measurement is to the true value. Accuracy in measurements depends   on how carefully the instrument of measurement has been calibrated.

Zeros As A Significant Figure

1. When a zero s between other nonzero digits, it is significant.

Example: 709 have three significant figures. Zeros between two nonzero digits are always significant.

2. Zeros to the right of a nonzero digit and to the right of the decimal point are significant.

Example1: 8.0 has two significant figures, just as 7.9 and 8.1 do.

Example2: 7.900 has four significant figures.

3. Zeros to the left of the first nonzero digit are not significant.

Example1: 0.0078 and 0.45 both have two significant figures

Example2: 0.04060 has four significant figures. In this case, the zeros to the left of the digit are simply showing the decimal place and are not measured or estimated digits. Therefore, they are not significant.

4. Zeros to the right of an implied decimal point may or not be significant. In most cases, they are not.

Example1: The crowd of 12,000 has two significant figures, as does 6600.

Example2: What if 890?...

Exercise 1-1:  How many significant figures are in the following measurements? What is the uncertainty in each of the measurements?

A) 1580 cm             B) 300.0 ft               C) 20.003 lb             D) 0.00705 gal        E) 45000 s               F) 450 in

A.2 Significant Figures and Mathematical Operations

Mathematical Operations:

1. Addition

2. Subtraction

3. Multiplication

4. Division

Rounding Off

Rules for rounding off a number are as follows:

1. If the digit to be dropped is less than 5, simply drop that digit

Example: Round off 12.44 to its nearest three significant figures.

Answer: 12.44 is rounded down to 12.4

2. If the digit to be dropped is 5 or greater, increase the preceding digit by one.

Example1: Round off 0.3568

Answer: 0.357

Example2: Round off 13.65

Answer: 13.7

Example3: Expressed 12.448 to its nearest 3 significant.

Answer:___________

Exercises – Exercise – Exercise – Exercise – Exercise – Exercise

A.3 Expressing Large and Small Numbers: Scientific Notation

Changing Numbers into Scientific Notation

Scientific Notation  - a given value is expressed as a number written with one nonzero digit to the left of the decimal point and all other digits to the right of it. This number is thenmultiplied by 10 raised to a given power called exponent. The exponent indicated the magnitude of the number.

Mathematical Manipulation of Scientific Notation

A huge number that will soon deal with 602,200,000,000,000,000,000,000 = . Notice that the number(6.022, known as the coefficient) expresses the procper precision of four significant figures. This expression means that 6.022 is multiplied by (which is 1 followed by 23 zeros).

Express each of the following numbers in scientific notation and then identify its significant figures.

1. 47,500

2. 5,030,000

3. 0.0023

4. 0.0000470

5. 508000