Chapter 2 Section 3. Measuring & Calculating No experimentally obtained value is exact Human errors Method errors Instrument errors.

Chapter 2Section 3

Measuring & Calculating No experimentally obtained value is

exact

Human errors

Method errors

Instrument errors

Measurements Errors can arise depending on the

instrument that is used.

It is important to use the right instrument

Would you use a balance that is calibrated to 1 g to weigh 0.155 g of a substance?

Which graduated cylinder would you use from Figure 2-7 to measure 8.6 mL

Accuracy vs. Precision 2 things to consider when making a

measurement

1. Accuracy

2. Precision

What is the difference between accuracy and precision?

Accuracy vs. Precision Accuracy:

How exact it is

The extent to which a measurement approaches the true value of a quantity

Example: You measure 35.8

ML

Lab partner measures 37.2 mL

True volume = 36.0 mL

Your measurement is more accurate than your lab partner’s

Accuracy vs. Precision Precision:

How closely several measurements of the same quantity made in the same way agree with each other

Measure the mass of a substance four times using the same balance 110 g, 109 g, 111 g, and 110 g.

Accuracy vs. Precision The measurements were close to each

other so they are precise

Remember that precise measurements are not always accurate measurements

Ex: If the balance was not reset to zero the

measurements are close to each other (precise) but not but not accurate

Significant Figures Significant Figures:

Measurement or calculation that consists of all the digits known with certainty plus one estimated or uncertain digit

Ex: 10.7834 g is accurate to 5 places

The 6th place 00.0004 is the estimated digit

Significant Figures Report the

measurements with the correct number of significant figures

Example:

Measuring temperature with a thermometer marked in intervals of 1 degree C

Using the markings on the thermometer we can estimate the temperature to be 28.4 degree C

28.4 is 3 significant figures

The first two digits we know for certain

The third digit is an estimate

The actual temperature is between 28.2 and 28.6

Significant Figures Burets vs. Graduated Cylinders

Significant Figures Buret vs. Graduated Cylinder

100 mL graduated cylinders are calibrated to the nearest 1 mL

Burets are calibrated to the nearest 0.1 mL

Best measurement with a graduated cylinder is 25.0 mL – uncertainty is in the tenths place

Best measurement with a buret is 25.00 mL – uncertainty is in the hundredths place

Rule Example

Zeroes appearing between nonzero digits are significant

40.7 has 3 significant figures

87009 has 5 significant figures

Zeroes appearing in front of nonzero digits are not significant

0.009587 has 4 significant figures

0.0009 has 1 significant figure

Zeroes at the end of a number and to the right of a decimal point are significant

85.00 g has 4 significant figures

9.070000000 has 10 significant figures

Zeros at the end of a number with no decimal point may or may not be significant. Read the rest of 4 in the book

2000 may contain 1-4 significant figures

2000. Has 4 significant figures

Significant Figures Be careful when calculating with

significant figures Ex: Mass of a 32.4 mL sample = 25.42 g

If we used this information to determine density D = m/v we would get 0.7845689012 g/mL

The volume has 4 significant figures while the mass has 3 and the density has 10

So what do we do?

Operation Rule Example

Multiplication and Division

The answer can have no more

significant figures than there are in the measurement with the smallest

amount of significant figures

12.257X 1. 162 ________ 14.2426340

Answer = 14.24

Addition and Subtraction

The answer can have no more digits to the right of the decimal point than

there are in the measurement with

the smallest number of digits to

the right of the decimal point

3.952.879

+ 213.6 ------------------

220.429

Answer = 220.4

Significant Figures Multiplication and Division

The answer should have the same number of significant figures as the measurement with the least amount of significant figures

Do NOT round until the end when doing calculations

Significant Figures Addition and Subtraction

The answer can have no more digits to the right of the decimal than there are in the measurement with the smallest number of digits to the right of the decimal

Remember it is only significant figures to the right of the decimal not total significant figures

Significant Figures Exact value:

Value that has no uncertainty Has an unlimited number of significant

figures

2 categories of exact values Count Values Conversion Factors

Significant Figures1. Count Values

Value that is determined by counting and not by measuring

Example a water molecule has 2 hydrogen atoms and 1 oxygen atom

No uncertainty in this value because we count the number of atoms NOT measure them

Significant Figures2. Conversion Factors

1 m = 1000 mm

No uncertainty because a millimeter is determined as exactly one-thousandth of a meter 1 mm = 0.001 m

Exact values ALWAYS have more significant figures than any other value in the calculation

Never use counted or conversion factors to determine the number of significant figures in your calculated results

Scientific Notation Very large and very small numbers are

written in scientific notation

2 parts to each value written in scientific notation

1. Number between 1 and 10 2. A power of 10

Scientific Notation 1st part:

Move the decimal to the right or left so only 1 nonzero digit is to the left of it

2nd part: Exponent Determined by counting the number of

decimal places the decimal point must be moved.

Scientific Notation If the decimal point is moved to the left

the exponent is positive

If the decimal point is moved to the right the exponent is negative

Eliminates the need to count zeroes

Rule

Addition & Subtraction: All values must have the same exponent before they can be added or subtracted. The

result is the sum or difference of the first factors all multiplied by the same exponent of 10.

Multiplication: The first factors of the numbers are multiplied and the exponents of 10 are added

Division: The first factors of the number are divided, and the exponent of 10 in the denominator is subtracted from the exponent of 10 in the numerator

Table 2-6• Examples are in the Book page 63

Scientific Notation Table 2-7 on page 64

Questions to Check for Learning Page 64 Problems 5-10 and 12

Additional Problems 1. Determine the # of significant figures

in each of the following quantities 218 kPa 0.025 L 200. m2

1.05 g

Additional Problems 2. Round the following quantities to the

# of significant figures indicated in parentheses

1. 32.068 km (3) 155.8 g (3) 0.02274 cm (2) 12000 kPa (3)