MEASUREMENT, ACCURACY, PRECISION, AND SIGNIFICANT FIGURES

“0-9”, Jasper Johns, 1960

Vocabulary:

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qualitative temperature

quantitative SI Units

length base units

volume precise measurements

time significant figures

mass

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MEASUREMENT

Some of science is qualitative (observations that do not involve measurement.)

Classifying organisms

Interpreting rock strata

Understanding the Skeletal System

MEASUREMENT

However, a very important aspect of science is that much of it is quantitative (observations that involve measurements)

Determining the amount of CO₂ in the atmosphere

Measuring the age of the earth

Calculating the amount of energy produced by uranium

WHAT TYPES OF MEASUREMENTS DO WE MAKE OR USE IN EVERYDAY LIFE?

The distance from one end of an object to the other end.

WHAT TYPES OF MEASUREMENTS DO WE MAKE OR USE IN EVERYDAY LIFE?

The amount of space that a substance or object occupies.

WHAT TYPES OF MEASUREMENTS DO WE MAKE OR USE IN EVERYDAY LIFE?

The measured period during which an action, process, or condition exists or continues.

WHAT TYPES OF MEASUREMENTS DO WE MAKE OR USE IN EVERYDAY LIFE?

The amount of matter in an object.

WHAT TYPES OF MEASUREMENTS DO WE MAKE OR USE IN EVERYDAY LIFE?

A measure of the average kinetic energy of the particles of a substance.

STANDARDIZATION

For scientists to communicate quantitative measurements, there must be standardized units (units that are agreed upon between scientists.) These agreed upon units make a system of measurement.

WHAT SYSTEM OF MEASUREMENT DO MOST OF US USE HERE IN THE UNITED STATES?

The Imperial System (Also called the British system or the Standard system)

WHAT SYSTEM OF MEASUREMENT DO MOST OF US USE HERE IN THE UNITED STATES?

The Imperial System (Also called the British system or the Standard system)

WHAT SYSTEM OF MEASUREMENT DO MOST OF US USE HERE IN THE UNITED STATES?

The Imperial System (Also called the British system or the Standard system)

WHAT SYSTEM OF MEASUREMENT DO MOST OF US USE HERE IN THE UNITED STATES?

The Imperial System (Also called the British system or the Standard system)

WHAT SYSTEM OF MEASUREMENT DO MOST OF US USE HERE IN THE UNITED STATES?

The Imperial System (Also called the British system or the Standard system)

WHAT SYSTEM OF MEASUREMENT DO MOST OF US USE HERE IN THE UNITED STATES?

The Imperial System (Also called the British system or the Standard system)

WHAT SYSTEM OF MEASUREMENT DO MOST OF THE REST OF THE WORLD (AND ALL SCIENTISTS) USE?

The International System (Also called the SI system and is based on the metric system.)

WHAT SYSTEM OF MEASUREMENT DO MOST OF THE REST OF THE WORLD (AND ALL SCIENTISTS) USE?

The International System (Also called the SI system and is based on the metric system.)

WHAT SYSTEM OF MEASUREMENT DO MOST OF THE REST OF THE WORLD (AND ALL SCIENTISTS) USE?

The International System (Also called the SI system and is based on the metric system.)

WHAT SYSTEM OF MEASUREMENT DO MOST OF THE REST OF THE WORLD (AND ALL SCIENTISTS) USE?

The International System (Also called the SI system and is based on the metric system.)

WHAT SYSTEM OF MEASUREMENT DO MOST OF THE REST OF THE WORLD (AND ALL SCIENTISTS) USE?

The International System (Also called the SI system and is based on the metric system.)

WHAT SYSTEM OF MEASUREMENT DO MOST OF THE REST OF THE WORLD (AND ALL SCIENTISTS) USE?

The International System (Also called the SI system and is based on the metric system.)

Base units (kms) are the basis of derived units. More on this later.

WHAT IS THE ADVANTAGE OF SI UNITS?

All SI units use the same prefixes which mean the same thing!

centi- means 1/100; milli- means 1/1000; kilo- means 1000

SI UNITS

We will only use SI units as the International System is the accepted system in science.

HOW TO READ LAB EQUIPMENT CORRECTLY AND PRECISELY

Precision: the number of digits that a piece of lab equipment can measure.

How?

1. Determine the scale on the device.
2. Estimate between the lines of the scale and record one more digit than the scale on the device.

HOW TO READ LAB EQUIPMENT CORRECTLY AND PRECISELY

Example: What is the length of the red object?

2.33 cm

HOW TO READ LAB EQUIPMENT CORRECTLY AND PRECISELY

Example: What is the length of the pencil?

2.59 cm

HOW TO READ LAB EQUIPMENT CORRECTLY AND PRECISELY

Example: What if the pencil was exactly on the line?

2.60 cm

HOW TO READ LAB EQUIPMENT CORRECTLY AND PRECISELY

Example: What is the reading on the graduated cylinder? (Always read from the bottom of the meniscus, the curved section of the liquid in the cylinder.)

15.3 mL

ACCURACY VS. PRECISION

Accuracy: How closely a measured value agrees with an accepted value.

ACCURACY VS. PRECISION

Precision: How closely multiple measured values agree with each other.

ACCURACY VS. PRECISION

Determine if each of the following is accurate, precise, both, or neither.

ACCURACY VS. PRECISION

Determine if each of the following is accurate, precise, both, or neither.

Both accurate and precise

Precise but not accurate

Overall accurate, but not precise

SIGNIFICANT FIGURES

When making a measurement, a measured digit is called a “significant figure” (sometimes called significant digits)

2.33 cm

3 sig figs

SIGNIFICANT FIGURES

When making a measurement, a measured digit is called a “significant figure” (sometimes called significant digits)

2.60 cm

3 sig figs

SIGNIFICANT FIGURES

When making a measurement, a measured digit is called a “significant figure” (sometimes called significant digits)

15.3 cm

3 sig figs

HOW TO DETERMINE SIGNIFICANT FIGURES IN A NUMBER: THE 5 RULES

1. All non-zeros are significant

2. All “trapped” zeros are significant.

If decimal is present:

3. Trailing zeros are significant.

4. Leading zeros are NOT significant

If decimal is absent:

5. Trailing zeros are NOT significant.

Ex: 25 781 1.824

Ex: 15,002 4.0056 20.001

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Ex: 42.00 4.5100 1200.0

Ex: 0.03 0.00041 0.003060

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Ex: 4500 304,000 12,000

SIGNIFICANT FIGURES PRACTICE

40,024

0.004160

906.400

4500

5125

0.00080200

200.000

5

4

6

2

4

5

6

SIGNIFICANT FIGURES IN CALCULATIONS

RULES FOR CALCULATIONS:�MULTIPLICATION AND DIVISION

Your answer should only have the total number of sig fig as the measurement in the problem with the least total number of sig fig.

EXAMPLE 1

34.29 x 0.93 =

31.8897

32

EXAMPLE 2

0.2658 / 34.0036 =

0.007816819

0.007817

RULES FOR CALCULATIONS:�ADDITION AND SUBTRACTION

• Your answer should be rounded to the same place as the number with the least precise place.

EXAMPLE 1

931.25 + 145.2 =

1076.45

1076.5

EXAMPLE 2

198.065 – 23 =

175.065

175

PRACTICE

45.2 x 9.4 =

1500 + 24 =

50,000 + 0.95 =

424.88

= 420

1524

= 1524

47500

= 50000

TIME FOR YOU TO PRACTICE!