Chapter 3 - Scientific measurement

Using and expressing measurements

How far off was Usain Bolt from winning gold in the 100m last weekend?

What is a measurement? How do scientists make reporting measurement easier? ● Scientific notation! ● For example - every gram of Hydrogen contains

602,000,000,000,000,000,000,000 atoms● 6.02 x 1023 is much easier to understand

○ Positive exponent = very large number○ Negative exponent = very small number

Using Scientific notation (Division and multiplication)

Using Scientific notation (Division and multiplication)

What is the difference between accuracy and precision?

● Accuracy: The closeness of the measurement to the true value● Precision: The closeness of a set of measurement taken under the same

conditions

How do you determine whether a measurement take in a lab is a suitable value? You asses the error of your measurement, by comparing the experimental value with the accepted value

Experimental value = value measured in the lab

Accepted value = correct value for the measurement based on reliable references

Error = the difference between these two values

Percent error = the relative error of a measurement

How do you calculate percent error?

What is a significant figure?

• The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated.

• Instruments differ in the number of significant figures that can be obtained from their use

• and thus in the precision of measurements.

What are the rules in how significant figures are used?

Example problem● Suppose that the winner of a 100-meter dash finishes the race in

9.98 seconds. The runner in second place has a time of 10.05 seconds. How many significant figures are in each measurement? Is one measurement more accurate than the other? Explain your answer.

● There are three significant figures in 9.98 and four in 10.05. Both measurements are equally accurate because both measure the actual time of the runner to the hundredth of a second.

How do you use significant figures in calculations? ● In general, a calculated answer cannot be more precise than the least precise

measurement from which it was calculated.● The calculated value must be rounded to make it consistent with

themeasurements from which it was calculated. ● When rounding

• you must first decide how many significant figures the answer should have.• This decision depends on the given measurements and on the

mathematical process used to arrive at the answer.• Once you know the number of significant figures your answer should have,

round to that many digits, counting from the left• If less than 5, number os dropped, Greater than 5 round to 1

Additional rules for significant figures

● Addition/Subtraction problems○ The answer to an addition or subtraction calculation should be rounded to the same number of

decimal places (not digits) as the measurement with the least number of decimal places

● Multiplication/Division○ Like addition/subtraction probems you need to round the answer to the same number of

significant figures as the measurement with the least number of significant figures.○ The position of the decimal point has nothing to do with the rounding process when multiplying

and dividing measurements.

Section 3.2: Units of Measurement

Why does science use the metric system?

● The international system of units was first used in France in 1795

● In 1960, the SI was accepted internationally

● There are seven base SI units

Electric current

Luminous intensity

Amount of substance

TimeTemperature

MassLength

Quantity

Aampere

cdcandela

molmole

ssecondKkelvinkgkilogrammmeter

SymbolSI base unitSI Base Units

Why do we not always use base units? How is the metric system made more user friendly? Prefixes are commonly used to express measurements in suitable units

10-91 billion times smaller than the unit it precedesnnanopico

micromillicentidecikilo

megaPrefix

p

μmcdkM

Symbol

10-121 trillion times smaller than the unit it precedes

10-61 million times smaller than the unit it precedes10-31000 times smaller than the unit it precedes10-2100 times smaller than the unit it precedes10-110 times smaller than the unit it precedes1031000 times larger than the unit it precedes1061 million times larger than the unit it precedes

FactorMeaningCommonly Used Metric Prefixes

What is the difference between mass and weight?

● Weight is a force that measures that pill on a given object by gravity

○ Your weight is different on Earth and the Moon

● Mass is the measure of quantity of matter

○ An object can become weightless but never massless

What is the difference between the celsius scale and the kelvin scale? The difference is 273.15 C

That is because the Kelvin system starts at absolute zero

A one degree increase on the Kelvin scale is equal to one degree increase on the Celsius scale

How do you calculate density? Density is the ratio of the mass of an object to it’s volume

Do gases have density? ● Yes!● Density difference is what allows helium balloons to rise

How is density related to temperature? ● In general, as temperature of a substance increases, so to does its volume● As such, the density will increase with temperature● Water is an important exception● Volume increases as temperature decreases

○ You will learn about this in chapter 15!

Section 3.3: Solving conversion problems

What is a conversion factor? A conversion factor is a ratio of equivalent measurements

For example

What is dimensional analysis? ● Dimensional analysis is a method of problem solving that uses the units that

are part of a measurement to solve a problem● It allows you to solve conversion problems in which a measurement with one

unit is changed into an equivalent measure with another unit