Unit 2: Measurement and Problem Solving

measurements

quantitative data(information) about a system

all measurements must be made of 2 parts:

quantity and a unit

quantity

tells us the magnitude of the measurement (large or small)

ex. 35^o celsius (tells us the magnitude of the temperature)

unit

enables us to understand what the measurement represents

ex. 35^o celsius (celsius is the unit)

what does all measurements must have when they are made

a certain level of accuracy and precision about them.

accuracy

pertains to how correct the measurement is

precision

pertains to how consistent the measurement is.

measurements should be made in triplicate

how accurate is a measurement?

the accuracy of a measurement is due to the instrument or measuring device that is used.

how to make measurements as accurate as they can be

to assure that all measurements are as accurate as they can be, instruments must periodically get calibrated

calibrate - (only for moving part instruments) use known amount and adjust accordingly

ex. scale - 20lb weight
balance - 250g object (weights)

measurements can be accurate or precise, but what can they never be?

measurements can never be exact!
there is no such thing as an exact measurement
- flawless
- perfect
- without error

2 reasons why measurements can’t be exact

1. The final last digit that is recorded or written in any measurement is always uncertain

   always uncertain - we use our best judgement to decide what this is (personal bias)

2. all measurements are exposed to 3 sources:

   • random error

   • careless error

   • systemic (or systematic) error

random error

due to the lack of skills or familiarity of the measuring equipment by the person making the measurement

careless error

due to rushing, not paying attention to detail. easiest form of error to minimize or completely eliminate

systematic error

is “built in” (minimal or signficant, unknown to us.) error that the measuring device is manufactured (people or robots) with

Significant Figures

significant - does not mean important, it means “recognize” (for zeros!)

Zeros

may or may not be recognized as being part of the measurement. must consider magnitude of quantity quantity and presence/absence of decimal point

what determines how many sig figs a measurement has?

the measuring instrument

rules to recognize significant figures

1. all non zero digits are ALWAYS significant.

remainder of the rules are all for Zeros

2. “sandwiched” zeros, zeros that are between other nonzeros digits are significant

   ex. 205mL

3. If the measurement is 10 or greater and the instrument records a decimal point. the zero(s) at the end of the measurement are significant

   ex. 125 000 000. mg - 9 sig figs

   note - space, no commas for big numbers

4. If the measurement is 10 or greater and the instrument does not record a decimal point, the zero(s) at the end of the measurement are not significant!

   ex. 125 000 000 mg

5. If the measurement is less than 1, the zero in front of the decimal point is called a “cosmetic” zero, it does not get counted as being significant

   ex. 0.503L 3sigfigs

6. If there are zero(s) after the decimal point in a quantity less than one, these zeros are called placeholder zeros, they are not significant.

   ex. 0.00039g - 2 sigfigs

7. If the measurement is less than 1 and there are zero(s) at the end of the measurement, these are called trailing zeros, they are significant

   ex. 00200 mg - 3 sigfigs

8. If the measurement is 1 or greater and there is a decimal point present, all digits on the left and all digits on the right of the decimal point.