MEASUREMENT Cartoon courtesy of Lab-initio.com.

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MEASUREMENT Cartoon courtesy of Lab-initio.com

2 types of measurement Qualitative-a non-numerical description of matter. (ex: red stone, heavy brick, hot steel) Quantitative- a numerical measure. It must include a number, followed by a unit. (ex: 2.14 grams, 49.6 ml, kg)

Uncertainty in Measurement
A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

Why Is there Uncertainty?
Measurements are performed with instruments No instrument can read to an infinite number of decimal places Which of these balances has the greatest uncertainty in measurement?

Taking Measurements When taking measurements:
Read to the smallest increment(mark) on the instrument Estimate one digit past the smallest increment(mark)

Liquids in glass and some plastic containers curve at the edges Changing the diameter of the cylinder will change the shape of the curve This curve is called the MENISCUS

Your eye should be level with the top of the liquid You should read to the bottom of the MENISCUS

Use the smallest increments to find all certain digits, then estimate 1 more digit.
There are two unlabeled graduations below the meniscus, and each graduation represents 1 mL, so the certain digits of the reading are… mL.

Estimate the uncertain digit and take a reading
The meniscus is about eight tenths of the way to the next graduation, so the final digit in the reading is 0.8 mL The volume in the graduated cylinder is mL.

What is the volume of liquid in the graduate? ___mL

What is the volume of liquid in the graduate? ___mL

What is the volume of liquid in the graduate? ____mL

What is this reading? ___ ml

What is this reading? ____ ml

Measuring Liquid Volume
What is the volume of water in each cylinder? Images created at A B C Pay attention to the scales for each cylinder.

All of the equipment below measures volume in mL but the scales for each are different. ___mL ___mL ____mL

Reading a Buret On the graduated cylinder, zero was at the bottom of the scale, with values increasing going up the cylinder. However, a buret has zero at the top with values increasing going down the scale. Determine the scale. Read at the bottom of the meniscus with your eye level with the liquid. ____mL

What is the volume in the buret?

What is the volume in the buret?

Lets play darts!

Precision and Accuracy
Accuracy how close a result is to its true value. Precision refers to the repeatability of results. Neither accurate nor precise Precise but not accurate Precise AND accurate

Types of Error Error- the difference between a measurement and the accepted value. Random Error - measurement has an equal probability of being high or low. Systematic Error – a repeated error, often resulting from poor technique or incorrect calibration.

Scientific Notation

Scientific Notation In science, we deal with some very LARGE numbers:
1 mole = In science, we deal with some very SMALL numbers: Mass of an electron = kg

Imagine the difficulty of calculating the mass of 1 mole of electrons!
kg x ???????????????????????????????????

Scientific Notation: A method of representing very large or very small numbers in the form: M x 10n M is a number between 1 and 10 n is the exponent

. 9 8 7 6 5 4 3 2 1 Step #1: Insert an understood decimal point Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10n

2.5 x 109 The exponent is the number of places we moved the decimal.

0.0000579 1 2 3 4 5 Step #2: Decide where the decimal must end
up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10n

5.79 x 10-5 The exponent is negative because the number we started with was less than 1.

Convert each standard number to scientific notation:
2000 g m m 6.55 s kg 71.9 ms 96.3 g 8999 cm m 450 g

Convert each to floating decimal form:
7.00 x 102 m 17 x 100 cm 2.22 x 10-4 cm 3.00 x 108 m/s 9.45 x 10-8 m 6.02 x 1023 atoms 4.00 x 103 g 8.75 x 10-1 m 5.99 x 10-5 kg 6.78 x 10-6 m

Significant Figures-all the digits that are known to be true.

Rules for Counting Significant Figures - Details
Nonzero Digits(1-9) always count as significant figures. 3456 has 4 significant figures

Rules for Counting Significant Figures - Details
Zeros - Leading zeros never count as significant figures. has 3 significant figures

Rules for Counting Significant Figures - Details
Zeros - Captive zeros(sandwiched zeros) always count as significant figures. 16.07 has 4 significant figures

Rules for Counting Significant Figures - Details
Zeros Trailing zeros are significant only if the number contains a decimal point. 9.300 has 4 significant figures

Rules for Counting Significant Figures - Details
Exact numbers have an infinite number of significant figures. They tend to be numbers of indivisible objects. 7 computers or 1 inch = cm, exactly

Sig Fig Practice #1 1.0070 m  5 sig figs(0) 17.10 kg  4 sig figs(0)
How many significant figures in each of the following & which is the estimated digit? m  5 sig figs(0) 17.10 kg  4 sig figs(0) 100,890 L  5 sig figs(9) 3.29 x 103 s  3 sig figs(9) cm  2 sig figs(4) 3,200,000  2 sig figs(2)

Rules for Significant Figures in Mathematical Operations
Multiplication and Division: # sig figs in the answer equals the least number of sig figs used in the calculation. 6.38 cm x 2.0 cm = 12.76  13 cm2 (2 sig figs)

Sig Fig Practice #2 Calculation Calculator says: Answer 3.24 m x 7.0 m
100.0 g ÷ 23.7 cm3 g/cm3 4.22 g/cm3 0.02 cm x cm cm2 0.05 cm2 710 m ÷ 3.0 s m/s 240 m/s lb x 3.23 ft lb·ft 5870 lb·ft 1.030 g ÷ 2.87 mL g/mL 0.359 g/mL

Rules for Significant Figures in Mathematical Operations
Addition and Subtraction: The number of decimal places in the answer equals the number of decimal places in the least accurate measurement. 6.8 g g =  18.7 g (3 sig figs)

Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m + 7.0 m
100.0 g g 76.27 g 76.3 g 0.02 cm cm 2.391 cm 2.39 cm 713.1 L L L 709.2 L lb lb lb lb 2.030 mL mL 0.16 mL 0.160 mL