CH 2: Scientific Measurement

Renee Y. BeckerCHM 1025

Valencia Community College

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Measurements

• Measurement

– A number with an attached unit

Examples: 15 inches 3 cups 36 cm

Every measurement must include units!!

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Example 1: Measurements

In the following, what are the measurements and what are the units?

a) 12 trees

b) 2.3 mm

c) 100 ¢

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Measurements

• Instrument– A device for recording a measurement• Examples: Ruler (length), electronic balance (mass),

Graduated cylinder (volume)

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Uncertainty

• An instrument may give a very sensitive reading, but EVERY measurement has UNCERTAINTY

• No measurement instrument is perfect and neither is the person using it

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Example 2: Length Measurements

• If we need to measure the length of this candycane, which ruler should we use? Why?

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Mass

• Mass– Measure of the amount of matter it possesses– Measured by a balance– Not affected by gravity– Typical units: kilogram (kg), gram (g), pound (lb),

ounce (oz)

• Weight– Force exerted by gravity on an object

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Balances

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Example 3: Mass

• Would you have the same mass on the moon as on Earth? Why?

• Would you have the same weight on the moon as on Earth? Why?

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Volume

• Volume– The amount of space occupied by a solid, gas, or

liquid

– Graduated cylinder, pipet, buret, volumetric flask, syringe

– Typical units: milliliter (mL), Liter (L), centimeter cubed (cm3), quart (qt), gallon (gal),

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Buret

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Accuracy, Precision, and Significant Figures in Measurement

• Accuracy is how close to the true value a given measurement is.

• Precision is how well a number of independent measurements agree with one another.

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Accuracy, Precision, and Significant Figures in Measurement

• Significant Figures are the total number of digits in the measurement.

• The results of calculations are only as reliable as the least precise measurement!!

• Rules exist to govern the use of significant figures after the measurements have been made.

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Accuracy, Precision, and Significant Figures in Measurement

• Rules for Significant Figures:

– Zeros in the middle of a number are significant

– Zeros at the beginning of a number are not significant

– Zeros at the end of a number and following a period are significant

– Zeros at the end of a number and before a period may or may not be significant.

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Example 4: Significant Figures

How many Sig. Figs ?

a) 0.000459

b) 12.36

c) 36,450

d) 8.005

e) 28.050

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Accuracy, Precision, and Significant Figures in Measurement

• Rules for Calculating Numbers:

– During multiplication or division, the answer

can’t have more sig figs than any of the original

numbers.

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Example 5: Significant Figures

a) 238.5 x 79 =

b) 12 / 0.1272 =

c) 0.2895 x 0.29 =

d) 32.567 / 22.98 =

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-During addition or subtraction, the answer can’t have more digits to the right of the decimal point than any of the original numbers.

Accuracy, Precision, and Significant Figures in Measurement

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Example 6: Significant Figures

a) 238.5 + 79 =

b) 12.3 - 0.1272 =

c) 0.2895 + 0.29 =

d) 32.567 - 22.98 =

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Accuracy, Precision, and Significant Figures in Measurement

• Rules for Rounding Numbers:

– If the first digit removed is less than 5 - round down

– If the first digit removed is greater than 5 - round up

– If the first digit removed is 5 and following numbers are nonzero - round up

– If the first digit removed is 5 and following numbers are zero - round down

– Only final answers are rounded off, do not round intermediate calculations

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Example 7: Rounding

Round off each of the following measurements

(a)3.774499 L to four significant figures

(b) 255.0974 K to three significant figures

(c) 55.265 kg to four significant figures

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Example 8: Accuracy & Precision

Which of the following is precise but not accurate?

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Scientific Notation

• Changing numbers into scientific notation– Large # to small #– Moving decimal place to left, positive exponent

123,987 = 1.23987 x 105

– Small # to large #– Moving decimal place to right, negative

exponent0.000239 = 2.39 x 10-4

• Correct scientific notation: #.#### x 10n

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Scientific Notation

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How to put into calculator??

Example 9: Scientific Notation

Put into or take out of scientific notation

a) 87542

b) 2.1956 x 10-3

c) 0.784

d) 2.78 x 106

e) 92000

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Significant Figures

• When we count something, it is an exact number.

– It has an infinte number of significant figures

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