Scientific MeasurementScientific Measurement

What is measurement…What is measurement…

Measurement is a quantity that has Measurement is a quantity that has bothboth a a numbernumber and a and a unitunit..

12 meters or 2612 meters or 26ooC or 2 gramsC or 2 grams

Numbers in Chemistry can be very Numbers in Chemistry can be very large or very smalllarge or very small

For example….For example…. A single gram of hydrogen gas contains A single gram of hydrogen gas contains

602,000,000,000,000,000,000,000 atoms!602,000,000,000,000,000,000,000 atoms!

The mass of one atom of gold is The mass of one atom of gold is 0.000 000 000 000 000 000 000 327 grams!0.000 000 000 000 000 000 000 327 grams!

Simplified way to write very large or very Simplified way to write very large or very small numbers.small numbers.

ALWAYS follows the same format:ALWAYS follows the same format:a a coefficientcoefficient with the with the first digitfirst digit in in

the the ones placeones place x 10x 10 raised to a power. raised to a power.

602,000,000,000,000,000,000,000 atoms!602,000,000,000,000,000,000,000 atoms!Becomes…Becomes…

6.02 x 106.02 x 1023 23 atomsatoms

0.000 000 000 000 000 000 000 327 grams0.000 000 000 000 000 000 000 327 gramsBecomes…Becomes…

3.27 x 103.27 x 10-22-22 grams grams

Scientific NotationScientific Notation

The exponent tells you how many places The exponent tells you how many places you move the decimal to the right or to you move the decimal to the right or to

the left.the left.

Positive exponentPositive exponent move decimal to the move decimal to the right (bigger #)right (bigger #)

Negative exponentNegative exponent move decimal to the move decimal to the left (smaller #)left (smaller #)

LetLet’’s practice…s practice…

88,00088,000

8.8 x 108.8 x 1044

0.0003410.000341

3.41 x 103.41 x 10-4-4

2.41 x 102.41 x 1055

241,000241,000

6.93 x 106.93 x 10-3-3

0.006930.00693

Now try some Now try some on your own.on your own.

Check your Check your answers answers when done.when done.

Measurements are always read to the certain markings AND then estimated one place beyond that marking.

cm 1 2 3 4 5 6

cm 1 2 3 4 5 6

This line reads as 3.5 cm

2 significant figures

This line reads as 3.55 cm

3 significant figures

Accuracy and PrecisionAccuracy and Precision

AccuracyAccuracy is a measure of how close a is a measure of how close a measurement comes to the actual or true measurement comes to the actual or true value of whatever is being measured.value of whatever is being measured.

PrecisionPrecision is how close a series of is how close a series of measurements are to each other.measurements are to each other.

Graphic from: http://elchem.kaist.ac.kr/vt/chem-ed/data/acc-prec.htmGraphic from: http://elchem.kaist.ac.kr/vt/chem-ed/data/acc-prec.htm

poor

ErrorError

Error is how far your experimental answer is Error is how far your experimental answer is from the accepted valuefrom the accepted value

Error = Experimental value – accepted valueError = Experimental value – accepted value

Experimental value – accepted valueExperimental value – accepted value accepted valueaccepted value

X 100%Error =%Error =

Significant DigitsSignificant Digits

Significant figures Significant figures = digits in a = digits in a measurement we are confident are free measurement we are confident are free from error.from error.

Significant figures include all of the digits Significant figures include all of the digits that are known for sure, plus a last digit that are known for sure, plus a last digit that is estimated.that is estimated.

Guide to Guide to Significant DigitsSignificant Digits

Counting Significant DigitsCounting Significant Digits

1. Every non-zero digit is 1. Every non-zero digit is significant.significant.

346346

3 sig digs3 sig digs

2. Any zeroes between other sig 2. Any zeroes between other sig figs figs areare significant. significant.

346346000077

6 sig digs6 sig digs

3. Zeroes to the left of the first 3. Zeroes to the left of the first non-zero digit are NOT non-zero digit are NOT significant.significant.

0.0000.0002828

2 sig digs2 sig digs

4. Zeroes at the end of a number 4. Zeroes at the end of a number AND to the right of the decimal AND to the right of the decimal point ARE significant.point ARE significant.

78.478.40000

5 sig digs5 sig digs

5. Zeroes to the right of a 5. Zeroes to the right of a number with no decimal are NOT number with no decimal are NOT significant. significant.

3463460000

3 sig digs3 sig digs

6. For a number in scientific 6. For a number in scientific notation, all of the digits to the notation, all of the digits to the left of the left of the ““xx”” are significant, and are significant, and these are the only sig figs in the these are the only sig figs in the number.number.

3.4603.460 x 10 x 1044

4 sig digs4 sig digs

1. When 1. When multiplying or dividingmultiplying or dividing, , count the number of sig figs in all count the number of sig figs in all the numbers you start with. The the numbers you start with. The number with the number with the fewest sig figsfewest sig figs determines the number of sig figs determines the number of sig figs our answer should have.our answer should have.

36 36 2 sig fig2 sig fig

X255 X255 3 sig fig3 sig fig

x 3 x 3 1 sig fig1 sig fig

27540 27540

30000 30000 1 sig fig1 sig fig

2. When 2. When adding or subtractingadding or subtracting, , look at look at which place the last sig fig which place the last sig fig is inis in for each of the numbers you for each of the numbers you start with. Whichever place is start with. Whichever place is highesthighest is the last place that answer is the last place that answer can have sig digs.can have sig digs.

325 325 (one(one’’s place)s place)

+ 9.1+ 9.1 (tenth(tenth’’s place)s place)

+20+20 (ten(ten’’s place)s place)

354.1354.1

350 350 (ten(ten’’s place)s place)

Calculating with Calculating with ““Sig FigsSig Figs””How many sig figs should your answer have?How many sig figs should your answer have?