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An experimental scienceinterested in understanding

the behavior and compositionof matter.

Chemistry, as an experimental science, is always involved in the acquisition of data, most of it is the product of a measurement.What Is a Measurement? • a quantitative observation• a comparison to an agreed-upon standard• every measurement has a number and a unit

4.5 g5.082 kg25.0 ºC0.0004 lb.

CHEMISTRY

it is a statement of accuracy:(very accurate = very close to the real value)Here we use significant figures

number + unit

it is a statement of magnitude: (very small, small, large, very large)Here we use scientific notation

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A number in scientific notation contains a coefficient and a power of 10. 1.5 x 102

7.35 x 10-4

To write a number in scientific notation Move the decimal point so as to place it after the first non-zero digit.

This step makes the coefficient always greater than 1 but less than 10.

The spaces moved and the direction are shown as a power of ten.

Positive if moved to the left 52 000. = 5.2 x 104

4 spaces left

Negative if moved to the right 0.00378 = 3.78 x 10-3

3 spaces right

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Every measured number has a degree of uncertainty.

The more uncertain, the less accurate.

Determine the length of the wood.

1. Find the smallest graduation:Subtract the values of any two adjacent labeled graduations and divide by the number of intervals between them.

3-4 = 1 = 1 cm graduations 1 1

2. Take the uncertainty to be 10% of the smallest graduation:

To obtain the correct reading:

We assume that one can measure accurately to one-tenth of the smallest markings = absolute uncertainty

10% of 1 = 0.10 x 1 = 0.1

Therefore your measurement should have:

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1 decimal place 4.74.7 ± 0.1 { 4.6, 4.7, 4.8 }

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Follow the steps and determine the length.

The first digit 4 known plus the second digit 4.5 known

The third and last digit is obtained by estimating. 4.56

Known + estimated number = Significant figures

or Significant numbers

4.56 has 3 significant numbers 6

Summary

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Zero as a Measured Number

1. Find the smallest graduation:Subtract the values of any two adjacent labeled graduations and divide by the number of intervals between them.

4-3 = 1 = 0.1 cm graduations10 10

2. Take the uncertainty to be 10% of the smallest graduation:

4.50 cm

10% of 0.1 = 0.10 x 0.1 = 0.01

Therefore your measurement should have 2 decimal placesThe last digit can be any digit between 0 and 9 in increments of 0.01

Follow the steps and determine the length.

Rules to determine significant figures

1. Use a scientific calculator to carry out the following mathematical operations. Provide answers in scientific notation and one decimal place.

a. (7.2 x 10–3) (2.4 x 105 ) b. 2.4 x 105

7.2 x 10–3

Practice

2. State the number of significant figures in each of the following measurements:

a. 0.030 m b. 4.050 L c. 0.0008 g d. 2.80 m

3. Which answer(s) contains 3 significant figures?

a) 0.4760 b) 0.00476 c) 4.76 x 103

4. All the zeros are significant in a) 0.00307 b) 25.300 c) 2.050 x

103

5. Follow the steps and obtain a measurement for the solids and liquid.

(c)

Practice

Significant Figures in Calculations

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One can not increase significant figures (reduce the uncertainty) by means of a mathematical operation.

2.73 2.7325471Calculator This can only be done by

the measuring instrument.

To remove non-significant numbers one must round-off .

Rules for Rounding Off

If the first digit to be dropped is 4 or less, it and all following digits are dropped. To round 45.832 to 3 significant figures

45.8 32 drop the digits 32 = 45.8

If the first digit to be dropped is 5 or greater, the last retained digit is increased by 1.

To round 2.4884 to 2 significant figures

2.4 884 drop the digits 884 and increase the 4 by 1 = 2.5

Sometimes a calculated answer requires more significant digits. Here one or more zeroes are added.

4.0 x 1.0 = 4 needs to be reported as 4.0

Mathematical operations & Significant FiguresWhen multiplying or dividing use

The same number of significant figures as the measurement with the fewest significant figures.

Example: 110.5x 0.048

8840 4420

0000 0000 005.3040

When adding or subtracting use

The same number of decimal places as the measurement with the fewest decimal places.

4 2 . 5 4 two decimal places- 3 6 . 3 one decimal place

6 . 2 4 6 . 2 answer with one decimal place

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110.5 x 0.048 = 5.304 = 5.3 (rounded)

4 SF 2 SF calculator 2 SF

Not every number is a measured number, non-measured numbers are said to be exact.

When objects are counted.Counting objects

2 soccer balls4 pizzas

From numbers in a defined relationship.Defined relationships

1 foot = 12 inches1 meter = 100 cm

From integer values in equations.In the equation for the radius of a circle, the 2 is

exact.radius of a circle = diameter of a circle

2

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Exact Numbers

Units of Measurement

The units used in most of the world, and everywhere by scientists, are those found in the metric system (~ 1790).

In an effort to improve the uniformity of units used in the sciences, the metric system was modified and called the International System of Units (Système International) or SI (~ 1960).

Measurement Metric SILength meter (m) meter (m)Volume liter (L) cubic meter (m3)Mass gram (g) kilogram (kg)Time second (s) second (s)Temperature Celsius (C) Kelvin (K)

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The metric system or SI (international system) is a decimal system based on 10.

A unit can be increased or decrease by a factor of 10

Unit x 10 increases its value1 x 10 = 10 = 1x101

1 x 10 x 10 = 100 = 1x102

1 x 10 x 10 x 10 = 1000 = 1x103

Unit ÷ 10 decreases its value1/10 = 0.10 = 1x10-1

1/10x10 = 0.010 = 1x10-2

1/10x10x10 = 0.001 = 1x10-3

kilo

decicenti

milli

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An equality states the same magnitude of measurement in two different units.

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The numbers in an equality of the same system are definitions and use exact numbers.

1 m = 1000 mm both 1 and 1000 are exact and not used to determine significant figures.

Different systems (metric and U.S.) use measured numbers and count as significant figures.

1 lb. = 454 g Here, 454 has 3 sig. figs. and the 1 is considered to be exact.

It is a ratio obtained from an equality . Equality: 1 in. = 2.54 cm

It can be inverted to give a second conversion factors . 1 in. and 2.54 cm

2.54 cm 1 in.

• May be obtained from information in a word problem.

The cost of one gallon (1 gal) of gas is $2.54.

1 gallon of gas and $2.54$2.54 1 gallon of gas

• Any ratio can be used as a conversion factor.

Percent % = part x 100 A food contains 30% fat:whole

30 g fat and 100 g food100 g food 30 g fat

Density d = mass the density of a liquid is 3.8g volume mL

Equalities provide conversion factors.

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1 in. 2.54 cm

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6. Perform the following calculations of measured numbers. Give the answers with the correct number of significant figures:

7. For each calculation, round the answer to give the correct number of significant figures.

a. 235.05 + 19.6 + 2 = 1) 257 2) 256.7 3) 256.65

b. 58.925 - 18.2 = 1) 40.725 2) 40.73 3) 40.7

8. Write the equality and conversion factors for each of the following:

a. jewelry that contains 18% gold

b. one gallon of gas is $ 2.95

Practice

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Problem Solving

A person has a height of 180 cm. What is the height in inches?

180 cm x 1 in = 71 in 2.54 cm

How many minutes are in 1.4 days?

1.4 days x 24 hr. x 60 min = 2.0 x 103 min 1 day 1 hr.

You must read the problem carefully and identify what data is given and what they want you to find.

The info is usually a conversion factor. Start solving the problem by the following set-up:

given wantinfo

given x conversion factor(s) = want

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9. Write a complete set-up and solve:

a. If a ski pole is 3.0 feet in length, how long is the ski pole in mm?

b. How many lb of sugar are in 120 g of candy if the candy is 25% (by mass) sugar?

c. An antibiotic dosage of 500 mg is ordered. If the antibiotic is supplied in liquid form as 250 mg in 5.0 mL, how many mL would be given?

d. Synthroid is used as a replacement or supplemental therapy for diminished thyroid function. A dosage of 0.200 mg is prescribed with tablets that contain 50 µg of Synthroid. How many tablets are required to provide the prescribed medication?

Practice