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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

4.3210 metersnumber + 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 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 1 decimal place4.7 ± 0.1 { 4.6, 4.7, 4.8 }

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

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

Follow the steps and determine the length.

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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.

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

Follow the steps and determine the length.

Rules to determine significant figures

Exact Numbers 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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1.4 Significant Figures in Calculations

This can only be done by the measuring instrument.• When we carry out a mathematical operation such as:

4.25 3 sf

X 0.10 2 sf least

0.425 3 sf

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

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

2.7 2.735Calculator

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

45.8 32drop the digits 32 = 45.8

Rules for Rounding Off

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

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

4.0 x 1.0 = 4 needs to reported as 4.0

Mathematical operations & Significant Figures

When multiplying or dividing use The same number of significant figures as the measurement with the fewest significant

figures.

Rounding to obtain the correct number of significant figures.

Example:

110.5 x 0.048 = 5.304 = 5.3 (rounded)

4 SF 2 SF calculator 2 SF

When adding or subtracting use The same number of decimal places as the measurement with the fewest decimal

places.

Rounding rules to adjust the number of digits in the answer.

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

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

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1.1 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.

Unit x 10 increases its value

1 x 10 = 10 = 1x101

1 x 10 x 10 = 100 = 1x102

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

Unit ÷ 10 decreases its value

1/10 = 0.10 = 1x10-1

1/10x10 = 0.010 = 1x10-2

1/10x10x10 = 0.001 = 1x10-3

kilo

deci

centi

milli

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

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An equality states the same 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 exact.

It is a ratio obtained from an equality (see p. 33 table 1.9). 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 $2.94.

1 gallon of gas and $2.94$2.94 1 gallon of gas

• Any ratio can be used as a conversion factor.Percent % = part x 100

wholeA food contains 30% fat: 30 g fat and 100 g food

100 g food 30 g fat

Density d = mass volume

the density of a liquid is 3.8gmL

Equalities provide conversion factors.

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1.7 Problem Solving

Use Conversion factors to solve problems:

In general, problems give you something and want you to find something else

given x conversion factor(s) = want

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.

Practice

4. 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

5. Which answer(s) contains 3 significant figures? a) 0.4760 b) 0.00476 c) 4.76 x 103

3. 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

2. Write the following as standard numbers:a. 7.2 x 10–3 m b. 2.4 x 105 g

1. Write the following measurements in scientific notation:a. 0.000 16 L b. 5 220 000 m

6. All the zeros are significant in 1) 0.00307 2) 25.300 3) 2.050 x

103

7. The number of significant figures in 5.80 x 102 is 1) one 2) two 3) three

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

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

10. 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

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

a. meters and centimeters b. jewelry that contains 18% gold c. one gallon of gas is $ 2.95

d. hours and minutes e. Density of water is 1.00 g/mL

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12. 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. If olive oil has a density of 0.92 g/mL, how many liters of olive oil are in 285 g of olive oil?

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

d. 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?

e. 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?