**Chapter 3: Scientific Measurement**

Scientific Notation

In

Scientific Notation

, a given number is written as the product of two numbers:

A coefficient and 10 raised to a power

Ex: the number 702,000,000,000,000,000,000,000 can be wrtten as 7.02 x 10^23

The coefficient is 7.02

The power of 10 or exponent is 23

Scientific Notation

How do you write numbers in scientific notation?

The coefficient is always a number greater than or equal to one and less than ten. The exponent is an integer.

A

positive exponent

indicates how many times the coefficient must be multiplied by 10

A

negative exponent

indicates how many times coefficient must be divided by 10.

Scientific Notation

Multiplication and Division

To multiply numbers written in scientific notation multiply the coefficients and add the exponents

To divide numbers written in scientific notation, divide the coefficients and subtract the exponent in the denominator from the exponent in the numerator

Measurement

Measurement

is a quantity that has both a number and a unit

Measurements are fundamental to the experimental sciences

In Chemistry you often encounter

very large

numbers

Ex:

a single gram of hydrogen contains 602,000,000,000,000,000,000,000 hydrogen atoms

Or

very small

numbers

Ex:

the mass of an atom of gold is 0.000 000 000 000 000 000 000 327 gram

**By:**

Krystiana Ceselka and Jasmine Varma

Krystiana Ceselka and Jasmine Varma

Positive

Negative

Scientific Notation

Addition and Subtraction

When adding and subtracting numbers in scientific notation without a calculator

Exponents

must

be the same

Decimal points

must

be aligned before you add and subtract

Accuracy and Precision

Accuracy

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

Precision

is a measure of how close a series measurements are to one another, irrespective of the actual value

How do you evaluate accuracy and precision?

Accuracy

: the measured value must be compared to the correct value

Precision

: must compare the values of two or more repeated measurements

Percent Error

Accepted value

is the correct value for the measurement based on reliable references

Experimental Value

the value measured in a lab

Error

is the difference between the

experimental value

and the

accepted value

Percent Error

is the absolute value of the

error

divided by the

accepted

value

multiplied by 100%

Significant Figures

Significant figures

in a measurement include all of the digits that are known, plus a last digit that is estimated

Why must measurements be reported to the correct number of significant figures?

Because calculated answers often depend on the number of significant figures in the values used in the calculations

Significant Figure Rules

All digits 1-9 are significant

Embedded zeros embedded between significant digits

are always

significant

Trailing zeros in a number are significant

only

if the number contains a decimal point

The leading zeros at the beginning of a number are

never

significant

Zeros following a decimal significant figure

are always

significant

Exceptions to the rule are number with an

unlimited

number of sig figs

Significant Figures

Rounding

First determine the number of sig figs, then count from the left, and round

< 5: stays the same

> 5: increases by 1

Multiplying and Dividing

Limit and round the the

least number

of

significant figures

in any of the factors

Addition and Subtraction

Limit and round your answer the to the

least number

of

decimal places

in any of the numbers that make up your answer

Units of Measurement

The standards of measurement used in science are those of the metric system

All metric units are based on multiples of 10

They can be converted between units easily

The

International System of Units

(SI) is a revised version of the metric system

Temperature Scales

Scientists commonly use two equivalent units of temperature: the degree Celsius and the kelvin

The

Celsius scale

uses the freezing point of water (0°C) and the boiling point of water (100°C) as reference values

On the

Kelvin scale

the freezing point of water is 273.15 kelvins (K) and the boiling point is 373.15 K

Density

Density

is the ratio of the mass of an object to its volume

It is an intensive property that depends only on the composition of a substance, not on the size of the sample

Conversion Factor

A

conversion factor

is a ratio of equivalent measurements

The measurement in the numerator is equivalent to the denominator

Examples: the ratios

100 cm/1 m

and

1 m/ 100 cm

What happens when a measurement is multiplied by a conversion factor?

The numerical value changes

The actual size of the quantity measured remains the same

Dimensional Analysis

Dimensional analysis

is a way to analyze and solve problems using the units, or dimensions, of the measurements

Many problems in chemistry are conveniently solved using dimensional analysis

What kind of problems can you solve using dimensional analysis?

Conversion problems in which a measurement with one unit is changed to an equivalent measurement with another unit

1.

When multiplying with scientific notation

A) divide the coefficients, subtract exponents

B)multiply coefficients, add exponents

C) subtract exponents, divide exponents

D) add coefficients, multiply exponent

2.The standards of measurements in science are those of the metric system. All metric units are based on multiples of:

A) 5

B)100

C)10

D)1000

3. Conversion factor is:

A) a ratio of equivalent measures

B) the ratio of the mass of an object to its volume

C) a quantity that has a number and a unit

D) a given number written as a product of two numbers

4. What is the formula for converting Celsius to Kelvin?

A) K= C-273

B) K= C*273

C) K= C/273

D) K= C+273

5. If the temperature is 478K, what is the temperature in Celsius?

A) 204C

B) 207C

C) 205C

D) 206C