Basic Concepts needed for Chemistry

Scientific Notation

Scientists have developed a shorter method to express very large numbers. This method is called scientific notation. Scientific Notation is based on powers of the base number 10.

The number 123,000,000,000 in scientific notation is written as 1.23 x 1014

The number 0.00000508 in scientific notation is written as 5.08 x 10-6

There is a significant advantage to writing very large or very small numbers this way – they take much less space!

Scientific Notation

Weight of a rabbit: 1420 g

How many significant digits?

On first inspection, we would say 3 sig dig. But, maybe the scale measures to the closest gram

and we have 4 significant digits. How can we be sure? We can’t UNLESS …

We can take the ambiguity out by using scientific notation:

If the value is 1.420 X 103, then we know that the fourth digit is significant

Scientific Notation and Significant Digits

For example, the number 65000000 would be written 6.5 x 107.

In this example the coefficient equals 6.5 (which meets the requirement that 1<y<10)

Since there are seven digits trailing the decimal between the 6 and 5 we must move the decimal point 7 places to the left:

Scientific Notation

For example, the number 0.0000987 would be written 9.87 x 10-5.

In this example the coefficient equals 9.87 (which meets the requirement that 1<y<10)

Since there are seven digits preceding the decimal between the 9 and 87 we must move the decimal point 5 places to the right:

Scientific Notation

An electron's mass is about 0.00000000000000000000000000000091093822 kg.In scientific notation, this is written 9.1093822×10−31 kg.

The Earth's mass is about 5973600000000000000000000 kg.In scientific notation, this is written 5.9736×1024 kg.

The Earth's circumference is approximately 40000000 m.In scientific notation, this is 4×107 m.

An inch is 25400 micrometers.In scientific notation, this is 2.5400×104 µm

Examples

RULE #1: Standard Scientific Notation is a coefficient (y), with 1 ≤ y < 10 followed by a decimal and the remaining significant digits

y is multiplied by 10 raised to an exponent (where the exponent (b) is an integer).

y x 10b: y = coefficient or mantissa or significand b = exponent or power

where 1 ≤ y < 10 and b = Z (integer)

Scientific Notation RULES

Converting a number in these cases means to either convert the number into scientific notation form, convert it back into decimal form or to change the exponent part of the equation.

None of these changes alter the actual number, only how it's expressed.

Converting Numbers

RULE #2: When the decimal is moved to the left the exponent gets larger, but the overall value of the number stays the same. Each place the decimal moves changes the exponent by one. When the decimal is moved to the right the exponent gets smaller,

Example: 6000 = 6000. x 100 (Note: 100 = 1) = 600.0 x 101

= 60.00 x 102

= 6.000 x 103

All the previous numbers are equal, but only 6.000 x 103 is in proper Scientific Notation.

Scientific Notation RULES

2450000 0.000472

▣ Decimal moves 6 places left ▣ Decimal moves 4 places right▣ Coefficient becomes 2.45 ▣ Coefficient becomes 4.72▣ exponent becomes (+) 6 ▣ exponent becomes -4

2.45 x 106 4.72 x 10-4

1) First, move the decimal point to make the coefficient’s (number's) value between 1 & 10.

2) If the decimal was moved to the left, increase the exponent (positive numbers will be produced).

3) If the decimal was moved to the right, decrease the exponent (negative numbers will be produced).

Decimal to Scientific Notation

4.282 x 104 7.5 x 10-5

▣ Decimal moves 6 places left ▣ Decimal moves 4 places right▣ Coefficient becomes 2.45 ▣ Coefficient becomes 4.72▣ exponent becomes (+) 6 ▣ exponent becomes -4

42820 0.0000751) When converting a number from scientific notation to

decimal notation, first remove the x 10b on the end2) If the exponent (b) is positive, shift the decimal

separator b digits to the right. You will have to place zeros for unfilled place values. See red zeros in the example.

3) If the exponent (b) is negative, shift the decimal separator b digits to the left. You will have to place zeros for unfilled place values. See red zeros in the example.

Scientific Notation to Decimal

Convert Decimals to Scientific Notation1) 72.02) 6740003) 0.0000008054) 704.02Convert Scientific Notation to Decimals5) 3.39 × 10-4

6) 8.05 × 106 7) 2.400 × 105 8) 8.205 × 10-5

Try these examples

RULE #3: To add/subtract in scientific notation, the exponents must first be the same.

Example: (3.0 x 102) + (6.4 x 103); since 6.4 x 103 is

equal to 64. x 102. Now add.

(3.0 x 102)+ (64. x 102)

67.0 x 102 = 6.70 x 103 = 6.7 x 10 3

Adding/Subtracting Rules

RULE #4: To multiply, find the product of the numbers, then add the exponents.

Example: (2.4 x 102) (5.5 x 10 –4) = [2.4 x 5.5 = 13.2] exponents [2 + -4 = -

2] so (2.4 x 102) (5.5 x 10 –4) = 13.2 x 10 –2 = 1.3 x 10 – 1

Multiplication RULE

RULE #5: To divide, find the quotient of the number and subtract the exponents.

Example: (3.3 x 10 – 6) / (9.1 x 10 – 8) = [3.3 / 9.1 = .36]; exponents [-6 – (-8) = 2],

so: (3.3 x 10 – 6) / (9.1 x 10 – 8) = .36 x 102 = 3.6 x 10 1

Division Rule

1) 4.90 × 102 + 7.93 × 103

2) 6.95 × 10-4 - 4.89 × 10-5

3) 2.390 × 10-2 + 8.153 × 10-3 + 2.034 × 10-2

4) 1.252 × 106 - 7.08 × 105

Addition and Subtraction Practice

1) (9.2 × 10-6) × (3.0 × 1010)

2) (3.5 × 106) / (5.0 × 102)

3) (4.18 × 10-1) × (3.05 × 1010)

4) (7.15 × 10-6) / (2.735 × 10-4)

5) (3.0 × 107) × (4.0 × 10-4) / (6.0 × 103)

Multiplication and Division Practice

Introduction (13:56) http://www.youtube.com/watch?v=Dme-G4r

c6NI

Just watch this one!

But if you need more help or more practice watch these Tyler DeWitt Videos (see next page)

Tyler DeWitt YouTube Videos

Practice with Scientific Notation (13:31) http://www.youtube.com/watch?v=7iGAa0BVS9I

Scientific Notation: Addition & Subtraction (7:12) http://www.youtube.com/watch?v=PYTp75sryWA

Scientific Notation: Multiplication & Division (5:31)

http://www.youtube.com/watch?v=ciFOlirz4Js

Scientific Notation & Significant Digits (7:58) http://www.youtube.com/watch?v=IIQPHC5gZT8

Tyler DeWitt YouTube Videos

Review: Basic Scientific Notation