Scientific Notation

Scientific Notation

• Do you know this number, 300,000,000 m/sec.?

• It's the Speed of light !

• Do you recognize this number,

0.000 000 000 753 kg.

• This is the mass of a dust particle!

• Scientists have developed a shorter method to express very large numbers or very small numbers.

• This method is called scientific notation.• The number 123,000,000,000 in scientific

notation is written as :

Scientific Notation

• The first number 1.23 is called the base. It must be greater than or equal to 1 and less than 10.

• The second number is written in exponent form or 10 to some power.

• The exponent is the number of decimal places needed to arrive at the bass number.

To write a number in scientific notation:

• Put the decimal after the first digit and drop the zeroes.

• This gives you the base number. • In the number 123,000,000,000

The base number will be 1.23 • To find the exponent count the

number of places from the decimal to the end of the number.

• In 123,000,000,000 there are 11 places

Multiplying Scientific Notated Numbers

• Multiply the base numbers

• Add the exponents of the Tens

• Adjust the base number to have one digit before the decimal point by raising or lowering the exponent of the Ten

+

3.25 X 10 3 X 2.50 x10 5 =

3.25 X 2.50 3 + 5= 8

8.125 X 10 8

Dividing Scientific Notation Numbers • Divide the base numbers

• Subtract the exponents of the Tens

• Adjust the base number to have one digit before the decimal point by raising or lowering the exponent of the Ten

Dividing

• Divide 3.5 x 108 by 6.6 x 104 • You may rewrite the problem as: • 3.5 x 108

6.6 x 104

• Now divide the two base numbers • Subtract the two powers of 10 • Adjust base number to have one number

before the decimal

3.5 x 108

6.6 x 104

3.5 is now divided by 6.6 in this order on the calculator.

0.530303 x 104

4 is now subtracted

from 8

Change to correct scientific notation to get: 5.3 x 103 Note - We subtract one from the exponent because we moved the decimal one place to the right.

Scientific Notation - Addition and Subtraction

• All exponents MUST BE THE SAME before you can add and subtract numbers in scientific notation. The actual addition or subtraction will take place with the numerical portion, NOT the exponent.

• You must change the base number on one of the digits by moving the decimal.

• Always make the powers of ten the same as the largest.

• Move the decimal on the smallest number until its power of ten matches that of the largest exponent.

• Ex. 1  Add 3.76 x 104 and 5.5 x 102

• move the decimal to change 5.5 x 102 to 0.055 x 104

• add the base numbers and leave the exponent the same:  3.76 + 0.055 = 3.815 x 104

• following the rules for rounding, our final answer is 3.815 x 104

• Subtraction is done exactly in the same manor.

Dimensional Analysis

• Dimensional Analysis (also called Factor-Label Method or the Unit Factor Method) is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value. It is a useful technique.

• Unit factors may be made from any two terms that describe the same or equivalent "amounts" of what we are interested in.

• For example, we know that

• 1 inch = 2.54 centimeters

Unit Factors• We can make two unit factors from this

information:

• When converting any unit to another there is a pattern which can be used.

• Begin with what you are given and always multiply it in the following manner.

• Given units X = Want units

• You will always be able to find a relationship between your two units.

• Fill in the numbers for each unit in the relationship.

• Do your math from left to right, top to bottom.

Want units

Given units

Given units X = Want units

• (1) How many centimeters are in 6.00 inches?

Want Units

Given Units

Metric System of Measurement

System International

Or

International System of Measurement

•Based on units of ten

Basic Units of Measure

• Length – Distance : meter (metre) m• Time – second s• Mass – grams g or kilograms kg• Volume – liter (litre) l

1cc=1cm3=1ml

1dm3=1liter (l)• Temperature – Celsius C or• Kelvin K = C + 273

Metric PrefixesPrefix: Symbol: Magnitude: Meaning (multiply by):

Yotta- Y 1024 1 000 000 000 000 000 000 000 000

Zetta- Z 1021 1 000 000 000 000 000 000 000

Exa- E 1018 1 000 000 000 000 000 000

Peta- P 1015 1 000 000 000 000 000

Tera- T 1012 1 000 000 000 000

Giga- G 109 1 000 000 000

Mega- M 106 1 000 000

myria- my 104 10 000 (this is now obsolete)

kilo- k 103 1000

hecto- h 102 100

deka- da 10 10

- - - -

deci- d 10-1 0.1

centi- c 10-2 0.01

milli- m 10-3 0.001

micro- u (mu) 10-6 0.000 001

nano- n 10-9 0.000 000 001

pico- p 10-12 0.000 000 000 001

femto- f 10-15 0.000 000 000 000 001

atto- a 10-18 0.000 000 000 000 000 001

zepto- z 10-21 0.000 000 000 000 000 000 001

yocto- y 10-24 0.000 000 000 000 000 000 000 001

Conversion in the Metric System • If you can remember something silly, 

• ("King Henry Died Monday Drinking Chocolate Milk"),  the metric

conversions are so easy. • King Henry Died Monday Drinking Chocolate Milk• (km) (hm) (dam) (m/unit) (dm) (cm) (mm)• Remember the 1st letter is the symbol for the prefix

and the second is the unit you are measuring in.• Just sketch the  chart above (K, H, D, M, D, C, M) and

place the number you wish to convert under the proper slot.

• Move the decimal point left or right the correct number of places to make the conversion.

Example: convert 43.1 cm to km. • King Henry  Died  Monday Drinking Chocolate Milk• (km) (hm) (dam) (m/unit) (dm) (cm) (mm)• 43.1• This is a move of 5 places to the left filling spaces

with zeros and you get• .000431 km

•King Henry  Died  Monday Drinking Chocolate Milk• (km) (hm) (dam) (m/unit) (dm) (cm) (mm)• 43.1•This is a move of 2 places to the right filling spaces with zeros and you get•4310 mm

Example:convert 43.1 dm to mm.

Significant Digits or Figures

• Significant digits, which are also called significant figures. Each recorded measurement has a certain number of significant digits.

• The significance of a digit has to due with whether it represents a true measurement or not.

• Any digit that is actually measured or estimated will be considered significant

Rules For Significant Digits

1. Digits from 1-9 are always significant.

2. Zeros between two other significant digits or counting numbers are always significant.

3. One or more zeros to the right of both the decimal place and another significant digit are significant.

Significant Digit Examples

1. All counting numbers: 1,238 there are

4 significant digits in this number.

2. Zero’s between counting number: 123,005 in this number there are 6 significant digits

3. Zero’s to the right of the decimal and the right or end of the number count as significant digits: 123.340 in this number there are 6 significant digits

Significant Digit Rules For Multiplication and Division Answers

1. Your final answer will have the same number of digits as that with the least number of significant digits in the problem.

2. Ex: 2.43 X 35 = 85.05 since in the problem the least number of significant digits is two then your answer will be 85

3. Do not forget to round up or leave where needed.

Significant Digit Rules for Subtraction and Addition

1. The correct number of digits in the final answer will be the same as the least number of decimal places in the problem.

2. Ex: 123.45 12.456 +1045.4 1181.306 since the least number of

decimal places is one then the final answer is 1181.33. Remember to check for round off or not.