Scientific Notation

Scientific NotationAt the conclusion of our time together, you should be able

to:

1. Define scientific notation2. Convert numbers into scientific notation3. Convert scientific notation to a standard

number

Testing Skill #5

What is Scientific Notation?What is Scientific Notation?

Scientific notation is a way of expressing really big numbers or really small numbers.

For very large and very small numbers, scientific notation is more concise.

Scientific Notation Consists Of Two Parts:Scientific Notation Consists Of Two Parts:

M = A number between 1 and 10

n = A power of 10

M x 10n

Scientific Notation

M x 10M x 10nn

M is the coefficient 1<M<1010 is the basen is the exponent or power of 10

Other Examples:

5.45E+6

5.45 x 10^6

Chemical Compound Quiz

What do sand and water have in common from a chemical point of view?

Oxygen

Numbers Less Than 1 Will Have A Negative Exponent.

A millionth of a second is:

0.000 001 sec 1 x 10-6 s 1.0E-6 s 1.0 x 10^-6

s

To Change Standard Form To Scientific To Change Standard Form To Scientific Notation…Notation…

Place the decimal point so that there is one non-zero digit to the left of the decimal point.

Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.

If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

ExamplesExamples

Given: #3 22 450 000 gUse: 2.245 g (moved 7 places)Answer: 2.245 x 107 gEasier Way = M term smaller, so make

n term larger - 100 to 107

Given: #2 0.005 45 gUse: 5.45 (moved 3 places)Answer: 5.45 x 10-3 gEasier Way = M term larger, so make

n term smaller - 100 to 10-3

To Change Scientific Notation To To Change Scientific Notation To Standard Form…Standard Form…

Simply move the decimal point to the right Simply move the decimal point to the right for for positivepositive exponent of 10. exponent of 10.

Move the decimal point to the left for Move the decimal point to the left for negativenegative exponent of 10. exponent of 10.

(Use zeros to fill in places.)(Use zeros to fill in places.)

ExampleExample

Given: #19 4.21 x 106 mAnswer: 4 210 000 m (moved 6 places to

the right)Easier Way = 106 to 100 = n smaller, so

make M term larger!Given: #17 8.4356 x 10-4 mAnswer: 0.000 843 56 m (moved 4 places

to the left)Easier Way = 10-4 to 100 = n larger, so

make M term smaller!

Scientific NotationLet’s see if you can:

1. Define scientific notation2. Convert numbers into scientific notation3. Convert scientific notation to a standard

number

I feel much better now...

that I have given up hope!!!

Learning Check

Express these numbers in Scientific Express these numbers in Scientific Notation:Notation:

1)1) 405 000 cm405 000 cm

2)2) 0.003 872 cm0.003 872 cm

3)3) 3 000 000 000 cm3 000 000 000 cm

4)4) 2 cm2 cm

5)5) 0.000 000 478 cm0.000 000 478 cm

4.05 x 105 cmcm

3.872 x 10-3 cmcm

3 x 109 cmcm

2 x 100 cmcm

4.78 x 10-7 cmcm

Scientific Notation

Calculations

Scientific NotationAt the conclusion of our time

together, you should be able to:

1. Multiply and divide numbers that are in scientific notation

2. Add and subtract numbers that are in scientific notation

ExampleExample

(3 x 102 m)(8 x 10-4 m)Answer: multiply M terms 24 Add n terms -2 24 x 10-2 m2

Adjust to correct scientific notation 2.4 x 10-1 m2

Adjust to correct number of sig figs 2 x 10-1 m2

Example #23Example #23

(3.890 x 108 km)/(1.97 x 103 s)Answer: divide M terms 1.974 619 km/sSubtract n terms 5 1.974 619 x 105 km/sAdjust to correct scientific notation 1.974 619 x 105 km/sAdjust to correct number of sig figs 1.97 x 105 km/s

ExampleExample

(5.0 x 104 m)(8.230 x 106 m)/(1.99 x 1018 m)

Answer: multiply and divide M terms 20.678 mAdd and subtract n terms -8 20.678 x 10-8 mAdjust to correct scientific notation 2.0678 x 10-7 mAdjust to correct number of sig figs 2.1 x 10-7 m

Example #15Example #15

(9.875 x 102 mL)-(2.343 x 101 mL)Answer: can only subtract like powersAdjust to larger power(9.875 x 102 mL)-(0.2343 x 102 mL) = 9.6407 x 102 mLAdjust to correct number of decimal

places 9.641 x 102 mLAdjust to correct scientific notation 9.641 x 102 mL

Example #12Example #12

(2.367 x 10-3 mL) + 5.4 x 10-2 mL Answer: can only add like powersAdjust to larger power(0.2367 x 10-2 mL) + 5.4 x 10-2 mL = 5.6367 x 10-2 mL Adjust to correct number of decimal

places 5.6 x 10-2 mL Adjust to correct scientific notation 5.6 x 10-2 mL

ExampleExample

(5.0 x 10-3 m) + (5.0 x 10-4 m) - 0.009 38 mAnswer: can only add like powersAdjust to larger power(0.0050 x 100 m) + (0.000 50 m) – 0.009 38

m -0.003 88 mAdjust to correct number of decimal places -0.003 9 mAdjust to correct scientific notation -3.9 x 10-3 m

Familiar Saying

Surveillance should precede salientation.

Look before you leap!!!

Scientific NotationLet’s see if you can:

1. Multiply and divide numbers that are in scientific notation

2. Add and subtract numbers that are in scientific notation