Scientific NotationScientific Notationand and

Powers of Ten Powers of Ten

77thth grade math grade math

Powers!! Powers!!

Power is a way to write a Power is a way to write a multiplication problem.multiplication problem.

It has two parts: base and an It has two parts: base and an exponentexponent

–BaseBase (big #) (big #)–Exponent (tiny #)Exponent (tiny #)

Base and ExponentBase and Exponent

BBEE

Base is the # you multiply.Base is the # you multiply.

Exponent is how many times Exponent is how many times you multiply it.you multiply it.

ExampleExample

553 3 = 5 x 5 x 5= 125= 5 x 5 x 5= 125

6644 = 6 x 6 x 6 x 6= 1296 = 6 x 6 x 6 x 6= 1296

Examples w/ exponent of 1Examples w/ exponent of 1

Anytime 1 is your exponent, the base Anytime 1 is your exponent, the base remains the same…remains the same…

6611 = 6 = 6

21521511= 215= 215

Examples w/ exponent of 0Examples w/ exponent of 0

Anytime zero is your exponent, your Anytime zero is your exponent, your answer is 1.answer is 1.

5500= 1= 1

75875800 = 1 = 1

Power of TenPower of Ten

Vocabulary: Vocabulary: – Standard form: traditional (normal) way Standard form: traditional (normal) way

to write numbersto write numbers– Scientific Notation: shorthand “sciency” Scientific Notation: shorthand “sciency”

way to write numbersway to write numbers

Power of TenPower of TenWhen you have a problem that uses a When you have a problem that uses a power of ten, then you will move the power of ten, then you will move the decimal right that many places…decimal right that many places…

Example: Example: 48 x 1048 x 1055= 4,800,000 (you moved the = 4,800,000 (you moved the

decimal 5 places right)decimal 5 places right)

7.29 x 107.29 x 1044= 72,900 (you moved the = 72,900 (you moved the decimal 4 places right)decimal 4 places right)

Power of TenPower of Ten

Writing numbers in scientific Writing numbers in scientific notation….notation….

428,000= 4.28 x 10428,000= 4.28 x 105 5

– Why? ---- You move the decimal so that Why? ---- You move the decimal so that 1 non zero number is in the ones spot 1 non zero number is in the ones spot and count how many places you had to and count how many places you had to move it--- that number becomes your move it--- that number becomes your exponent. exponent.

Negative PowersNegative PowersWhen you have a problem that uses a When you have a problem that uses a negative power of ten, then you will move negative power of ten, then you will move the decimal left that many places…the decimal left that many places…

Example: Example: 4.8 x 104.8 x 1055= .000048 (you moved the = .000048 (you moved the

decimal 5 places left)decimal 5 places left)

7.29 x 10-7.29 x 10-44= .000729 (you moved the = .000729 (you moved the decimal 4 places left)decimal 4 places left)

Negative PowersNegative Powers

Writing numbers in scientific Writing numbers in scientific notation….notation….

.0028= 2.8 x 10.0028= 2.8 x 10-3-3

– Why? ---- You move the decimal so that Why? ---- You move the decimal so that 1 non zero number is in the ones spot 1 non zero number is in the ones spot and count how many places you had to and count how many places you had to move it--- that number becomes your move it--- that number becomes your exponent. exponent.