7.2 Powers of 10 and Scientific Notation

Pg. 452

Definition• Powers of 10– Exponential form, where the base is 10 raised

to some power

• Scientific Notation– All numbers can be represented as a number

between 1 and 10, times 10 raised to a power

410 410 10000410 4 1

1010000

4657 34.657 x 10

.000046 54.65 x 10

Knowledge• Scientific Notation Numbers

– Numbers that are … something times 10 raised to a power

– When converting to Decimal Notation• Negative Exponents (powers), will move the decimal

point to the left• Positive Exponents (powers), will move the decimal

point to the right

• Decimal Notation– Any number that is not … times 10 raised to a

power– When converting to Scientific Notation

• Moving the decimal point to the right will have a negative exponent on the “10”

• Moving the decimal point to the left will have a positive exponent on the “10”

Powers of 10

• Each time you divide by 10, the decimal point moves one place to the left

• Each time you multiply by 10, the decimal point moves one place to the right

Power

Value

310 210 110 010 110 210 310

1000 100 101

0.0011000

10.01

1001

0.110

1

Example #1, Evaluating Powers of 10

• Find the value of each power of 10.– Always start with “1” and move the decimal

point

3 2 010 10 10

Example #2, Writing Powers of 10

• Write each number as a power of 10

10,000,000 0.001 10

Example #3, Multiplying by Powers of 10

• Find the value of each expression6

4

5

2

97.86 x 10

19.5 x 10

853.4 x 10

0.163 x 10

Homework• Pg. 455, 14 – 42 Even