Scientific Notation

Making Your Life Easier

Example Problem

N00,000,000,000,000,035,300,000F

m0,000150,000,00

kg,000,00000,000,000,000,000,019,900,000kg0000,000,000,000,000,005,980,000,000,06670.000,000,F

d

mmGF

g

2kgNm

g

2sunearth

g

2

2

Calculate the force of the sun

on the earth:

Decimal Notation (Normal)

My calculator can’t even handle this many digits!

Notes: Scientific Notation

4. Scientific Notation: M · 10n a. M is a number between 1 and 10 b. n is an exponent

i. n is positive: multiply M by 10 n times ii. n is negative: divide M by 10 n times

Example: 340 = 3.4 · 102

M n

· means multiply

Notes: Decimal Notation Scientific Notation

c. Decimal Notation Scientific Notation i. move the decimal point to after the

first nonzero digit ii. n = the number of spaces you moved

the decimal place 1. n is + for numbers bigger

than 1 2. n is - for numbers less than 1

Example:

658,000

Example:

658,000.

Note: if no decimal point is written it automatically goes at the end (right) of the number

Example:

6.58,000.

Example:

658,000.

Notes: Decimal Notation Scientific Notation

c. Decimal Notation Scientific Notation i. move the decimal point to after the

first nonzero digit to get M ii. n = the number of spaces you moved

the decimal place 1. n is + for numbers bigger than

1 2. n is - for numbers less than 1

Notes: Decimal Notation Scientific Notation

Example:

658,000

n = 5

Example:

6.58,000.

c. Decimal Notation Scientific Notation i. move the decimal point to after the

first nonzero digit to get M ii. n = the number of spaces you moved

the decimal place 1. n is + for numbers bigger than

1 2. n is - for numbers less than 1

Notes: Decimal Notation Scientific Notation

c. Decimal Notation Scientific Notation i. move the decimal point to after the

first nonzero digit to get M ii. n = the number of spaces you moved

the decimal place 1. n is + for numbers bigger than

1 2. n is - for numbers less than 1

Example:

658,000

n = 5

Example:

6.58,000.

Note: n is positive since 658,000 is bigger than 1

Notes: Decimal Notation Scientific Notation

Example:

658,000 = 6.58 ·105

c. Decimal Notation Scientific Notation i. move the decimal point to after the

first nonzero digit to get M ii. n = the number of spaces you moved

the decimal place 1. n is + for numbers bigger than

1 2. n is - for numbers less than 1

Notes: Scientific Notation Decimal Notation

Example:

7.04 ·10-3

d. Scientific Notation Decimal Notation i. move the decimal point n spaces

1. n is positive: move so your number is bigger than 1

2. n is negative: move so your number is less than 1

ii. fill in empty spaces with zeros

Notes: Scientific Notation Decimal Notation

Example:

7.04 ·10-3

d. Scientific Notation Decimal Notation i. move the decimal point n spaces

1. n is positive: move so your number is bigger than 1

2. n is negative: move so your number is less than 1

ii. fill in empty spaces with zeros

Notes: Scientific Notation Decimal Notation

Example:

7.04 ·10-3

d. Scientific Notation Decimal Notation i. move the decimal point n spaces

1. n is positive: move so your number is bigger than 1

2. n is negative: move so your number is less than 1

ii. fill in empty spaces with zeros

Example:

0.007.04 ·10-3

Notes: Scientific Notation Decimal Notation

d. Scientific Notation Decimal Notation i. move the decimal point n spaces

1. n is positive: move so your number is bigger than 1

2. n is negative: move so your number is less than 1

ii. fill in empty spaces with zeros

Example:

0.007.04 ·10 -3

Notes: Scientific Notation Decimal Notation

d. Scientific Notation Decimal Notation i. move the decimal point n spaces

1. n is positive: move so your number is bigger than 1

2. n is negative: move so your number is less than 1

ii. fill in empty spaces with zeros

Example:

7.04 ·10-3 = 0.007,04

Notes: Scientific Notation Decimal Notation

d. Scientific Notation Decimal Notation i. move the decimal point n spaces

1. n is positive: move so your number is bigger than 1

2. n is negative: move so your number is less than 1

ii. fill in empty spaces with zeros

Added so you notice the decimal point

Example Problem

N00,000,000,000,000,035,300,000F

m0,000150,000,00

kg,000,00000,000,000,000,000,019,900,000kg0000,000,000,000,000,005,980,000,000,06670.000,000,F

d

mmGF

g

2kgNm

g

2sunearth

g

2

2

Calculate the force of the sun

on the earth:

Decimal Notation (Normal)

My calculator can’t even handle this many digits!

Example Problem

Scientific Notation

Much easier! Your calculator can do this for you.

N10533.F

m1051.

kg101.99kg105.98106.67F

d

mmGF

22g

211

3024

kgNm11

g

2sunearth

g

2

2

Calculate the force of the sun

on the earth:

Notes:

4. Scientific Notation: M x 10n a. M is a number between 1 and 10 b. n is an exponent

i. n is positive: multiply M by 10 n times ii. n is negative: divide M by 10 n times

c. Decimal Notation Scientific Notation i. move the decimal point to after the first nonzero digit to get M

ii. n = the number of spaces you moved the decimal place 1. n is + for numbers bigger than 1 2. n is - for numbers less than 1

d. Scientific Notation Decimal Notation i. move the decimal point n spaces

1. n is positive: move so your number is bigger than M 2. n is negative: move so your number is less than M

ii. fill in empty spaces with zeros

SI PrefixesPrefix Abbreviation

ScientificNotation

Tera- T 1012

Giga- G 109

Mega- M 106

kilo- k 103

- - - centi- c 10-2

milli- m 10-3

micro- μ 10-6

nano- n 10-9

pico- p 10-12