Scientific Notation Making Your Life Easier
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