Transcript Scientific Notation

Scientific Notation
Making Your Life Easier
Mr. Gabrielse
Example Problem
Calculate the
force of the sun
on the earth:
Decimal Notation (Normal)
Fg  G

m earth m sun
d2
Fg  0.000,000,000,0667 Nm
kg 2
2
000 kg 19,900,000,000,000,000,000,000,000,000 kg 
5,980,000,000,000,000,000,000,150,000,00
0,000 m 
2
Fg  35,300,000,000,000,000,000,000 N
My calculator can’t even handle this many digits!
Mr. Gabrielse
Notes: Scientific Notation
· means multiply
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
Mr. Gabrielse
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.
658,000
Note: if no decimal point is written it
automatically goes at the end (right) of the
number
Mr. Gabrielse
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:
6.58,000.
658,000.
Mr. Gabrielse
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:
6.58,000.
658,000
n=5
Mr. Gabrielse
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:
6.58,000.
658,000
n=5
Note: n is positive since 658,000 is bigger than 1
Mr. Gabrielse
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 = 6.58 ·105
Mr. Gabrielse
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
Mr. Gabrielse
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
Mr. Gabrielse
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
Mr. Gabrielse
Notes: Scientific Notation  Decimal Notation
Example:
0.007.04 ·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
Mr. Gabrielse
Notes: Scientific Notation  Decimal Notation
Example:
0.007.04 ·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
Mr. Gabrielse
Notes: Scientific Notation  Decimal Notation
Example:
7.04 ·10-3 = 0.007,04
Added so you notice the decimal point
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
Mr. Gabrielse
Example Problem
Calculate the
force of the sun
on the earth:
Decimal Notation (Normal)
Fg  G

m earth m sun
d2
Fg  0.000,000,000,0667 Nm
kg 2
2
000 kg 19,900,000,000,000,000,000,000,000,000 kg 
5,980,000,000,000,000,000,000,150,000,00
0,000 m 
2
Fg  35,300,000,000,000,000,000,000 N
My calculator can’t even handle this many digits!
Mr. Gabrielse
Example Problem
Calculate the
force of the sun
on the earth:
Scientific Notation
Fg  G

m earth m sun
d2
Fg  6.67 10
11 Nm 2
kg 2
5.98 10 kg 1.99 10
1.5 10 m 
24
11
30
kg

2
Fg  3.53 10 22 N
Much easier! Your calculator can do this for you.
Mr. Gabrielse
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
Mr. Gabrielse
Your Turn!
1. Convert to Scientific Notation: 55,601
2. Convert to Scientific Notation: 30,800,000
3. Convert to Scientific Notation: 0.034
4. Convert to Scientific Notation: 0.005,000,702
Mr. Gabrielse
Your Turn!
1. Convert to Scientific Notation: 55,601
55,601 = 5.560,1 ·104
2. Convert to Scientific Notation: 30,800,000
30,800,000 = 3.08 ·107
3. Convert to Scientific Notation: 0.034
0.034 = 3.4 ·10-2
4. Convert to Scientific Notation: 0.005,000,702
0.005,000,702 = 5.000,702 ·10-3
Mr. Gabrielse
Your Turn!
5. Convert to Decimal Notation: 6.0 ·104
6. Convert to Decimal Notation: 9.05 ·10-11
7. Convert to Decimal Notation: 8.820 ·10-1
8. Convert to Decimal Notation: 4.532,1 ·1013
Mr. Gabrielse
Your Turn!
5. Convert to Decimal Notation: 6.0 ·104
6.0 ·104 = 60,000
6. Convert to Decimal Notation: 9.05 ·10-11
9.05 ·10-11= 0.000,000,000,090,5
7. Convert to Decimal Notation: 8.820 ·10-1
8.820 ·10-1= 0.882,0
8. Convert to Decimal Notation: 4.532,1 ·1013
4.532,1 ·1013= 45,321,000,000,000
Mr. Gabrielse