SCIENTIFIC NOTATION & DIMENSIONAL ANALYSIS
I.
SCIENTIFIC NOTATION
A. Basics: Scientific notation is useful when numbers are very _________
or _________. The original number is converted into a more manageable expression.
The first number in the expression must be at least____ but less than ________.
If the original number is a _____________ then the exponent is negative. If the
original number is _______ or greater then the exponent is positive.
Examples: Change to scientific notation
1) 0.000 000 045 =_______________
2) 323,300 = _______________
3) 3400 = ____________________
4) 0.000 99 = ______________
Change to ordinary notation:
1) 5.45 x 106 =________________
2) 6.1114 x 10-4 = _______________
3) 4.3 x 104 = ________________
3) 8.9 x 10
II.
-7
= ________________
DIMENSIONAL ANALYSIS (D.A.)
D.A. is a _____________________ method often used in physics.
Conversion Factor (CF): Relates 2 different units that are ________ to each other
Examples of CFs:__________________________________________________
General Format for D.A.: New Value = (Given #) x (CF 1) x (CF 2) x (CF3) ….
The KEY to using Dimensional Analysis is to _______________ out
_________________ until you get the ______________ you want.
Example 1: How many minutes are in 1 MHS school day?
Given/Know:
Plan:
Solve:
Example 2: If you can drive 12 hours in 1 day at an average speed of 45 miles per
hour, how long will it take you to drive to New Mexico, which is 3450 miles away?
Given/Know:
Plan:
Solve:
Example 3: How many seconds have you been alive?
Given/Know:
Plan:
Solve:
Remember: 1) Write out all the steps before multiplying.
2) Check to make sure your answer makes sense!
SCIENTIFIC NOTATION & DIMENSIONAL ANALYSIS
III. SCIENTIFIC NOTATION
A. Basics:
Scientific notation is useful when numbers are very large_____
or small_____. The original number is converted into a more manageable expression.
The first number in the expression must be at least_1_ but less than ____10____.
If the original number is a _decimal_______ then the exponent is negative. If the
original number is __one_____ or greater then the exponent is positive.
Examples: Change to scientific notation
1) 0.000 000 045 =______4.5 x 10-8_
2) 323,300 = ___3.233 x 105__
3)
3400 = 3.4 x 103
4) 0.000 99 = 9.9 x 10-4
Change to ordinary notation:
1) 5.45 x 106 =____5,450,000___
2) 6.1114 x 10-4 = ____0.00061114_
3) 4.3 x 104 = 43000
4) 8.9 x 10
-7
= _0.000 000 89
IV.
DIMENSIONAL ANALYSIS (D.A.)
D.A. is a ____problem solving___________ method often used in physics.
Conversion Factor (CF): Relates 2 different units that are _equal__ to each other
Examples of CFs:_(1in = 2.54cm) (1mL = 0.034oz)_(1gal = 3.8L) (1mi = 1.6km)
General Format for D.A.: New Value = (Given #) x (CF 1) x (CF 2) x (CF3) ….
The KEY to using Dimensional Analysis is to _cancel________ out
_units___________ until you get the ___units________ you want.
Example 1: How many seconds are in 5 MHS school days?
Given/Know: (1 MHSday = 6hr) (1 hr = 60 min) (1 min = 60 s)
Plan: day  hour  min  sec
Solve: 5 day (6hr/day)(60 min/ 1hr) = 1800 min
Example 2: If you can drive 12 hours a day at an average speed of 45 miles per hour, how
long will it take you to drive to New Mexico, which is 3450 miles away?
Given/Know: (12hr=1day) (1 hour = 45 miles)
Plan: miles  hours  days
Solve: 3450 mi (1 hr/ 45 mi) (1 day/ 12 hr) = 6.38888 = 6.39 days
Example 3: How many seconds have you been alive?
17 yrs(365 days/1yr) (24hr/day) (60 min/hr) ( 60s / min) = 536,112,000 s