changing units
DESCRIPTION
Changing Units. Δ. The Problem. Example: You need to know an answer in μ g but your scale measures in mg. Sometimes you need a different metric prefix than you have. ( )(1) =. Math Fact # 1. Any quantity multiplied or divided by 1 does not change. Math Fact # 2. - PowerPoint PPT PresentationTRANSCRIPT
J. Gabrielse
ΔChanging Units
J. Gabrielse
The Problem
Example: You need to know an answer in μg but your scale measures in mg.
Sometimes you need a different metric prefix than you have.
J. Gabrielse
Math Fact # 1
Any quantity multiplied or divided
by 1 does not change.
A2.3A)(1)(2.3
mol151
mol15
( )(1) =
J. Gabrielse
Math Fact # 2
Any quantity divided by itself is equal to 1.
J. Gabrielse
Math Fact # 2EXAMPLE
Any quantity divided by itself is equal to 1.
It doesn’t matter if it is written differently!
1340
103.4 2
?
J. Gabrielse
Math Fact # 2EXAMPLE
Any quantity divided by itself is equal to 1.
It doesn’t matter if it is written differently!
1g10700
mg7003
?
J. Gabrielse
Math Fact # 2Example
= 1
Any quantity divided by itself
equals 1.
Any quantity multiplied by 1 does
not change.
J. Gabrielse
The Problem
Example: You measure 1,435 mg but you need to know in μg.
Sometimes you need a different metric prefix than you have.
J. Gabrielse
The Solution:Use Math Facts 1 & 2 to Change Units
Turn your metric prefix into a power of ten.
J. Gabrielse
The Solution:Use Math Facts 1 & 2 to Change Units
g101,435mg 1,435 3
Turn your metric prefix into a power of ten.
J. Gabrielse
The Solution:Use Math Facts 1 & 2 to Change Units
Math Fact # 1:
Any quantity multiplied by 1 does not change.
g101
μg1 g101,435
63 (1)
Multiply by a fraction equal to 1.
J. Gabrielse
STOP
Complete
Metric Conversion Factors Worksheet
J. Gabrielse
The Solution:Use Math Facts 1 & 2 to Change Units
Math Fact # 2:
Any quantity divided by itself is equal to 1.
g101
μg1 g101,435
63
1 μg = 1·10-6 g
Multiply by a fraction equal to 1.
J. Gabrielse
The Solution:Use Math Facts 1 & 2 to Change Units
g101
μg1 g101,435
63
Multiply by a fraction equal to 1
Pick the fraction so:
old units cancel out & new units are left
J. Gabrielse
The Solution:Use Math Facts 1 & 2 to Change Units
g101
μg1 g101,435
63
Cancel Out
old units cancel out & new units are left
J. Gabrielse
The Solution:Use Math Facts 1 & 2 to Change Units
6
3
101
μg1 101,435
Let your calculator do the rest
J. Gabrielse
The Solution:Use Math Facts 1 & 2 to Change Units
μg10435.1μg000,435,1μg10435,1g101
μg1 g101,435mg 1,435 63
63
Rewrite
J. Gabrielse
Notes
6. Changing Units (p. 20) a. Write what you are given b. Turn the SI prefix into a power of ten c. Multiply by a fraction equal to 1
i. The old units should cancel out ii. The new unit should be left over
iii. Use powers of ten to balance SI prefixes iv. The top of the fraction has to equal the
bottom of the fraction d. Cancel e. Write the answer
J. Gabrielse
Example:
How many ms are in 560 ps?
ps560
Write what you are given.
J. Gabrielse
Example:
How many ms are in 560 ps?
s10560ps560 12
Turn the SI prefix into a power of ten.
J. Gabrielse
Example:
How many ms are in 560 ps?
s101
ms1 s10560
s10560ps560
312
12
Multiply by a fraction equal to 1
J. Gabrielse
Example:
How many ms are in 560 ps?
s101
ms1 s10560
s10560ps560
312
12
Note: I put s (the old unit) on the bottom so it will cancel out
Multiply by a fraction equal to 1
J. Gabrielse
Example:
How many ms are in 560 ps?
s101
ms1 s10560
s10560ps560
312
12
Note: I put ms (the new unit) on the top so it will be left over
Multiply by a fraction equal to 1
J. Gabrielse
Example:
How many ms are in 560 ps?
s101
ms1 s10560
s10560ps560
312
12
Note:
Use SI prefixes to pick numbers.
The top of the fraction has to equal the bottom of the fraction.
Multiply by a fraction equal to 1
1 ms = 1·10-3 s
J. Gabrielse
Example:
How many ms are in 560 ps?
s101
ms1 s10560
s10560ps560
312
12
Cancel
J. Gabrielse
Example:
How many ms are in 560 ps?
ms105.6s101
ms1 s10560
s10560ps560
73
12
12
Write the answer
Note: your calculator can do all the hard work