http://www.ck12.org Chapter 3. Measurement
Different Base Units
Example 3.6
- 5 × 102 liters− 3. 45 × 102 deciliters
Step 1: Convert numbers to regular notation.
150 liters−345 deciliters
Step 2: Decide on which unit you want the final answer to be expressed as and convert the numbers to this unit.
(^345) dL×
(
1 L
(^10) dL
)
= 34 .5 L
Step 3: Subtract.
150 L− 34 .5 L= 115 .5 L
Step 4: Convert to scientific notation.
- 155 × 102 L
Multiplying and Dividing
Same Base Units
Example 3.7
( 4. 65 × 103 meters)×( 3. 56 × 102 meters)
Step 1: Group the coefficients and the exponential terms together.
( 4. 65 × 3. 56 )×( 103 × 102 )meters×meters
Step 2: Multiply coefficients and add the exponents.
( 16. 55 )×( 105 )meters^2
Step 3: Change to scientific notation. Remember that the coefficient must be a number between 1 and 10.
- 655 × 106 m^2
Note that when two values are multiplied together, the units are multiplied as well. This is different than the case for
addition and subtraction, where the units for the answer are the same as the units for each of the starting values.
Different Base Units
The procedure here is the same, except that a conversion is made so that both values are expressed in the same units.
Example 3.8
( 4. 65 × 10 −^4 liters)×( 3. 56 × 102 milliliters)
Step 1: Convert to a common unit.
In this case, we chose the common unit to be milliliters.
- 65 × 10 −^4 L×
(
1000 mL(^1) L
)
= 4. 65 × 10 −^1 mLStep 2: Group the coefficients and the exponential terms together.
( 4. 65 × 3. 56 )×( 10 −^1 × 102 )mL^2
Step 3: Multiply coefficients and add the exponents.
( 16. 55 )×( 101 ) = 165 .5 mL^2
Step 4: Change to scientific notation.