When the exponent signs are the same SUBTRACT the exponents to determine how many decimal places to move. 3 - 1 = 2 places.
Do not associate this metric trick using exponents with any form of mathematics!
Move the decimal point two places to the left. You move left because decigrams are larger units than milligrams, therefore you need less of them (a smaller number).
The answer is 0.167 25 dg
Things to remember:
- Always place a zero in front of the decimal point.
- NEVER use commas - use a little space instead
- Always group numbers in three's beginning at the decimal and moving in both directions.
- You must label your answer to receive any credit in lab work or on examinations.
There are many ways to calculate temperature conversion. We will use what I call the 40/40 method. Refer to your lab manual on page 15 "Temperature Calculations."
If the temperature you want to convert is in Fahrenheit - remember this saying "5/9 Fahrenheit." This tells you that in step #2 you multiply by 5/9.
Step 1 = 75 + 40 = 115
Step 2 = 115/1 times 5/9 = 575/9 = 63.89
Step 3 = 63.89 - 40 = 23.89 C degrees
We will make it our practice in this class to always round to the nearest whole degree. The answer then is 24.0 C degrees.
Let's prove our answer by converting back to Fahrenheit from Celsius.
Step 1 = 24 + 40 = 64
Step 2 = 64 times 1.8 = 115.20
Step 3 = 115.20 - 40 = 75.20 F degrees or 75 Fahrenheit degrees
To convert from C to F multiply by 1.8 in step two.
Step 1 = 108 + 40 = 148
Step 2 = 148 times 1.8 = 266.40
Step 3 = 266.40 - 40 = 226.4 F degrees = 226.0 F degrees
When the exponent signs are different ADD the exponents to determine how many decimal places to move.
3 + 3 = 6 places.
Move the decimal point to the right since millimeters are smaller units than kilometers, so you need more of them.
Hint: Commit Figure 1.1 - Meter table on page 2 of the lab manual to memory. If you begin a kilometer, to reach millimeter you go down on the chart. When you go down on the chart you move the decimal point to the right.
The answer is 1 726 000.0 mm
Since the signs are the same subtract the exponents. 9 - 1 = 8 places
Move the decimal to the left because you are moving up on the charts and because decimeters are larger units so you need less of them.
The answer is 0.000 383 773 25 dm (scientific notation is not begin used to prevent confusion)
Since only one sign (10-3) has an exponent value it tells you how many places to move the decimal point.
In this case the decimal is moved 3 places to the right. To the right because milliliters are smaller units than liters, so you need more of them.
The answer is 68 750.0 ml
Things to remember:
- In the case of whole numbers, place a decimal followed by a zero.
- Numbers should be grouped in 3's starting at the decimal point.
- Always label the answer
Isodiametric means that the cell is a perfect cube. Let's face it, cells aren't really perfect cubes. We are going to pretend they are for this calculation just so it is easy to review the principles of doing the calculation.
Review:
To determine surface area one multiples the length times the width.
To determine the total surface area one multiples the length times the width times the number of sides. In the case of a cube it is 6 sides.
Total surface area is 2.75 times 2.75 times 6 sides = 45.375
TSA = 45.375 square millimeters
Review:
Volume is determined by multiplying the length times the width times the height.
Volume = 2.75 mm (times) 27.5 mm (times) 2.75 mm = 20.80 cubic millimeters
Volume = 20.80 cubic millimeters
Now we have the two calculations we need to complete the ratio. We want a surface area to volume ratio.
ALWAYS use the volume as the division (regardless of it's size compared to surface area)
45.375 divided by 20.80 = 2.18 : 1
This means that there are 2.18 units of surface area (membrane in the case of cells) for molecules to move across to service each unit of volume.
This problem presents more calculations because the cell is not isodiametric. This cell is closer to the shape of many real cells. Real cells don't usually have sharp corners, nor are they perfect rectangles. We are going to ignore that and base our calculations on pure rectangles.
We follow the same process as the first problem, the difference is that they are three surfaces that need to be calculated.
I suggest that you sketch this cell on a piece of paper, entering all of the dimensions given. This will help you visualize what you are doing.
When you make your sketch you will be able to see that . . .:
- The top and bottom have a dimension of 23.5 mm by 14.25 mm
- The two sides have a dimension of 23.5 mm by 7.65 mm
- The two ends have a dimension of 14.25 mm by 7.65 mm
Now we will determine the TSA [total surface area for all 6 sides]
23.5 mm (x) 14.25 mm (x) 2 sides (top & bottom) = 669.75 mm squared
23.5 mm (x) 7.65 mm (x) 2 sides = 359.55 mm squared
14.25 mm (x) 7.65 mm (x) 2 sides (ends) = 218.03
TSA = 669.75 + 359.55 + 218.03 = 1 247.33 mm squared
Now calculate the volume
23.5 mm (x) 14.25 mm (x) 7.65 mm = 2 561.79 cubic millimeters
Now determine the surface area to volume ratio by dividing the volume into the TSA.
1 247.33 divided by 2 561.79 = 0.49
ANSWER = 0.49 : 1
This means that there are 0.49 units of surface area available to service each unit of volume.
You will soon learn that cells are small because they are more efficient small based on surface area to volume ratios.