## Chem – Unit Conversions

What sections should I know before attempting to learn this section?

How do you convert from one scientific unit to another?

Conversions are taking a number (quantity) with units and changing the number to represent a new set of units. We use these unit conversions in every day life. Whenever you buy more than one item in a store, you are using a unit conversion to calculate the cost. For example, if we say that a person walked 300 meters and a person’s stride is 0.25 meters between the front foot of one step and the front foot of another step, we can now convert between meters and strides. How many strides did that person take? Follow below:

 300 m 1 stride = 1200 strides 0.25 m

So the answer is 1200 strides. We converted from the unit of meters to the unit of strides. VIDEO Unit Conversions Demonstrated Example 1:If you know that a certain length is 3.5 meters. What would that be in centimeters?

Step 1:  highlight numbers and units

If you know that a certain length is 3.5 meters. What would that be in centimeters?

Step 2:  write numbers and units

3.5m = distance

Step 3:  restate the question

? cm = distance

Step 4:

How many conversions must we do?

Answer: Look at the conversion map. We pass through 1 arrow when we go from Meters —> Centimeters. 1 arrows = 1 conversion

Step 5:

How do I start laying out the problem?

Answer: Write out 3 boxes. The first box has the information the question gave us (3.5 m), the second is where we will put the 1 conversion we will have and the last (third) box is where the units that the question asked (cm) for will be.

 3.5 m cm 1

Step 6:

What is the first conversion?

Answer: meters (m) to centimeter (cm) ratio

Step 7:

How do I put that in?

Answer: units first, set up the units that need to cancel out (in red)

 3.5 m cm         = cm m

Step 8:

Fill in the numbers next to the units of the conversion (in red)

 3.5 m 100 cm = cm 1 m

Step 9:

Cross out the units that are found on top and bottom of your conversion.

 3.5 m 100 cm = cm 1 m

Step 10:

Simplify the problem by getting rid of all the crossing out.

 3.5 100 cm = cm 1

Step 11:

How do I know I am done with conversions?

Answer: The only units left are the units that match the answer. In this case cm.

 3.5 100 cm = cm 1

Step 12:

How do I do the calculations?

Answer: (3.5 * 100) / 1 = 350

 3.5 100 cm = 350 cm 1

Step 13:

VIDEO Unit Conversions Demonstrated Example 2:How many centimeters are in 0.27 kilometers?

What numbers and units does the question give you?

Step 1:  highlight numbers and units

How many centimeters are in 0.27 kilometers?  What numbers and units does the question give you?

Step 2:  write numbers and units

0.27km = distance

Step 3:  restate the question

? cm = distance

Step 4:

How many conversions must we do?

Answer: Look at the conversion map. We pass through 2 arrows when we go from Kilometers —> Meters —> Centimeters. 2 arrows = 2 conversion

Step 5:

How do I start laying out the problem?

Answer: Write out 4 boxes. The first box has the information the question gave us (0.27 km), the second and third box are the 2 conversions we will have and the last (fourth) box is where the units that the question asked (cm) for will be.

 0.27 km cm 1

Step 6:

What is the first conversion?

Answer: kilometers (km) to meters (m) ratio

Step 7:

How do I put that in?

Answer: units first, set up the units that need to cancel out (in red)

 0.27 km m cm km

Step 8:

Fill in the numbers next to the units of the conversion (in red)

 0.27 km 100 m cm 1 km

Step 9:

Cross out the units that are found on top and bottom of your conversion.

 0.27 km 1000 m cm 1 km

Step 10:

Simplify the problem by getting rid of all the crossing out.

 0.27 100 m cm 1

Step 11:

What is the next conversion?

Step 12:

How do I set it up?

Answer: Units first, set up the units that you need to cancel out (in red)

 0.27 1000 m cm = cm 1 m

Step 13:

Fill in the numbers next to the units of the conversion (in red)

 0.27 km 1000 m 100 cm = cm 1 km 1 m

Step 14:

Answer: Cross out the units that are found on top and bottom of your conversion.

 0.27 1000 m 100 cm = cm 1 1 m

Step 15:

Simplify the problem by getting rid of all the crossing out.

 0.27 1000 100 cm = cm 1 1

Step 16:

How do I know when I am done with the conversions?

Answer: The only units left are the units that match the answer. In this case cm

 0.27 1000 100 cm = cm 1 1

Step 17:

How do I do the calculations?

Answer: (0.27 * 1000 * 100) / (1*1) = 27000

 0.27 1000 100 cm = 27000 cm 1 1

Step 18:

COMPLETE ANSWER: 27000 cm or 2.7 * 104 cm

VIDEO Unit Conversions Demonstrated Example 3: If you measure 0.86 mm how many kilometers is that?

Step 1:  highlight numbers and units

If you measure 0.86 mm how many kilometers is that?

Step 2:  write numbers and units

0.86mm = distance

Step 3:  restate the question

? km = distance

Step 4:

How many conversions must we do?

Answer: Look at the conversion map. We pass through 2 arrows when we go from Centimeters —> Meters —> Kilometers. 2 arrows = 2 conversion

Step 5:

How do I start laying out the problem?

Answer: Write out 4 boxes. The first box has the information the question gave us (0.86 mm), the second and third box are the 2 conversions we will have and the last (fourth) box is where the units that the question asked (cm) for will be.

 0.86 mm km 1

Step 6:

What is the first conversion?

Step 7:

How do I put that in?

Answer: units first, set up the units that need to cancel out (in red)

 0.86 mm m km mm

Step 8:

Fill in the numbers next to the units of the conversion (in red)

 0.86 mm 1 m km 1000 mm

Step 9:

Cross out the units that are found on top and bottom of your conversion.

 0.86 mm 1 m km 1000 mm

Step 10:

Simplify the problem by getting rid of all the crossing out.

 0.86 1 m km 1000

Step 11:

What is the next conversion?

Step 12:

How do I set it up?

Answer: Units first, set up the units that you need to cancel out (in red)

 0.86 1 m km = km 1000 m

Step 13:

Fill in the numbers next to the units of the conversion (in red)

 0.86 1 m 1 km = km 1000 1000 m

Step 14:

Cross out the units that are found on top and bottom of your conversion.

 0.86 1 m 1 km = km 1000 1000 m

Step 15:

Simplify the problem by getting rid of all the crossing out.

 0.86 1 1 km = km 1000 1000

Step 16:

How do I know when I am done with the conversions?

Answer: The only units left are the units that match the answer. In this case km

 0.86 1 1 km = km 1000 1000

Step 17:

How do I do the calculations?

Answer: 0.86 / (1000 * 1000) = 8.6 * 107

 0.86 1 1 km = 8.6 * 107 km 1000 1000

Step 18:

COMPLETE ANSWER: 8.6 * 107 km

PRACTICE PROBLEMS: Give the final answer for these questions.

How many centimeters in 78 meters?

How many millimeters in 6.3 meters?

How many meters in 700 kilometers?

How many kilometers in 96000 millimeters?

If you measure 0.42 cm how many millimeters is that?  