Scientific Understanding

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

—> Introduction to Problem Solving

**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.

UNIT CONVERSION CAN BE MADE EASIER BY WHAT I CALL A conversion map. Please open this link and then follow reading the text. A conversion map is simply a guide that you can use to help you through the conversion process. Like a regular map, it has points of interest that you want to go to and streets you have to take to get there. In a conversion map, these “points of interest” are the different units that you want to go from or get to. The “streets” are the conversions or numbers and units that you have to use to get to your “points of interest”. The first conversion map is in the link above and displays the units of kilometers, meters, centimeters, and millimeters. You can see that to go from millimeters to kilometers you have to use two conversions and pass through the units of meters. There are several different versions of conversions maps I have on this website. I have made a different one in each lesson where you learn new units and therefore need to know new conversions. You should use these conversion maps as a guild to help you when you are starting out. Once you get better, help yourself prepare for the test by taking the conversions maps away while you solve practice problems.

**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 ****1****3****:**

COMPLETE ANSWER: 350 cm

**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?

Answer: meters to centimeters ratio

**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 ****1****3****:**

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 ****1****4****:**

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 ****1****5****:**

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

0.27 | 1000 | 100 cm = | cm |

1 | 1 |

**Step ****1****6****:**

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 ****1****7****:**

How do I do the calculations?

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

0.27 | 1000 | 100 cm = | 27000 cm |

1 | 1 |

**Step ****1****8****:**

COMPLETE ANSWER: 27000 cm or 2.7 * 10^{4} 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?

Answer: millimeters to meters ratio

**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?

Answer: meters to kilometers ratio

**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 ****1****3****:**

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

0.86 | 1 m | 1 km = | km |

1000 | 1000 m |

**Step ****1****4****:**

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 ****1****5****:**

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

0.86 | 1 | 1 km = | km |

1000 | 1000 |

**Step ****1****6****:**

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 ****1****7****:**

How do I do the calculations?

Answer: 0.86 / (1000 * 1000) = 8.6 * 10^{7}

0.86 | 1 | 1 km = | 8.6 * 10^{7} km |

1000 | 1000 |

**Step ****1****8****:**

COMPLETE ANSWER: 8.6 * 10^{7} km

**PRACTICE PROBLEMS**: Give the final answer for these questions.

How many centimeters in 78 meters?

Answer: 7800 cm

How many millimeters in 6.3 meters?

Answer: 6300 mm

How many meters in 700 kilometers?

Answer: 700000 m

How many kilometers in 96000 millimeters?

Answer: 0.096 km

If you measure 0.42 cm how many millimeters is that?

Answer: 4.2 mm

If you measure 0.35 m how many kilometers is that?

Answer: 0.00035 km