Tools to help us with unit conversions are called conversion factors. Most books have tables either in the front or as appendices in the back with all different kinds of conversions factors, such as from one unit system to another (Metric to English) or within the same unit system.

Unit analysis technique

Step 1. Get the conversion factors needed.

Step 2. Draw lines to create boxes

Column 1| Column 2| Column 3|

1| 3| 5|

2| 4| 6|

Note: Depending on how many conversions we need we can have more or less columns.

Column 1 will have the number that we want to convert

Columns 2, 3, etc will have the conversion factors. In this example having two more columns after column 1 means that there will be two conversions (one for column 1 and one for column 2).

Step 3. Take the number we want to convert and put it in the upper left box, box 1.

Step 4. Look at your conversion factors and find one that has the same units with the number we want to convert.

Step 5. Put the side of the conversion factor with the same units as that of the number in box 1 in the bottom in column 2 in box 4. That way the units will cancel out.

Step 6. Since we placed the part of the conversion factor in box 4 that has the same units as 1, we must put the other part in column 2 box 3.

Step 7. Repeat steps 4-6 until we end up with the appropriate units.

Step 8. Now time to calculate the answer. We multiply any numbers in the top and divide by the ones in the bottom.

Step 9. Don’t forget your units! Whichever units did not cancel will be your answer. Example 1. One Step conversion

How many kg are in 1640g?

Step 1. Conversion factors (get this from reference tables)

1 kg = 1000 grams

Step 2. Draw lines to create boxes (Note one step conversion only need 2 columns) | |

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Step 3. Take the number we want to convert and put it in the upper left box, box 1 1640 grams| |

| |

Step 4. Look at your conversion factors and find one that has the same units with the number we want to convert. (If can’t find the one you need from the ones you gathered in Step 1 go back to your reference tables to look for an appropriate conversion factor)

1 kg = 1000 grams

Step 5. Put the side of the conversion factor with the same units as that of the number in box 1 in the bottom in column 2 in box 4. That way the units will cancel out. 1640 grams| |

| 1000 grams|

Step 6. Since we placed the part of the conversion factor in box 4 that has the same units as 1, we must put the other part in column 2 box 3. 1640 grams| 1 kg|

| 1000 grams|

Step 7. Repeat steps 4-6 until we end up with the appropriate units. No need for this step so can skip to step 8

Step 8. Now time to calculate the answer. We multiply any numbers in the top and divide by the ones in the bottom.

Step 9. Don’t forget your units! Whichever units did not cancel will be your answer. We see that the only units left are kg and they are on the top so the answer will be: 1640 grams = 1.640 kg

Example 2. Multi-Step conversion

19 yards is the same as how many meters?

Step 1.

3 ft = 1yd1 in = 2.54 cm

1 ft = 12 in.1 m = 100 cm

Step 2.

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Step 3.

19 yards| | | | | |

| | | | | |

Step 4.

3 ft = 1yd

Step 5.

19 yards| | | | | |

| 1 yard| | | | |

Step 6.

19 yards| 3 ft| | | | |

| 1 yard| | | | |

Step 7.

ft is not the units we want, need another conversion

4.

1 ft = 12 in.

5.

19 yards| 3 ft| | | | |

| 1 yard| 1 ft| | | |

6.

19 yards| 3 ft| 12 in| | | |

| 1 yard| 1 ft| | | |

in is not the units we want, need another conversion

4.

1 in = 2.54 cm

5.

19 yards| 3 ft| 12 in| | | |

| 1 yard| 1 ft| 1 in| | |

6.

19 yards| 3 ft| 12 in| 2.54 cm| | |

| 1 yard| 1 ft| 1...