Dimensional Analysis

For example, converting 76 centimeters (76 cm) to meters or Dimensional Analysis is a method for converting from one measurement type to another. For example, converting 76 centimeters (76 cm) to meters or 76 cm = ? meters

1. The first step is to copy the number with the units. 76 cm x ________ 1 100 m = 0.76 m cm 2. Multiply the number by a fraction which is called a conversion factor. 3. Whatever the units are on the first measurement, copy those units to the bottom of the conversion factor. 4. In the top part of the conversion factor, put in the units you want to change to. 5. Put in the numbers that relate the two units in the conversion factor. 6. Do the math.

Let’s try a similar problem. 34 meters would be how many millimeters? or 34 m = ? mm

1. The first step is to copy the number with the units. x ________ 1000 1 mm = 34000 mm m 2. Multiply the number by a fraction which is called a conversion factor. 3. Whatever the units are on the first measurement copy those units to the bottom of the conversion factor. 4. In the top part of the conversion factor, put in the units you want to change to. 5. Put in the numbers that relate the two units in the conversion factor. 6. Do the math.

Let’s do another. 12 kilograms would be how many grams? or 12 kg = ? g

1. The first step is to copy the number with the units. 12 kg x ________ 1000 1 g = 12000 g kg 2. Multiply the number by a fraction which is called a conversion factor. 3. Whatever the units are on the first measurement copy those units to the bottom of the conversion factor. 4. In the top part of the conversion factor, put in the units you want to change to. 5. Put in the numbers that relate the two units in the conversion factor. 6. Do the math.

A more difficult problem would be 12 kilograms would be how many milligrams? or 12 kg = ? mg

12 kg x ________ ? ? mg kg Changing kg to mg in one step is hard so you break the problem up into easier steps.

12 kg x ________ 1000 1 g x ________ 1000 1 mg kg g Instead of kg a mg Change kg a g then a mg

What conversion factor would you use to convert 2 What conversion factor would you use to convert 2.6 liters to milliliters? 1 L 10 mL A. ______ 1 L 100 mL _______ D. 1000 L 1 mL _______ B. 100 L 1 mL _____ E. 1000 mL 1 L _______ C.

What conversion factor would you use to convert 2 What conversion factor would you use to convert 2.6 liters to milliliters? 2.6 L = ? mL 2.6 L x _______ = ? mL ? ?

2.6 L x _______ = ? mL 1000 mL 1 L ? ? 2.6 L x _______ 1000 1 mL = 2600mL L

What conversion factor would you use to convert 2 What conversion factor would you use to convert 2.6 liters to milliliters? 1 L 10 mL A. ______ 1 L 100 mL _______ D. 1000 L 1 mL _______ B. 100 L 1 mL _____ E. 1000 mL 1 L _______ C.

But you’ll need a conversion factor to get from one system to another. Conversions from one system to another can also be done using dimensional analysis. But you’ll need a conversion factor to get from one system to another. Conversions 1.0 meter = 1.1 yard 1.0 liter = 1.06 quarts 1.0 kg = 2.2 pounds (lb)

distance 1.0 meter = 1.1 yard 1.0 yard = ? cm volume 1.0 liter = 1.06 quarts mass 1.0 kg = 2.2 pounds (lb) 1.0 yd x ________ 1.0 1.1 m x ______ 100 1 cm = 91 cm yd m

American Units of Length 1.0 meter = 1.1 yard 2.0 miles = ? cm ft yd m cm 2.0 miles x _________ 5280 x _____ 1 x _____ 1 x ______ 100 American Units of Length Metric Units of Length mile ft 1.1 yd 1 m 1 3 = 320,000 cm miles km nm feet yards meters cm inches mm