Dimensional Analysis is a simple method for changing from one unit of measure to another. How many yards are in 49 ft?

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1 HFCC Math Lab NAT 05 Dimensional Analysis Dimensional Analysis is a simple method for changing from one unit of measure to another. Can you answer these questions? How many feet are in 3.5 yards? Revised 5/20 How many yards are in 49 ft? Did you ever get confused about whether to multiply or divide in these situations? Then Dimensional Analysis is what you need to know! Dimensional Analysis makes use of the fact that everyone knows from arithmetic, namely: Any number (or quantity) = the number (or the quantity) Stated another way, a = a For example: 5 = 5 = 3 3 s = 3yds 7.25 mi = 7.25 mi Conclusion: Multiplying by does not change the value of a number or quantity. From your work with fractions, you know that the number can take on many forms: =, =, =, = etc Or using the following conversion equations: We can think of the number in the following ways: foot (ft) = 2 inches (in) 3 ft = yard (yd) 5280 ft = mile (mi) ft 3 ft 5280 ft = = = 2 in yd mi 2 in yd mi = = = ft 3 ft 5280 ft NOTE: Fractions that are equal to are called unit fractions. a quantity We can use these two ideas, a = a and =, to convert from one unit to an equivalent quantity another.

2 Ex: How many feet are in 3 2 yards? 3 yards= (Multiplying by does not change the value of s.) ft 3ft = Since 3 ft= yd, then = ( See note below. ) yd yd = 2 3 ft (Cancel yd, which is the unwanted unit. You then yd are left with ft, the unit that you are changing to.) ft ft ft 2 = = = = 0 ft (Do the arithmetic.) 2 Therefore = 0 ft. yd NOTE: From the conversion equation, 3 ft= yd, we could also get =. However, if we 3 ft yd multiply 2 the yd would not cancel. 3ft Steps to follow when converting from one unit of measure to another:. Find the conversion that relates the units you have and the units you want. 2. Multiply the measurement you are given by a fraction equal to (unit fraction) using the conversion you chose in Step. Be sure to write the unit fraction in such a way so that you can cancel the unwanted units. 3. Cancel the unwanted units. 4. Find an answer to the arithmetic problem that is left. COMMONLY USED CONVERSION FACTORS: The HESI assumes you know many common conversions. Many people have the following conversions memorized: LENGTH VOLUME WEIGHT/MASS TIME 2 inches = foot 000 ml = L 6 oz. = lb. 60 sec. = min. inch = 2.54 cm 8 ounces = cup 2.2 lb. = kg 60 min. = hour 00 cm = m 6 ounces = pint 2000 lb. = ton 24 hours = day 000 m = km pint = 2 cups 000 g = kg 365 days = year mile =.6 km 2 pints = quart 000 mg = g 4 quarts = gallon Revised 5/20 2

3 Ex 2: How many miles are in 400 km? Revised 5/ km= 400 km Multiplying by does not change the value of 400 km. 400 km 0.62 mi = km 0.62 mi Since km= 0.62 mi, =. We place km km in the denominator so we can cancel km. 400 km 0.62 mi = ( Cancel km, the unwanted unit. ) km mi mi = = = mi Do the arithmetic. Therefore: 400 km = mi. Ex 3: Change liters to milliliters L= L Multiplying by does not change the value of L L 000 ml = L L 000 ml = L ml = = 825 ml Do the arithmetic. Therefore: L = 825 ml. 000 ml Since L= 000 ml, =. We place L in the L denominator so we can cancel L. ( Cancel L, the unwanted unit. ) Sometimes it is necessary to multiply by two unit fractions in order to obtain the correct unit. Ex 4: How many yards are in 2 miles? (Since our conversion equations do not directly relate miles and yards, we must first convert miles to feet, then feet to yards.) 2 mi= 2 mi Multiplying by does not change the value of 2 mi ft Since 5280 ft mi, 2 mi 5280 ft yd = = mi = mi 3 ft yd and yd 3 ft, so. = = 3 ft 2 mi 5280 ft yd = mi 3 ft ( Cancel mi and ft, the unwanted units. ) yd = = 2,20 yd Do the arithmetic. 3 Therefore 2 mi= 2,20 yd.

4 Exercises: Use Dimensional analysis to convert the units.. Convert 5 feet to inches 2. Convert 96 inches to feet. 3. Convert 2 gallons to pints. 4. Convert 48 meters to millimeters. 5. Convert milligrams to grams. 6. How many pounds are in 36 ounces? 7. How many miles are in 600 kilometers? 8. Convert 7,920 feet to miles. 9. How many seconds are in hours? 0. Convert 6 quarts to liters.. Convert 20 inches to centimeters. 2. Convert 7.62 centimeters to inches. 3. Convert 9 gallons to liters. 4. How many yards are in 24 miles? 5. Convert 5 pounds to grams. 6. Convert 70 weeks to hours. Revised 5/20 4

5 Selected Answers and Solutions:. 5 ft 2 in ft 5 2 in 60 in = = = 60in 2. 8 ft 3. 2 gal 4 qt 2 pt gal qt pt 96 pt = = = 96pt 4. 48,000 mm mg g 000 mg 2 lb g = = g km 0.62 mi km mi = = mi ft mi 5280 ft 7920 mi = =.5mi sec 0. 6 qt gal L L = = 5.42L 4 qt gal cm cm in 2.54 cm 7.62 in = = 3 in L mi 5280 ft yd mi 3 ft yd = = 42, 240 yd ,268 g wk 7 da 24 hr wk da hr = =,760 hr Revised 5/20 5

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