# 6th Grade - Converting Units

 Grade Level: 6th Skill: Algebra Topic: Converting Units Goal: Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches). Skill Description: Use a proportion, along with customary and metric unit equivalents to estimate and convert measurements within the same system and between systems. For example, change one unit of customary measure into another (i.e. inches to feet). Also, convert one unit of metric measure into another (i.e. centimeters to meters). In addition, relate the customary units of measure, used in the United States, to metric measures, used elsewhere around the world, (i.e. inches to centimeters). Lastly, use equivalent relationships and similar steps to make conversions with currencies, temperature, time etc…

### Sample Problems

 (1) ____ft = 4 yd (12) (2) 34 oz = _____ lb (4.25) (3) 14 m = _____ cm (1,400) (4) 300 g = ______ kg (.300) (5) 6 m ≈ ______ km (.006) (6) When temperature is measured in both Celsius (C) and Fahrenheit (F) it is known that they are related by the following formula: 9 ´ C = (F  32) ´ 5. What is 50 degrees Fahrenheit in Celsius? (7) Suppose that one British pound is worth \$1.50. In London a magazine costs 3 pounds. In San Francisco the same magazine costs \$4.25. In which city is the magazine cheaper?

### Learning Tips

(1)

Begin each problem by identifying the units that are being converted to determine which table of measures to use to solve a given problem. There are three types of equivalents: customary to customary, metric to metric and customary to metric. On each table there are three types of measurements: length, capacity, and weight/mass. The table of measures will give unit equivalents. Customary measures are the measures we’re used to seeing in the U.S. (i.e. inches, feet, miles, gallons, pounds, etc…). The common measures used for length are: inch (in.), foot (ft), yard (yd) and mile (mi). Normally, the ounce (oz), pound (lb) and ton (t) are used for units of weight. When measuring capacity, liquid/dry measure, the most common units are: fluid ounce (fl oz), cup (c), pint (pt), quart (qt) and gallon (gal). So, as table of measures comparing customary measures for length will have 1 yard = 3 feet, for example. Most countries of the world use the metric system and its measures. In this system, the meter (m), liter (L) and gram (g) are the basic units of length, capacity and mass. The metric system is designed using the powers of 10, as you will see when you look at a metric table of measures. Conversions can be made between customary and metric measures of length capacity and weight/mass by using a table that shows the relationships between customary and metric measurements. However, the equivalents between the measures are approximate. For example, 1mi ≈ 1.61 km.

(2)

When you use a table of measures to find equivalents to make conversions you will always multiply or divide. When you are converting from a smaller unit to a larger unit, you will always divide. When you are converting from a larger unit to a smaller unit, you will always multiply.

(3)

Relationships among units in the metric system are uniform. In this system, ten units always makes the next (larger) unit. For example, 10 cm = 1 dm. This makes conversions from one metric unit to another easy. You have two choices on how to solve these problems, either multiply or divide by 10 or a power of 10 or move from one place value to another. The table below shows the relationships between the metric measures. The measures on the left are the smallest, the right are largest. So, if your moving from left to right, you’ll divide or change the place value by moving the decimal to the left. However, if you’re moving from right to left, you’ll multiply or change the place value by moving the decimal to the right.

 milli- centi- deci- basic unit deka- hecto- kilo- millimeter (mm) centimeter (cm) decimeter (dm) meter (m) dekameter (dam) hectometer (hm) kilometer (km) milligram (mg) centigram (cg) decigram (dg) gram (g) dekagram (dag) hectogram (hg) kilogram (kg) milliliter (mL) centiliter (cL) deciliter (dL) liter (L) dekaliter (daL) hectoliter (hL) kiloliter (kL)

To use this table to convert milligrams to grams, you can see that you would move to 3 boxes to the right or divide by ten three times (10 x 10 x 10 = 1,000). So, to change from milligrams to grams you divide by 1,000. This would mean that 3,000 milligrams = 3 grams. Changing the place value is another way to solve this problem. To do this, you will move the decimal point. Remember, if you have a whole number without a decimal point, it is behind the last number (3,000 = 3,000.). Now, as stated earlier, to get from milligrams to grams you move 3 boxes to the right. Since milligrams are the smaller unit, you need to divide to find how many grams. Instead of dividing, you can move the decimal 3 spaces to the left, one space for each box. If you choose to use place value just remember to count your boxes moved. If you move to the right, you’ll move the decimal to the left. If you move to the left, you’ll move your decimal to the right. So, if I want to change 3,000 grams to centigrams, I move 2 boxes left. This will mean I move the decimal 2 places to the right. So, 3,000 g = 300,000 cg.

(4)

One easy and consistent way to solve all conversions is to use a proportion. To do this, you will need to set up a word ratio for the units you’re comparing. For the problem, 54 inches = ____ feet. Your word ration would be in./feet. You would then use numbers from the table of measures and from the problem to write your proportion. The table of measures says that 12 in. = 1 ft. This equivalency should be used to write the first ratio of the proportion. It would look like, 12in/1ft. The information from the problem should be used to write the second ratio. It is important when writing the second ratio that you keep each unit of measure in the same place as it was for your word ratio and your first ratio. So, for this problem, it will be very important that you keep inches as your numerator and feet as your denominator. Also, you will use a variable, such as “n” for unknown terms. Your second ratio will then be, 54 in/”n” ft. The next step is to write the two ratios as a proportion (12/1 = 54/n). To solve a proportion you need to cross cancel opposite terms across the diagonal, as shown below.

12 = 54

1 n

12 x n = 1 x 54

12 n = 54

n = 54 † 12

n = 4.5

54 inches = 4.5 feet

(5)

When converting measures from different systems (i.e. miles to kilometers) you will see the ≈ symbol. This symbols means that equivalents are approximate. This is because the relationships between customary and metric measurements are one exactly equivalent for inches and centimeters. All other measures relationships are approximate.

(6)

For a more visual/kinesthetic approach, use a ruler, yardstick, or meter stick to make real world comparisons. To begin with, compare the inches on the ruler to the entire length of the ruler (most rulers are one foot in length). You can do the same thing for feet and inches in a yard stick. On a meter stick, you can compare millimeters to centimeters and both of these to the meter. You can have your child find commonplace objects around the house or on his/her arms and hands that are about the same length as a given unit. Some examples could be: a key is about one inch, when looking at the top of your fingernail sideways it’s about a millimeter, etc… Flashcards can be made with the items found drawn on one side and the name of the approximate unit of measure on the other. The next step would be to make comparisons against objects. For example, you could find out how many keys fit in a one foot frame. This will help children get used to the idea of relating different measures. As you compare items, make sure to talk about if you’d need to divide or multiply to change into a given unit. Finally, many rulers have both customary and metric measures. Children can use this type of ruler to visually see the relationships between the different systems (i.e. centimeters and feet).

### Online Resources

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### Extra Help Problems

 (1) 56 oz. = _____ lb. (7) (2) ______ t. = 2,500 lb. (1.25) (3) 3 mi = ______ ft (15,840) (4) ______ yd = 180 in. (5) (5) 9 c = ______ pt (4.5) (6) 2 qt = ______ c (8) (7) 168 oz = ______ lb (21) (8) How many inches are in 7 ½ feet? (90) (9) 1,600 m = _____ km (1.6) (10) 2.4 L = ______ cL (240) (11) 11.25 kg = _____dag (1,125) (12) 2 L = _____ kL (.002) (13) 50, 278 cm = ________ m (502.78) (14) .2 g = ______ mg (200) (15) 450 m = ______ hm (4.5) (16) 2.3 m = _______ km (.0023) (17) 4 m ≈ ______ in. (157.48) (18) 12.7 cm = _______ in. (5) (19) 5.5 t ≈ _______T (6.061) (20) 6 gal ≈ _____ L (22.74) (21) When converting gallons to liters, do you multiply or divide by 3.79? Explain your answer. (Multiply, you’re converting from a larger unit to a smaller unit.) (22) The formula to convert Celsius (C) and Fahrenheit (F) is 9 x C = (F - 32) x 5. Use this formula to find the temperature in Fahrenheit if it is 10 degrees Celsius. (F = 50) (23) Allyson is taking a trip to Europe. She found out that one Euro (European dollar) is equivalent to 1.57 U.S. dollars. How many Euros can she change for \$500.00 U.S. dollars? (318.47) (24) If one Euro = \$1.57 and the same shirt costs \$15.50 in the U.S. and 12 Euros in France. In which city is the shirt more expensive? (The shirt is more expensive in France.) (25) Will works 8 hours a day, 5 days a week. He’s been working at his new job for one month. How many hours will be paid for his first month of work? (160 hours)