Using Ratios to Convert Within Measurement Systems

We can use ratios to convert within measurement systems (customary and metric) to solve problems that exist in
everyday life. The customary system of measurement is what we use in the United States to measure length, weight, capacity, and temperature. The customary units to measure distances and lengths are inches, feet, yards, and miles. For measuring weight, we use ounces, pounds, and tons. For measuring capacity or volume, we use ounces, cups, pints, quarts, and gallons. °Fahrenheit (degrees Fahrenheit) is what we use for measuring temperature.

We need to keep some basic information in mind when converting in the customary system-

Distance or Length-

1 foot = 12 inches

1 yard = 3 feet = 36 inches

1 mile = 1,760 yards = 5,280 feet

Weight-

1 pound = 16 ounces

1 ton = 2000 pounds = 32,000 ounces

Capacity-

1 pint = 2 cups

1 quart = 2 pints = 4 cups

1 gallon = 4 quarts = 8 pints = 16 cups

Please watch the following videos to learn more-

Same Length in Different Units

Converting Units: US Volume

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Let's try some sample problems!

1) Change 10 feet to inches.

We know that 1 foot = 12 inches

So we can solve that 10 feet = 12 × 10 = 120 inches

10 feet = 120 inches

2) Change 6 quarts to cups.

We know that 1 quart = 2 pints

So 6 quarts = 12 pints

We also know that 1 pint = 2 cups

So we can solve that 12 pints = 12 × 2 = 24 cups

6 quarts = 24 cups

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The metric system of measurement is what is used worldwide to measure length, width, capacity, and temperature also, but these have a consistent set of prefixes to remember the order. When measuring larger or smaller amounts, we can easily convert within the metric system to determine how much we have. To measure distance or length, we use meter or meter with a prefix. To measure weight, we use gram or gram with a prefix. To measure capacity, we use liter.

Metric System.png

The units that are on the right of the base unit are smaller than the base unit is. When moving to the right, each unit is 10 times smaller or one-tenth of the unit to its left. The units that are on the left of the base unit are larger than the base unit is. When moving to the left, each unit is 10 times larger of the unit to its right.

The prefixes of the metric system can be remembered using the mnemonic device saying of “King Henry Died Drinking Chocolate Milk.” That's just a funny way to remember the order from largest to smallest.

Metric System Comparison.png

When you're moving to the right in the chart, you multiply 10 for each step you move. When you're moving to the left in the chart, you divide by 10 for each step you move.

We need to keep some basic information in mind when converting in the metric system and we'll use meter as the example. It would work the same for any metric unit though-

1 kilometer = 10 hectometers = 100 decameters = 1,000 meters = 10,000 decimeters = 100,000 centimeters = 1,000,000 millimeters

1 meter = 1,000 millimeters

1 meter = 0.001 kilometers

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Let's try some more sample problems!

1) Change 50 meters to kilometers.

We know that to go from meters to kilometers in the chart, we go left 3 steps. That means we're dividing by 10 and then again by 10 and then again by 10. We can also think about that as dividing by 1,000.

So we can solve that 50 meters = 50 divided by 1,000 = 0.05 kilometers

50 meters = 0.05 kilometers

2) Change 12 meters to millimeters.

We know that to go from meters to millimeters in the chart, we go right 3 steps. That means we're multiplying by 10 and then again by 10 and then again by 10. We can also think about that as multiplying by 1,000.

So we can solve that 12 meters = 12 times 1,000 = 12,000 millimeters

12 meters = 12,000 millimeters

Please watch the following video to learn more-

Converting Units: Metric Distance

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