· describe the basic relationship in between the U.S. Customary units and also metric systems of length, weight/mass, and also volume.

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· define the metric prefixes and use them come perform basic conversions among metric units.

In the joined States, both the U.S. Customary measure system and also the metric system are used, especially in medical, scientific, and technical fields. In many other countries, the metric mechanism is the major system that measurement. If you travel to other countries, you will check out that road signs list distances in kilometers and also milk is offered in liters. Human being in plenty of countries usage words favor “kilometer,” “liter,” and “milligram” to measure the length, volume, and also weight of various objects. This measurement units are part of the metric system.

Unlike the U.S. Customary system of measurement, the metric device is based upon 10s. Because that example, a liter is 10 times larger than a deciliter, and a centigram is 10 times bigger than a milligram. This idea the “10” is not current in the U.S. Customary system—there room 12 inch in a foot, and also 3 feet in a yard…and 5,280 feet in a mile!

So, what if you have to uncover out how many milligrams space in a decigram? Or, what if you desire to convert meters to kilometers? Understanding exactly how the metric device works is a good start.

What is Metric?

The metric system uses systems such as meter, liter, and also gram to measure length, liquid volume, and also mass, simply as the U.S. Customary mechanism uses feet, quarts, and ounces to measure up these.

In enhancement to the difference in the simple units, the metric mechanism is based on 10s, and also different actions for length include kilometer, meter, decimeter, centimeter, and millimeter. Notification that the word “meter” is component of all of these units.

The metric system also applies the idea that units within the system get larger or smaller sized by a strength of 10. This means that a meter is 100 times larger than a centimeter, and a kilogram is 1,000 times heavier than a gram. Girlfriend will explore this idea a little bit later. For now, notification how this idea that “getting larger or smaller sized by 10” is really different 보다 the relationship between units in the U.S. Customary system, wherein 3 feet amounts to 1 yard, and also 16 ounces equates to 1 pound.

Length, Mass, and Volume

The table listed below shows the straightforward units the the metric system. Note that the surname of every metric systems follow from these three simple units.

 Length Mass Volume basic units meter gram liter other units you may see kilometer kilogram dekaliter centimeter centigram centiliter millimeter milligram milliliter

In the metric system, the an easy unit of length is the meter. A meter is slightly larger than a yardstick, or just over three feet.

The an easy metric unit of massive is the gram. A regular-sized paperclip has a fixed of about 1 gram.

Among scientists, one gram is characterized as the fixed of water that would certainly fill a 1-centimeter cube. You may notice that words “mass” is used below instead of “weight.” In the sciences and also technical fields, a distinction is made in between weight and mass. Load is a measure up of the traction of gravity on an object. Because that this reason, one object’s weight would certainly be different if it was weighed on earth or top top the moon due to the fact that of the distinction in the gravitational forces. However, the object’s massive would stay the same in both places because mass actions the lot of problem in one object. As lengthy as you space planning on only measuring objects ~ above Earth, you have the right to use mass/weight reasonably interchangeably—but it is precious noting the there is a difference!

Finally, the basic metric unit of volume is the liter. A liter is slightly bigger than a quart.

 The manage of a shovel is around 1 meter. A paperclip weighs about 1 gram. A medium-sized container the milk is about 1 liter.

Though it is rarely crucial to convert between the customary and also metric systems, occasionally it help to have actually a mental picture of how huge or tiny some units are. The table below shows the relationship in between some usual units in both systems.

 Common dimensions in Customary and also Metric Systems Length 1 centimeter is a little less than fifty percent an inch. 1.6 kilometers is about 1 mile. 1 meter is about 3 inches longer than 1 yard. Mass 1 kilogram is a little an ext than 2 pounds. 28 grams is around the very same as 1 ounce. Volume 1 liter is a little more than 1 quart. 4 liters is a little more than 1 gallon.

Prefixes in the Metric System

The metric device is a basic 10 system. This method that each succeeding unit is 10 times bigger than the vault one.

The surname of metric systems are formed by adding a prefix come the straightforward unit the measurement. Come tell how big or little a unit is, you look at the prefix. To tell whether the unit is measuring length, mass, or volume, girlfriend look in ~ the base.

 Prefixes in the Metric System kilo- hecto- deka- meter gram liter deci- centi- milli- 1,000 times larger 보다 base unit 100 times larger 보다 base unit 10 time larger 보다 base unit base units 10 times smaller than base unit 100 time smaller than base unit 1,000 times smaller 보다 base unit

Using this table together a reference, you can see the following:

· A kilogram is 1,000 times larger than one gram (so 1 kilogram = 1,000 grams).

· A centimeter is 100 times smaller than one meter (so 1 meter = 100 centimeters).

· A dekaliter is 10 times bigger than one liter (so 1 dekaliter = 10 liters).

Here is a comparable table that simply shows the metric devices of measurement for mass, along with their size loved one to 1 gram (the base unit). The common abbreviations for these metric units have been consisted of as well.

 Measuring mass in the Metric System kilogram (kg) hectogram (hg) dekagram (dag) gram (g) decigram (dg) centigram (cg) milligram (mg) 1,000 grams 100 grams 10 grams gram 0.1 gram 0.01 gram 0.001 gram

Since the prefixes remain consistent through the metric system, you could create similar charts for length and volume. The prefixes have the same meanings whether they space attached to the systems of size (meter), mass (gram), or volume (liter).

Which the the following sets of 3 units space all metric measurements of length?

A) inch, foot, yard

B) kilometer, centimeter, millimeter

C) kilogram, gram, centigram

D) kilometer, foot, decimeter

A) inch, foot, yard

Incorrect. Although these units execute measure length, they are all devices of measurement native the U.S. Customary system. The correct answer is kilometer, centimeter, millimeter.

B) kilometer, centimeter, millimeter

Correct. Every one of these measurements are native the metric system. You can tell castle are dimensions of length since they all contain words “meter.”

C) kilogram, gram, centigram

Incorrect. These dimensions are from the metric system, yet they are measurements of mass, not length. The exactly answer is kilometer, centimeter, millimeter.

D) kilometer, foot, decimeter

Incorrect. Kilometer and also decimeter are metric units of length, but foot is not. The exactly answer is kilometer, centimeter, millimeter.

Converting devices Up and also Down the Metric Scale

Converting between metric devices of measure requires knowledge of the metric prefixes and also an knowledge of the decimal system—that’s around it.

For instance, friend can number out how countless centigrams room in one dekagram by using the table above. One dekagram is bigger than one centigram, therefore you suppose that one dekagram will equal plenty of centigrams.

In the table, each unit is 10 times bigger than the one come its prompt right. This method that 1 dekagram = 10 grams; 10 grams = 100 decigrams; and 100 decigrams = 1,000 centigrams. So, 1 dekagram = 1,000 centigrams.

 Example Problem How numerous milligrams room in one decigram? kg hg dag g dg cg mg ^ ^

Identify locations of milligrams and also decigrams.

Decigrams (dg) are bigger than milligrams (mg), for this reason you expect there come be plenty of mg in one dg.

 ×10 ×10 kg hg dag g dg cg mg ^ ^ → →

Dg is 10 times bigger than a cg, and also a cg is 10 times bigger than a mg.

Since you are going indigenous a larger unit come a smaller sized unit, multiply.

1 dg · 10 · 10 = 100 mg

Multiply: 1 · 10 · 10, to discover the variety of milligrams in one decigram.

There room 100 milligrams (mg) in 1 decigram (dg).

 Example Problem Convert 1 centimeter come kilometers. km hm dam m dm cm mm ^ ^

Identify locations of kilometers and also centimeters.

Kilometers (km) are bigger than centimeters (cm), so you mean there to be less than one km in a cm.

÷10

 ÷10 ÷10 ÷10 ÷10 km hm dam m dm cm mm ^ ^ ← ← ← ← ←

Cm is 10 times smaller sized than a dm; a dm is 10 times smaller sized than a m, etc.

Since you room going indigenous a smaller unit to a bigger unit, divide.

1 centimeter ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10 = 0.00001 km

Divide: 1 ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10, to uncover the number of kilometers in one centimeter.

1 centimeter (cm) = 0.00001 kilometers (km).

Once you begin to know the metric system, you deserve to use a shortcut to convert amongst different metric units. The dimension of metric units boosts tenfold together you go up the metric scale. The decimal system works the very same way: a tenth is 10 times bigger than a hundredth; a hundredth is 10 times larger than a thousandth, etc. By using what girlfriend know about decimals to the metric system, converting among units is as simple as moving decimal points.

Here is the an initial problem indigenous above: How many milligrams room in one decigram? You deserve to recreate the order of the metric devices as displayed below:

This question asks you to start with 1 decigram and convert the to milligrams. As shown above, milligrams is two locations to the appropriate of decigrams. You have the right to just move the decimal suggest two places to the right to convert decigrams to milligrams:

.

The same an approach works once you are converting indigenous a smaller to a larger unit, together in the problem: convert 1 centimeter to kilometers.

Note that instead of moving to the right, you are now relocating to the left—so the decimal suggest must do the same:

.