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

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

In the unified States, both the U.S. Customary measurement system and also the metric system space used, especially in medical, scientific, and technical fields. In many other countries, the metric mechanism is the primary system the measurement. If you travel to other countries, friend will see that road indicators list distances in kilometers and milk is marketed in liters. Human being in countless countries use words like “kilometer,” “liter,” and “milligram” to measure the length, volume, and also weight of various objects. This measurement devices are component of the metric system.

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

So, what if you have to find out how plenty of milligrams are in a decigram? Or, what if you want to convert meters to kilometers? Understanding just how the metric mechanism works is a good start.

What is Metric?

The metric device uses units such as meter, liter, and gram to measure up length, fluid volume, and also mass, just as the U.S. Customary system uses feet, quarts, and also ounces to measure up these.

In addition to the difference in the basic units, the metric system is based upon 10s, and also different actions for length incorporate kilometer, meter, decimeter, centimeter, and also millimeter. Notice that the word “meter” is component of every one of these units.

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

Length, Mass, and Volume

The table below shows the an easy units of the metric system. Keep in mind that the name of all metric devices follow from these three an easy 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 size is the meter. A meter is slightly bigger than a yardstick, or just over 3 feet.

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

Among scientists, one gram is defined as the mass of water that would fill a 1-centimeter cube. Girlfriend may an alert that the word “mass” is used here instead that “weight.” In the sciences and also technical fields, a difference is made between weight and also mass. Load is a measure up of the traction of gravity on one object. Because that this reason, one object’s weight would certainly be various if it was weighed on planet or ~ above the moon since of the difference in the gravitational forces. However, the object’s fixed would continue to be the exact same in both places due to the fact that mass actions the lot of problem in one object. As lengthy as you space planning on only measuring objects top top Earth, you deserve to use mass/weight reasonably interchangeably—but it is worth noting the there is a difference!

Finally, the an easy metric unit of volume is the liter. A liter is slightly bigger than a quart.   The take care of of a shovel is about 1 meter. A paperclip weighs around 1 gram. A medium-sized container the milk is about 1 liter.

Though that is rarely necessary to convert between the customary and also metric systems, periodically it helps to have actually a mental photo of how large or little some units are. The table listed 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 small 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 much more than 2 pounds. 28 grams is around the same as 1 ounce. Volume 1 liter is a little much more than 1 quart. 4 liters is a little an ext than 1 gallon.

Prefixes in the Metric System

The metric system is a base 10 system. This way that each successive unit is 10 times bigger than the previous one.

The surname of metric systems are formed by including a prefix come the simple unit the measurement. Come tell how large or little a unit is, girlfriend look at the prefix. Come tell whether the unit is measure length, mass, or volume, friend look at 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 than base unit 10 times larger than base unit base units 10 time smaller than base unit 100 times smaller than base unit 1,000 time 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 sized than one meter (so 1 meter = 100 centimeters).

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

Here is a similar table that just shows the metric systems of measurement for mass, together with their size relative to 1 gram (the basic unit). The typical abbreviations for these metric units have actually 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 can create similar charts because that length and volume. The prefixes have actually the same interpretations whether they room attached to the units of size (meter), fixed (gram), or volume (liter).

Which of the complying with sets of three units room all metric dimensions 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 space all systems of measurement from the U.S. Customary system. The correct answer is kilometer, centimeter, millimeter.

B) kilometer, centimeter, millimeter

Correct. All of these dimensions are native the metric system. You have the right to tell they are measurements of length since they all contain the word “meter.”

C) kilogram, gram, centigram

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

D) kilometer, foot, decimeter

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

Converting units Up and also Down the Metric Scale

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

For instance, you can figure out how numerous centigrams space in one dekagram by utilizing the table above. One dekagram is larger than one centigram, for this reason you suppose that one dekagram will certainly equal plenty of centigrams.

In the table, each unit is 10 times larger than the one to its immediate right. This way that 1 dekagram = 10 grams; 10 grams = 100 decigrams; and also 100 decigrams = 1,000 centigrams. So, 1 dekagram = 1,000 centigrams.

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

Identify areas of milligrams and also decigrams.

Decigrams (dg) are larger than milligrams (mg), so you mean there to be plenty of mg in one dg.

 ×10 ×10 kg hg dag g dg cg mg ^ ^ → →

Dg is 10 times larger than a cg, and a cg is 10 times larger than a mg.

Since you room going native a larger unit to a smaller sized unit, multiply.

1 dg · 10 · 10 = 100 mg

Multiply: 1 · 10 · 10, to find the number of milligrams in one decigram.

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

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

Identify locations of kilometers and centimeters.

Kilometers (km) are larger than centimeters (cm), for this reason you suppose there come be much 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 than a m, etc.

Since you room going native a smaller unit come a bigger unit, divide.

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

Divide: 1 ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10, to discover the variety of kilometers in one centimeter.

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

Once you start to know the metric system, you can use a shortcut to convert amongst different metric units. The dimension of metric units boosts tenfold as you go up the metric scale. The decimal mechanism works the same way: a tenth is 10 times larger than a hundredth; a hundredth is 10 times bigger than a thousandth, etc. By applying what friend know about decimals to the metric system, converting among units is as simple as relocating decimal points.

Here is the an initial problem native above: How numerous milligrams space in one decigram? You can recreate the order of the metric units as presented below: This question asks friend to start with 1 decigram and convert the to milligrams. As shown above, milligrams is two areas to the right of decigrams. You can just relocate the decimal point two locations to the ideal to convert decigrams come milligrams: .

The same technique works when you room converting native a smaller to a bigger unit, as in the problem: transform 1 centimeter come kilometers. Note that instead of moving to the right, you are now relocating to the left—so the decimal point must execute the same: .