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

You are watching: Which of the following is the basic unit to measure volume in the metric system?

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

In the unified States, both the U.S. Customary measure system and also the metric system are used, particularly in medical, scientific, and technical fields. In many other countries, the metric mechanism is the major system that measurement. If you take trip to various other countries, you will check out that road signs list distances in kilometers and also milk is sold in liters. Human being in countless countries use words prefer “kilometer,” “liter,” and also “milligram” to measure up the length, volume, and weight of different objects. This measurement systems are component of the metric system.

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

So, what if you have actually to find out how countless milligrams space in a decigram? Or, what if you want to transform meters to kilometers? Understanding exactly how the metric system works is a an excellent start.

What is Metric?

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

In addition to the difference in the basic units, the metric system is based on 10s, and different steps for length incorporate kilometer, meter, decimeter, centimeter, and millimeter. Notification that words “meter” is part of all of these units.

The metric system additionally applies the idea that devices within the system acquire larger or smaller by a power 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. You will discover this idea a bit later. For now, notice how this idea that “getting enlarge or smaller by 10” is really different than the relationship between units in the U.S. Customary system, whereby 3 feet equates to 1 yard, and 16 ounces equals 1 pound.

Length, Mass, and also Volume

The table below shows the basic units that the metric system. Note that the name of every metric devices follow from this three simple units.

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

In the metric system, the simple unit of size is the meter. A meter is slightly bigger than a yardstick, or simply over 3 feet.

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

Among scientists, one gram is defined as the fixed of water that would fill a 1-centimeter cube. You may an alert that the word “mass” is used right here instead of “weight.” In the sciences and also technical fields, a distinction is made between weight and mass. Weight is a measure up of the pull of heaviness on an object. For this reason, one object’s weight would be various if it was weighed on planet or top top the moon because of the difference in the gravitational forces. However, the object’s mass would remain the same in both places due to the fact that mass procedures the quantity of problem in one object. As lengthy as you are planning on only measuring objects ~ above Earth, you deserve to use mass/weight reasonably interchangeably—but that is precious noting the there is a difference!

Finally, the straightforward metric unit the volume is the liter. A liter is slightly larger than a quart.

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

Though it is rarely important to convert in between the customary and also metric systems, sometimes it help to have actually a mental photo of how huge or little some units are. The table listed below shows the relationship in between some typical units in both systems.

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

Prefixes in the Metric System

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

The surname of metric systems are created by adding a prefix come the an easy unit of measurement. To tell how big or tiny a unit is, girlfriend look at the prefix. Come tell whether the unit is measuring 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 than base unit 100 time larger than base unit 10 times larger than base unit base units 10 time smaller 보다 base unit 100 times smaller than base unit 1,000 time smaller 보다 base unit

Using this table together a reference, you have the right to 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 larger than one liter (so 1 dekaliter = 10 liters).

Here is a similar table that just shows the metric units of measurement for mass, along with their size loved one to 1 gram (the basic unit). The typical abbreviations because that these metric units have actually been had 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 constant through the metric system, you can create similar charts because that length and also volume. The prefixes have the same interpretations whether they space attached to the devices of size (meter), mass (gram), or volume (liter).

Which of the following sets of three units space 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 this units execute measure length, they room all units of measurement indigenous the U.S. Customary system. The exactly answer is kilometer, centimeter, millimeter.

B) kilometer, centimeter, millimeter

Correct. Every one of these dimensions are native the metric system. You deserve to tell castle are dimensions of length due to the fact that they all contain the word “meter.”

C) kilogram, gram, centigram

Incorrect. These measurements are native the metric system, but they are dimensions of mass, no length. The exactly answer is kilometer, centimeter, millimeter.

D) kilometer, foot, decimeter

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

Converting devices Up and Down the Metric Scale

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

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

In the table, each unit is 10 times larger than the one to its prompt right. This means 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 space in one decigram? kg hg dag g dg cg mg ^ ^

Identify places of milligrams and also decigrams.

Decigrams (dg) are larger than milligrams (mg), for this reason you intend there come be many 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 larger than a mg.

Since you space going native a bigger 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 space 100 milligrams (mg) in 1 decigram (dg).

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

Identify areas of kilometers and also centimeters.

Kilometers (km) are larger than centimeters (cm), therefore you expect 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 are going native a smaller sized unit come a larger unit, divide.

1 cm ÷ 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 start to understand the metric system, you have the right to use a faster way to convert among different metric units. The dimension of metric units increases tenfold together you walk up the metric scale. The decimal mechanism works the very same way: a tenth is 10 times larger than a hundredth; a hundredth is 10 times larger than a thousandth, etc. By applying what friend know around decimals come the metric system, converting among units is as simple as moving decimal points.

Here is the very first problem from above: How plenty of milligrams room in one decigram? You have the right to recreate the order of the metric devices as shown below:

This question asks you to begin with 1 decigram and convert that to milligrams. As shown above, milligrams is two places to the ideal of decigrams. You deserve to just relocate the decimal suggest two areas to the best to convert decigrams come milligrams:

.

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

Note that rather of relocating to the right, you are now relocating to the left—so the decimal allude must do the same:

.