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

You are watching: Metric units of mass and liquid volume

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

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

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

So, what if you have actually to uncover out how many milligrams room in a decigram? Or, what if you want to transform meters come kilometers? Understanding just how the metric mechanism works is a great start.

What is Metric?

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

In addition to the distinction in the basic units, the metric device is based on 10s, and different actions for length include 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 systems within the system obtain larger or smaller sized by a power of 10. This means that a meter is 100 times larger than a centimeter, and a kilogram is 1,000 time heavier 보다 a gram. You will explore this idea a little bit later. For now, notification how this idea the “getting larger or smaller sized by 10” is really different than the relationship in between units in the U.S. Customary system, where 3 feet equates to 1 yard, and 16 ounces equals 1 pound.

Length, Mass, and Volume

The table listed below shows the an easy units that the metric system. Keep in mind that the names of all metric units 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 three feet.

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

Among scientists, one gram is defined as the mass of water that would fill a 1-centimeter cube. Friend may notification that words “mass” is used here instead that “weight.” In the sciences and also technical fields, a difference is made between weight and also mass. Weight is a measure up of the pull of heaviness on one object. Because that this reason, an object’s weight would be different if it was weighed on earth or top top the moon since of the difference in the gravitational forces. However, the object’s massive would remain the same in both places since mass actions the amount of substance in one object. As lengthy as you are planning on only measuring objects on Earth, you can use mass/weight reasonably interchangeably—but that is worth noting the there is a difference!

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

Though the is rarely necessary to convert between the customary and also metric systems, periodically it helps to have actually a mental image of how large or tiny some devices are. The table below shows the relationship in between some usual units in both systems.

 Common measurements in Customary and 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 more than 2 pounds. 28 grams is about the very 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 device is a basic 10 system. This method that each successive unit is 10 times larger than the previous one.

The name of metric systems are formed by including a prefix come the basic unit of measurement. To tell how huge or small a unit is, friend look at the prefix. To tell even if it is the unit is measure length, mass, or volume, you look at the base.

 Prefixes in the Metric System kilo- hecto- deka- meter gram liter deci- centi- milli- 1,000 time larger than base unit 100 times larger than base unit 10 times larger than base unit base units 10 time smaller 보다 base unit 100 time smaller 보다 base unit 1,000 time smaller than 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 larger than one liter (so 1 dekaliter = 10 liters).

Here is a similar table that simply shows the metric units of measurement because that mass, in addition to their size relative to 1 gram (the basic unit). The common abbreviations because that these metric units have actually been included 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 might create comparable charts because that length and volume. The prefixes have the same definitions whether they room attached to the systems of size (meter), fixed (gram), or volume (liter).

Which of the complying with sets of 3 units are 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 do measure length, they are all units of measurement native the U.S. Customary system. The exactly answer is kilometer, centimeter, millimeter.

B) kilometer, centimeter, millimeter

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

C) kilogram, gram, centigram

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

D) kilometer, foot, decimeter

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

Converting systems Up and also Down the Metric Scale

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

For instance, friend can figure out how numerous centigrams are in one dekagram by using the table above. One dekagram is larger than one centigram, therefore you mean that one dekagram will certainly equal countless centigrams.

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

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

Identify locations of milligrams and decigrams.

Decigrams (dg) are bigger than milligrams (mg), for this reason you suppose there come be numerous 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 are going indigenous a larger unit come a smaller sized unit, multiply.

1 dg · 10 · 10 = 100 mg

Multiply: 1 · 10 · 10, to uncover the number 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 places of kilometers and centimeters.

Kilometers (km) are larger than centimeters (cm), therefore you expect there come be much less than one kilometres in a cm.

÷10

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

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

Since you room going from a smaller unit come a larger 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 start to understand the metric system, you deserve to use a faster way to convert amongst different metric units. The dimension of metric units increases tenfold as you go up the metric scale. The decimal device works the very same way: a tenth is 10 times bigger than a hundredth; a hundredth is 10 times bigger than a thousandth, etc. By using what friend know around decimals to the metric system, converting among units is as an easy as moving decimal points.

Here is the first problem from above: How countless milligrams room in one decigram? You can recreate the bespeak of the metric units as presented below: This inquiry asks you to begin with 1 decigram and also convert that to milligrams. As shown above, milligrams is two locations to the best of decigrams. You deserve to just move the decimal point two areas to the appropriate to convert decigrams to milligrams: .

The same technique works once you room converting native a smaller sized to a bigger unit, as in the problem: convert 1 centimeter to kilometers. Note that rather of relocating to the right, you are now relocating to the left—so the decimal point must perform the same: .