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

You are watching: A liter is a little more than a

· define the metric prefixes and also use them to perform straightforward conversions amongst metric units.

In the joined States, both the U.S. Customary measurement system and the metric system are used, especially in medical, scientific, and also technical fields. In many other countries, the metric device is the primary system of measurement. If you take trip to other countries, you will watch that road indicators list distances in kilometers and milk is offered in liters. People in plenty of countries use words choose “kilometer,” “liter,” and “milligram” to measure up the length, volume, and weight of different objects. This measurement units are part of the metric system.

Unlike the U.S. Customary device of measurement, the metric system 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 that “10” is not present in the U.S. Customary system—there space 12 inches in a foot, and also 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 convert meters to kilometers? Understanding just how the metric device works is a good start.

What is Metric?

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

In enhancement to the distinction in the basic units, the metric mechanism is based upon 10s, and different steps for length incorporate kilometer, meter, decimeter, centimeter, and millimeter. An alert that the word “meter” is part of all of these units.

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

Length, Mass, and also Volume

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

 Length Mass Volume basic units meter gram liter other systems you might 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 larger than a yardstick, or just over three feet.

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

Among scientists, one gram is identified as the massive of water that would certainly fill a 1-centimeter cube. Girlfriend may notice that the word “mass” is used here instead that “weight.” In the sciences and technical fields, a distinction is made in between weight and mass. Load is a measure up of the pull of gravity on an object. For this reason, an object’s weight would be different if it was weighed on earth or top top the moon due to the fact that of the difference in the gravitational forces. However, the object’s massive would stay the very same in both places due to the fact that mass procedures the quantity of substance in an object. As lengthy as you room planning on just measuring objects on Earth, you deserve to use mass/weight relatively interchangeably—but the is precious noting the there is a difference!

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

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

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

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

Prefixes in the Metric System

The metric mechanism is a basic 10 system. This means that each succeeding unit is 10 times larger than the ahead one.

The names of metric devices are formed by including a prefix come the simple unit of measurement. To tell how huge or little a unit is, you look at the prefix. To tell even if it is the unit is measuring length, mass, or volume, girlfriend 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 time larger 보다 base unit 10 time larger 보다 base unit base units 10 time smaller 보다 base unit 100 time smaller 보다 base unit 1,000 times smaller than base unit

Using this table as a reference, you have the right to see the following:

· A kilogram is 1,000 times bigger 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 comparable table that simply shows the metric units of measurement because that mass, in addition to their size loved one to 1 gram (the base unit). The usual abbreviations for these metric units have actually been contained 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 comparable charts for length and volume. The prefixes have actually the same interpretations whether they space attached to the units of length (meter), fixed (gram), or volume (liter).

Which that 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 systems of measurement from the U.S. Customary system. The exactly answer is kilometer, centimeter, millimeter.

B) kilometer, centimeter, millimeter

Correct. All of these dimensions are from 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 indigenous the metric system, but they are measurements of mass, no length. The correct answer is kilometer, centimeter, millimeter.

D) kilometer, foot, decimeter

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

Converting systems Up and Down the Metric Scale

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

For instance, you can figure out how countless centigrams room in one dekagram by using the table above. One dekagram is bigger than one centigram, for this reason you mean that one dekagram will equal many centigrams.

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

Identify places of milligrams and also decigrams.

Decigrams (dg) are bigger than milligrams (mg), so you suppose 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 a cg is 10 times larger than a mg.

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

1 dg · 10 · 10 = 100 mg

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

Kilometers (km) are bigger than centimeters (cm), so you intend there to 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 are going indigenous a smaller sized unit to a larger unit, divide.

1 cm ÷ 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 have the right to use a faster way to convert among different metric units. The dimension of metric units rises tenfold as you go up the metric scale. The decimal system works the exact 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 around decimals come the metric system, converting among units is as simple as relocating decimal points.

Here is the very first problem native above: How plenty of milligrams room in one decigram? You deserve to recreate the stimulate of the metric systems as presented below:

This question asks friend to begin with 1 decigram and convert the to milligrams. As displayed above, milligrams is two locations to the right of decigrams. You have the right to just relocate the decimal point two areas to the appropriate to convert decigrams come milligrams:

.

The same method works once you space converting native a smaller to a bigger unit, as in the problem: transform 1 centimeter to kilometers.

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

.