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

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

In the unified States, both the U.S. Customary measure system and the metric system are used, specifically in medical, scientific, and also technical fields. In many other countries, the metric mechanism is the main system of measurement. If you travel to other countries, friend will see that road indicators list ranges in kilometers and also milk is marketed in liters. People in countless countries usage words choose “kilometer,” “liter,” and also “milligram” to measure the length, volume, and weight of various objects. These measurement devices are part of the metric system.

Unlike the U.S. Customary device of measurement, the metric mechanism is based upon 10s. For 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 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 numerous milligrams room in a decigram? Or, what if you desire to transform meters to kilometers? Understanding just how the metric mechanism works is a good start.

What is Metric?

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

In addition to the difference in the simple units, the metric device is based upon 10s, and different actions for length encompass kilometer, meter, decimeter, centimeter, and also millimeter. An alert that words “meter” is part of every one of these units.

The metric system additionally applies the idea that devices within the system get larger or smaller sized by a strength of 10. This way that a meter is 100 times bigger than a centimeter, and a kilogram is 1,000 times heavier than a gram. Girlfriend will check out this idea a 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 equates to 1 yard, and 16 ounces amounts to 1 pound.

Length, Mass, and also Volume

The table below shows the straightforward units that the metric system. Keep in mind that the name of all metric devices follow from this three an easy 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 straightforward unit of length is the meter. A meter is slightly larger than a yardstick, or just over three feet.

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

Among scientists, one gram is identified as the mass of water that would fill a 1-centimeter cube. Girlfriend may notice that words “mass” is used below instead that “weight.” In the sciences and technical fields, a difference is made in between weight and also mass. Load is a measure up of the traction of heaviness on an object. Because that this reason, an object’s weight would be different if it to be weighed on earth or ~ above the moon due to the fact that of the distinction in the gravitational forces. However, the object’s massive would continue to be the very same in both places because mass steps the quantity of substance in one object. As lengthy as you are planning on only measuring objects on Earth, you deserve to use mass/weight relatively interchangeably—but that is precious noting that 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 around 1 gram. A medium-sized container the milk is about 1 liter.

Though that is rarely vital to convert between the customary and metric systems, periodically it help to have a mental image of how large or small some systems are. The table below shows the relationship between some common units in both systems.

 Common measurements in Customary and Metric Systems Length 1 centimeter is a tiny less than half an inch. 1.6 kilometers is around 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 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 larger than the ahead one.

The name of metric devices are developed by adding a prefix come the basic unit of measurement. Come tell how big or little a unit is, friend look in ~ the prefix. To tell even if it is the unit is measure up 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 than base unit 100 time larger than base unit 10 times larger than base unit base units 10 time smaller than base unit 100 time smaller than base unit 1,000 times smaller than 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 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 devices of measurement for mass, together with their size loved one to 1 gram (the basic unit). The common abbreviations for these metric units have actually been included as well.

 Measuring fixed 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 continuous through the metric system, you could create comparable charts for length and also volume. The prefixes have the same definitions whether they are attached to the units of size (meter), massive (gram), or volume (liter).

Which of the adhering to 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 space all systems of measurement from the U.S. Customary system. The exactly answer is kilometer, centimeter, millimeter.

B) kilometer, centimeter, millimeter

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

C) kilogram, gram, centigram

Incorrect. These measurements are indigenous the metric system, but they are dimensions of mass, no 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 systems Up and Down the Metric Scale

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

For instance, you can figure out how numerous centigrams space in one dekagram by using the table above. One dekagram is larger than one centigram, so you intend that one dekagram will equal countless centigrams.

In the table, every unit is 10 times larger than the one to its immediate 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 many milligrams space in one decigram? kg hg dag g dg cg mg ^ ^

Identify locations of milligrams and decigrams.

Decigrams (dg) are larger than milligrams (mg), therefore you suppose there to be many 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 bigger than a mg.

Since you space going native a larger unit come a smaller 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 to kilometers. km hm dam m dm cm mm ^ ^

Identify areas of kilometers and centimeters.

Kilometers (km) are larger than centimeters (cm), so you expect there come 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 are 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 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 amongst different metric units. The size of metric units rises tenfold as you go up the metric scale. The decimal device works the very same way: a tenth is 10 times larger than a hundredth; a hundredth is 10 times bigger than a thousandth, etc. By using what girlfriend know about decimals to the metric system, converting amongst units is as basic as relocating decimal points.

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

This concern asks you to begin with 1 decigram and convert the to milligrams. As displayed above, milligrams is two places to the best of decigrams. You can just move the decimal point two locations to the best to convert decigrams to milligrams:

.

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

Note that rather of moving to the right, you space now relocating to the left—so the decimal suggest must execute the same:

.