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

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

In the united States, both the U.S. Customary measure system and also the metric system room used, specifically in medical, scientific, and also technical fields. In many other countries, the metric system is the major system that measurement. If you travel to other countries, friend will check out that road signs list distances in kilometers and milk is sold in liters. People in many countries usage words prefer “kilometer,” “liter,” and “milligram” to measure up the length, volume, and also weight of various objects. This measurement units are part of the metric system.

Unlike the U.S. Customary mechanism of measurement, the metric mechanism is based upon 10s. For example, a liter is 10 times bigger than a deciliter, and also a centigram is 10 times bigger than a milligram. This idea the “10” is not present 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 actually to uncover out how many milligrams are in a decigram? Or, what if you want to convert meters to kilometers? Understanding how the metric system works is a an excellent start.

What is Metric?

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

In addition to the difference in the basic units, the metric system is based on 10s, and also different procedures for length encompass kilometer, meter, decimeter, centimeter, and also millimeter. An alert that the word “meter” is component of all of these units.

The metric system likewise 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 also a kilogram is 1,000 time heavier than a gram. Friend will explore this idea a bit later. For now, notification how this idea that “getting enlarge or smaller by 10” is really different 보다 the relationship between units in the U.S. Customary system, whereby 3 feet equates to 1 yard, and 16 ounces equates to 1 pound.

Length, Mass, and Volume

The table listed below shows the basic units that the metric system. Note that the surname of all metric systems follow from these three basic units.

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

In the metric system, the an easy unit of length is the meter. A meter is slightly larger than a yardstick, or simply over three feet.

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

Among scientists, one gram is characterized as the massive of water that would fill a 1-centimeter cube. Friend may notice that words “mass” is used here instead of “weight.” In the sciences and technical fields, a distinction is made in between weight and also mass. Load is a measure of the pull of heaviness on an object. For this reason, one object’s weight would be different if it to be weighed on earth or on the moon since of the distinction in the gravitational forces. However, the object’s fixed would continue to be the same in both places since mass steps the lot of substance in an object. As lengthy as you space planning on just measuring objects on Earth, you can use mass/weight fairly interchangeably—but that is worth noting the there is a difference!

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

Though that is rarely crucial to convert in between the customary and also metric systems, sometimes it help to have a mental picture of how huge or little some systems are. The table listed below shows the relationship between some common 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 around 1 mile. 1 meter is about 3 inches much longer than 1 yard. Mass 1 kilogram is a little much more than 2 pounds. 28 grams is about the very same as 1 ounce. Volume 1 liter is a little more than 1 quart. 4 liters is a little an ext than 1 gallon.

Prefixes in the Metric System

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

The surname of metric systems are created by including a prefix come the basic unit that measurement. Come tell how large or small a unit is, friend look in ~ the prefix. To 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 보다 base unit 10 times larger than base unit base units 10 time smaller than base unit 100 time smaller than base unit 1,000 time smaller than base unit

Using this table together a reference, you deserve 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 similar table that simply shows the metric systems of measurement because that mass, in addition to their size loved one to 1 gram (the base unit). The common abbreviations for these metric units have actually been contained as well.

 Measuring massive 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 might create similar charts for length and volume. The prefixes have the same meanings whether they space attached come the devices of length (meter), mass (gram), or volume (liter).

Which the the adhering to sets of 3 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 this units do measure length, they room all devices of measurement native 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 they are dimensions of length since they every contain the word “meter.”

C) kilogram, gram, centigram

Incorrect. These measurements are from the metric system, however 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 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 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 numerous centigrams space in one dekagram by using the table above. One dekagram is bigger than one centigram, therefore you intend that one dekagram will certainly equal many centigrams.

In the table, every unit is 10 times bigger than the one to its prompt 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 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), for this reason you mean 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 also a cg is 10 times larger than a mg.

Since you room going from a bigger unit to a smaller unit, multiply.

1 dg · 10 · 10 = 100 mg

Multiply: 1 · 10 · 10, to uncover the variety 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 also centimeters.

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

Since you space going indigenous a smaller sized unit come a bigger unit, divide.

1 cm ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10 = 0.00001 km

Divide: 1 ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10, to find the number of kilometers in one centimeter.

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

Once you begin to understand 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 together you go up the metric scale. The decimal system works the exact same way: a tenth is 10 times larger than a hundredth; a hundredth is 10 times bigger than a thousandth, etc. By applying what you know about decimals come the metric system, converting among units is as simple as moving decimal points.

Here is the first problem indigenous above: How numerous milligrams space in one decigram? You have the right to 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 displayed above, milligrams is two locations to the appropriate of decigrams. You have the right to just move the decimal allude two places to the best to convert decigrams to milligrams: .

The same technique works when you room converting indigenous a smaller to a larger unit, together in the problem: convert 1 centimeter come kilometers. Note that rather of relocating to the right, you are now moving to the left—so the decimal point must do the same: .