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

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· specify the metric prefixes and use them come perform straightforward conversions amongst metric units.


In the joined States, both the U.S. Customary measurement system and the metric system are used, specifically in medical, scientific, and technical fields. In most other countries, the metric device is the major system that measurement. If you take trip to other countries, girlfriend will view that road indications list ranges in kilometers and also milk is offered in liters. Human being in plenty of countries use words favor “kilometer,” “liter,” and also “milligram” to measure the length, volume, and weight of different objects. This measurement devices are component of the metric system.

Unlike the U.S. Customary mechanism of measurement, the metric system 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 the “10” is not present 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 to discover out how many milligrams space in a decigram? Or, what if you desire 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 together meter, liter, and gram to measure 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 system is based on 10s, and different procedures for length incorporate kilometer, meter, decimeter, centimeter, and millimeter. An alert that words “meter” is component of every one of these units.

The metric system also applies the idea that units within the system acquire larger or smaller by a strength of 10. This means that a meter is 100 times bigger than a centimeter, and a kilogram is 1,000 times heavier than a gram. You will explore this idea a little bit later. For now, an alert how this idea the “getting bigger or smaller by 10” is an extremely different than the relationship in between units in the U.S. Customary system, where 3 feet amounts to 1 yard, and 16 ounces amounts to 1 pound.


Length, Mass, and Volume


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


Length

Mass

Volume

basic units

meter

gram

liter

other devices you might see

kilometer

kilogram

dekaliter

centimeter

centigram

centiliter

millimeter

milligram

milliliter


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

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

Among scientists, one gram is defined as the massive of water that would certainly fill a 1-centimeter cube. Friend may notification that the word “mass” is used below instead of “weight.” In the sciences and technical fields, a distinction is made in between weight and mass. Weight is a measure up of the pull of gravity on an object. For this reason, one object’s weight would be various if it to be weighed on planet or top top the moon because of the difference in the gravitational forces. However, the object’s fixed would remain the exact same in both places since mass steps the lot of problem in one object. As long as you room planning on just measuring objects on Earth, you have the right to use mass/weight relatively interchangeably—but it is worth noting the there is a difference!

Finally, the an easy metric unit of volume is the liter. A liter is slightly larger than a quart.

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The take care of of a shovel is about 1 meter.

A paperclip weighs around 1 gram.

A medium-sized container the milk is around 1 liter.

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


Common measurements in Customary and also Metric Systems

Length

1 centimeter is a small less than fifty percent an inch.

1.6 kilometers is around 1 mile.

1 meter is around 3 inches much longer than 1 yard.

Mass

1 kilogram is a little more than 2 pounds.

28 grams is about the same as 1 ounce.

Volume

1 liter is a little much more than 1 quart.

4 liters is a little much more than 1 gallon.


Prefixes in the Metric System


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

The names of metric devices are created by including a prefix come the simple unit the measurement. Come tell how huge or small a unit is, friend look at the prefix. Come tell even if it is the unit is measure up 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 times larger than base unit

10 times larger 보다 base unit

base units

10 times smaller than base unit

100 time smaller 보다 base unit

1,000 times smaller 보다 base unit

Using this table together a reference, you deserve 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 than one meter (so 1 meter = 100 centimeters).

· A dekaliter is 10 times bigger than one liter (so 1 dekaliter = 10 liters).

Here is a comparable table that just shows the metric systems of measurement for mass, in addition to their size relative to 1 gram (the base unit). The usual abbreviations for these metric units have been had 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 might create similar charts because that length and also volume. The prefixes have actually the same meanings whether they are attached to the systems of length (meter), mass (gram), or volume (liter).


Which of the complying with sets of 3 units space all metric measurements of length?

A) inch, foot, yard

B) kilometer, centimeter, millimeter

C) kilogram, gram, centigram

D) kilometer, foot, decimeter


Show/Hide Answer

A) inch, foot, yard

Incorrect. Although these units perform measure length, they room all systems of measurement native the U.S. Customary system. The correct answer is kilometer, centimeter, millimeter.

B) kilometer, centimeter, millimeter

Correct. All of these dimensions are from the metric system. You deserve to tell they are dimensions of length because they all contain words “meter.”

C) kilogram, gram, centigram

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

D) kilometer, foot, decimeter

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

Converting devices Up and also Down the Metric Scale


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

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

In the table, each unit is 10 times larger than the one to its immediate right. This method 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 countless milligrams are in one decigram?


kg

hg

dag

g

dg

cg

mg

^

^


Identify places of milligrams and decigrams.

Decigrams (dg) are bigger than milligrams (mg), for this reason you mean there to 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 also a cg is 10 times bigger than a mg.

Since you space going indigenous a bigger unit to a smaller unit, multiply.

1 dg · 10 · 10 = 100 mg

Multiply: 1 · 10 · 10, to discover the number of milligrams in one decigram.

Answer

There are 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), for this reason you suppose there to 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 room 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 discover the variety of kilometers in one centimeter.

Answer

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


Once you start to know the metric system, you deserve to use a faster way to convert among different metric units. The dimension of metric units boosts tenfold as you go up the metric scale. The decimal device 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 applying what you know around decimals to the metric system, converting amongst units is as straightforward as moving decimal points.

Here is the an initial problem indigenous above: How many milligrams space in one decigram? You have the right to recreate the stimulate of the metric units as shown below:

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This concern asks you to start with 1 decigram and also convert that to milligrams. As displayed above, milligrams is two areas to the best of decigrams. You can just move the decimal suggest two locations to the appropriate to transform decigrams come milligrams:

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

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

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How plenty of milliliters room in 1 liter?

A) 0.001

B) 0.1

C) 100

D) 1,000


Show/Hide Answer

A) 0.001

Incorrect. One liter is bigger than one milliliter, so you would expect there to be an ext than one milliliter in 1 liter. The correct answer is 1,000.

B) 0.1

Incorrect. One liter is larger than one milliliter, so girlfriend would intend there come be more than one milliliter in 1 liter. The exactly answer is 1,000.

C) 100

Incorrect. There are 100 milliliters in 1 deciliter. The exactly answer is 1,000.

D) 1,000

Correct. There space 10 milliliters in a centiliter, 10 centiliters in a deciliter, and also 10 deciliters in a liter. Multiply: 10 · 10 · 10, to find the number of milliliters in a liter, 1,000.

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Summary


The metric mechanism is an different system that measurement supplied in many countries, and in the unified States. The metric system is based upon joining among a series of prefixes, consisting of kilo-, hecto-, deka-, deci-, centi-, and also milli-, with a basic unit the measurement, such as meter, liter, or gram. Systems in the metric device are all connected by a power of 10, which means that each succeeding unit is 10 times bigger than the vault one. This makes converting one metric measure to one more a simple process, and is often as straightforward as moving a decimal point. It is constantly important, though, to think about the direction the the conversion. If you room converting a smaller unit come a bigger unit, climate the decimal allude has to relocate to the left (making your number smaller); if you space converting a larger unit to a smaller unit, climate the decimal suggest has to relocate to the best (making her number larger).