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

You are watching: How many grams are in a meter

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


In the united States, both the U.S. Customary measure up system and the metric system are used, specifically in medical, scientific, and technical fields. In most other countries, the metric mechanism is the primary system the measurement. If you travel to various other countries, you will view that road signs list distances in kilometers and milk is offered in liters. Human being in countless countries use words choose “kilometer,” “liter,” and also “milligram” to measure the length, volume, and weight of different objects. These measurement devices are component of the metric system.

Unlike the U.S. Customary device of measurement, the metric mechanism is based on 10s. For example, a liter is 10 times bigger than a deciliter, and a centigram is 10 times larger than a milligram. This idea of “10” is not present 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 find out how numerous milligrams space in a decigram? Or, what if you want to transform meters come kilometers? Understanding how the metric mechanism works is a good start.


What is Metric?


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

In enhancement to the distinction in the an easy units, the metric device is based on 10s, and also different steps for length encompass kilometer, meter, decimeter, centimeter, and millimeter. Notification that the word “meter” is component of all of these units.

The metric system additionally applies the idea that devices within the system acquire larger or smaller sized by a power of 10. This way that a meter is 100 times larger than a centimeter, and also a kilogram is 1,000 times heavier than a gram. Girlfriend will check out this idea a little bit later. For now, notification how this idea of “getting enlarge or smaller by 10” is an extremely different than the relationship between units in the U.S. Customary system, where 3 feet equals 1 yard, and 16 ounces equates to 1 pound.


Length, Mass, and Volume


The table below shows the simple units of the metric system. Keep in mind that the surname of all metric devices follow from these three simple 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 length is the meter. A meter is slightly larger than a yardstick, or just over 3 feet.

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

Among scientists, one gram is defined as the massive of water that would fill a 1-centimeter cube. Friend may notification that words “mass” is used below instead the “weight.” In the sciences and also technical fields, a distinction is made in between weight and also mass. Load is a measure 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 planet or on the moon because of the distinction 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 lot of problem in an object. As long as you are planning on just measuring objects ~ above Earth, you deserve to use mass/weight reasonably interchangeably—but that is precious noting that there is a difference!

Finally, the simple 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 around 1 gram.

A medium-sized container that milk is about 1 liter.

Though it is rarely crucial to convert between the customary and also metric systems, periodically it helps to have a mental photo of how huge or small some systems are. The table listed below shows the relationship between some typical units in both systems.


Common dimensions in Customary and Metric Systems

Length

1 centimeter is a small 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 much more than 1 gallon.


Prefixes in the Metric System


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

The name of metric units are developed by adding a prefix to the basic unit of measurement. Come tell how huge or little a unit is, you look in ~ the prefix. To tell whether the unit is measure up length, mass, or volume, you 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 보다 base unit

10 times larger 보다 base unit

base units

10 time smaller than base unit

100 times 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 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 simply shows the metric systems of measurement for mass, together with their size relative to 1 gram (the base unit). The usual abbreviations because that these metric units have been included 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 because that length and also volume. The prefixes have the same definitions whether they are attached to the units of size (meter), mass (gram), or volume (liter).


Which that 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


Show/Hide Answer

A) inch, foot, yard

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

B) kilometer, centimeter, millimeter

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

C) kilogram, gram, centigram

Incorrect. These measurements are native 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 decimeter are metric units of length, yet foot is not. The correct answer is kilometer, centimeter, millimeter.

Converting units Up and Down the Metric Scale


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

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

In the table, every unit is 10 times larger than the one to its prompt right. This means 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 numerous milligrams are in one decigram?


kg

hg

dag

g

dg

cg

mg

^

^


Identify locations of milligrams and also decigrams.

Decigrams (dg) are bigger than milligrams (mg), for this reason you suppose 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 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 discover the variety of milligrams in one decigram.

Answer

There room 100 milligrams (mg) in 1 decigram (dg).

Example

Problem

Convert 1 centimeter come kilometers.


km

hm

dam

m

dm

cm

mm

^

^


Identify locations of kilometers and centimeters.

Kilometers (km) are larger than centimeters (cm), therefore you mean 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 sized than a dm; a dm is 10 times smaller sized than a m, etc.

Since you are going native a smaller sized unit come 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.

Answer

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


Once you begin to recognize the metric system, you have the right to use a faster way to convert among different metric units. The size of metric units increases tenfold together you walk up the metric scale. The decimal mechanism works the same way: a tenth is 10 times bigger than a hundredth; a hundredth is 10 times larger than a thousandth, etc. By using what you know about decimals come the metric system, converting amongst units is as straightforward as moving decimal points.

Here is the very first problem indigenous above: How plenty of milligrams room in one decigram? You have the right to recreate the bespeak of the metric systems as presented below:

*

This inquiry asks friend to start with 1 decigram and convert the to milligrams. As shown above, milligrams is two places to the right of decigrams. You have the right to just move the decimal allude two locations to the best to transform decigrams to milligrams:

*
.

The same method works once you room converting from a smaller sized to a bigger unit, as in the problem: convert 1 centimeter come kilometers.

*

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

*
.

How numerous milliliters are 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 friend would suppose there come be an ext than one milliliter in 1 liter. The exactly answer is 1,000.

B) 0.1

Incorrect. One liter is larger than one milliliter, so you would suppose there come be more than one milliliter in 1 liter. The correct answer is 1,000.

C) 100

Incorrect. There room 100 milliliters in 1 deciliter. The correct answer is 1,000.

D) 1,000

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

See more: How Many Electrons In F Orbital S, How Many Electrons Can Each Hold?


Summary


The metric mechanism is an different system of measurement supplied in most countries, and in the united States. The metric mechanism is based on joining among a collection of prefixes, including kilo-, hecto-, deka-, deci-, centi-, and milli-, through a basic unit that measurement, such as meter, liter, or gram. Units in the metric mechanism are all related by a strength of 10, which way that each successive unit is 10 times larger than the previous one. This renders converting one metric measurement to an additional a straightforward process, and also is often as basic as moving a decimal point. That is constantly important, though, to take into consideration the direction the the conversion. If you space converting a smaller sized unit come a bigger unit, climate the decimal allude has to relocate to the left (making her number smaller); if you are converting a bigger unit come a smaller unit, climate the decimal allude has to move to the ideal (making her number larger).