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

You are watching: Is a milliliter bigger than a liter

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

In the joined States, both the U.S. Customary measure up system and the metric system are used, particularly in medical, scientific, and technical fields. In most other countries, the metric device is the major system the measurement. If you take trip to other countries, girlfriend will watch that road signs list ranges in kilometers and milk is marketed in liters. World in countless countries usage words prefer “kilometer,” “liter,” and also “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 mechanism of measurement, the metric mechanism is based on 10s. Because that example, a liter is 10 times larger than a deciliter, and also a centigram is 10 times larger than a milligram. This idea that “10” is not existing in the U.S. Customary system—there are 12 inch 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 numerous milligrams room in a decigram? Or, what if you desire to convert meters come kilometers? Understanding how the metric device works is a good start.

What is Metric?

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

In enhancement to the difference in the an easy units, the metric device is based on 10s, and also different actions 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 likewise applies the idea that devices within the system acquire larger or smaller sized by a strength 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. You will discover this idea a little later. For now, an alert how this idea of “getting larger or smaller by 10” is really different than the relationship in between units in the U.S. Customary system, wherein 3 feet equals 1 yard, and also 16 ounces equals 1 pound.

Length, Mass, and also Volume

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

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

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

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

Among scientists, one gram is identified as the mass of water that would certainly fill a 1-centimeter cube. Friend may an alert that words “mass” is used right here instead of “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 gravity on one object. Because that this reason, an object’s weight would be different if it to be weighed on planet or top top the moon since of the difference in the gravitational forces. However, the object’s mass would remain the very same in both places since mass measures the amount of problem in an object. As long as you are planning on just measuring objects on Earth, you can use mass/weight relatively interchangeably—but it is worth noting the there is a difference!

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

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

Though that is rarely essential to convert between the customary and also metric systems, sometimes it helps to have actually a mental image of how large or little some units are. The table listed below shows the relationship between some usual units in both systems.

 Common dimensions in Customary and Metric Systems Length 1 centimeter is a little less than fifty percent an inch. 1.6 kilometers is about 1 mile. 1 meter is around 3 inches much longer than 1 yard. Mass 1 kilogram is a little much more than 2 pounds. 28 grams is around 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 device is a base 10 system. This means that each succeeding unit is 10 times larger than the ahead one.

The name of metric units are developed by including a prefix to the an easy unit of measurement. To tell how large or small a unit is, you look at the prefix. Come tell whether the unit is measuring length, mass, or volume, you look at the base.

 Prefixes in the Metric System kilo- hecto- deka- meter gram liter deci- centi- milli- 1,000 time larger than base unit 100 times larger than base unit 10 time larger than base unit base units 10 times smaller than base unit 100 times smaller than base unit 1,000 times smaller 보다 base unit

Using this table together 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, along with their size family member to 1 gram (the basic unit). The usual abbreviations because that these metric units have actually been included 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 continuous through the metric system, you might create comparable charts for length and also volume. The prefixes have the same interpretations whether they space attached come the devices of length (meter), fixed (gram), or volume (liter).

Which that the following sets of three units space 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 these units do measure length, they room all systems of measurement indigenous the U.S. Customary system. The correct answer is kilometer, centimeter, millimeter.

B) kilometer, centimeter, millimeter

Correct. All of these measurements are native the metric system. You have the right to tell castle are dimensions of length because they every contain words “meter.”

C) kilogram, gram, centigram

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

Converting systems Up and also Down the Metric Scale

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

For instance, girlfriend can number out how countless centigrams room in one dekagram by making use of the table above. One dekagram is bigger than one centigram, for this reason you mean that one dekagram will certainly equal numerous centigrams.

In the table, every unit is 10 times bigger than the one to its instant 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), so you suppose there to be many 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 come a smaller sized unit, multiply.

1 dg · 10 · 10 = 100 mg

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

There are 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), so 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 room going indigenous a smaller unit come a bigger unit, divide.

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

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

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

Once you begin to know the metric system, you have the right to use a shortcut to convert amongst different metric units. The size of metric units increases tenfold together you walk up the metric scale. The decimal device 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 using what girlfriend know around decimals to the metric system, converting amongst units is as basic as relocating decimal points.

Here is the very first problem native above: How many milligrams are in one decigram? You have the right to recreate the bespeak of the metric units as presented below:

This concern asks you to start with 1 decigram and also convert that to milligrams. As shown above, milligrams is two places to the ideal of decigrams. You can just relocate the decimal suggest two locations to the ideal to transform decigrams to milligrams:

.

The same method works as soon as you are converting from a smaller to a larger unit, together in the problem: transform 1 centimeter come kilometers.

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

.