While discovering the various units provided in the metric device is important, the real function behind learning the metric mechanism is because that you to be able to use these measurement units to calculation the size, mass, or volume of different objects. In practice, that is often vital to convert one metric measurement to one more unit—this happens commonly in the medical, scientific, and technical fields, whereby the metric mechanism is typically used.

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If you have actually a prescription because that 5,000 mg of medicine, and also upon acquiring it filled, the dosage reads 5 g that medicine, go the pharmacist make a mistake?

For a moment, imagine that you space a pharmacist. You obtain three prescriptions for fluid amoxicillin: one calls because that 2.5 centiliters, one calls for 0.3 deciliters, and also one calls because that 450 milliliters. Amoxicillin is save on computer in the frozen refrigerator in 1 liter, 1 deciliter, and also 1 centiliter containers. I m sorry container have to you usage to for sure you are not wasting any kind of of the unused drug?

To fix this problem, you need to know just how to convert from one measurement to another as well as how to add different quantities together. Let’s take it a look at at just how to carry out this.


Converting from larger to smaller sized Units


Converting between measurements in the metric system is merely a issue of identifying the unit the you have, the unit the you want to convert to, and then counting the number of units in between them. A basic example the this is displayed below.


Example

Problem

Convert 1 kilometre to decimeters.


km

hm

dam

m

dm

cm

mm

^

^


Identify locations of kilometers and decimeters.

Kilometers (km) are bigger than decimeters (dm), therefore you suppose there to be more than one dm in a km.


×10

×10

×10

 ×10

km

hm

dam

m

dm

cm

mm

^

^

 


Count the intermediate units, multiplying by 10 as you go.

(Since you space going from a larger unit come a smaller sized unit, girlfriend multiply.)

1 km · 10 · 10 · 10 · 10 = 10,000 dm

Multiply to discover the variety of decimeters in one kilometer.

Answer

1 kilometre = 10,000 decimeters


This trouble is straightforward since you space converting 1 kilometer to one more unit. The example below shows how you would solve this difficulty if you were asked to transform 8.2 kilometers to decimeters. Notification that most procedures are the same; the an important difference is the you multiply by 8.2 in the last step.


Example

Problem

Convert 8.2 kilometers come decimeters.


km

hm

dam

m

dm

cm

mm

^

^


Identify places of kilometers and also decimeters.

Kilometers (km) are bigger than decimeters (dm), therefore you mean there to be more than one dm in a km.


×10

×10

×10

 ×10

km

hm

dam

m

dm

cm

mm

^

^

 


Count the intermediary units, multiply by 10 as you go.

Since you space going from a larger unit come a smaller sized unit, multiply.

8.2 km · 10 · 10 · 10 · 10 = 82,000 dm

Multiply to uncover the variety of decimeters in 8.2 kilometers.

Answer

8.2 kilometers = 82,000 decimeters


You can also apply the rule of base 10 to use the “move the decimal” shortcut technique in this example. An alert how decimeters (dm) is four places come the appropriate of kilometers (km); similarly, you move the decimal suggest four areas to the right once converting 8.2 kilometers to decimeters.

*

*


Example

Problem

Convert 0.55 liters to centiliters.

*

Count two areas from liters to centiliters.

*

In 0.55 l, relocate the decimal suggest two areas to the right.

*

Answer

0.55 liters = 55 centiliters



Notice the the shortcut an approach of counting prefixes and also moving the decimal the same variety of places additionally works here. Just make sure you are moving the decimal allude in the correct direction because that the conversion.


How plenty of dekaliters room in 0.5 deciliters?

A) 500

B) 5

C) 0.5

D) 0.005


Show/Hide Answer

A) 500

Incorrect. A dekaliter is larger than a deciliter, so you would mean the variety of dekaliters in 0.5 deciliters come be smaller sized than 0.5. The exactly answer is 0.005.

B) 5

Incorrect. A dekaliter is larger than a deciliter, so friend would mean the number of dekaliters in 0.5 deciliters to be smaller sized than 0.5. The exactly answer is 0.005.

C) 0.5

Incorrect. Deciliters and also dekaliters are different units of measurement, for this reason you would certainly not suppose 0.5 deciliters to equal 0.5 dekaliters. The exactly answer is 0.005.

D) 0.005

Correct. One deciliter is 100 times smaller than a dekaliter, for this reason you relocate the decimal suggest two locations to the left to transform 0.5 deciliters to 0.005 dekaliters.

Converting from smaller sized to larger Units


You deserve to use comparable processes as soon as converting from smaller sized to bigger units. As soon as converting a bigger unit come a smaller one, friend multiply; when you convert a smaller sized unit come a bigger one, girlfriend divide. Right here is an example.


Example

Problem

Convert 739 centigrams to grams.


kg

hg

dag

g

dg

cg

mg

^

^


Identify places of centigrams and grams.

Centigrams (cg) are smaller sized than grams (g), so you suppose there come be much less than 739 g in 739 cg.


 ÷10

÷10

kg

hg

dag

g

dg

cg

mg

^

^

*


Count the intermediate units, splitting by 10 together you go.

Since you room going indigenous a smaller unit to a bigger unit, divide.

739 ÷ 10 ÷ 10 = 7.39 g

Divide to discover the variety of grams in 739 centigrams.

Answer

739 centigrams = 7.39 grams

Example

Problem

Convert 205.5 milliliters to kiloliters.

*

Count six places from milliliters come kiloliters.

*

Milliliters is smaller than kiloliters, therefore you mean the number 205.5 to obtain smaller together you move up the metric chart.

In 205.5 ml, move the decimal allude six areas to the left.

*

Answer

205.5 milliliters = 0.0002055 kiloliters


Convert 3,085 milligrams to grams.

A) 3,085,000 grams

B) 308.5 grams

C) 3.085 grams

D) 0.3085 grams


Show/Hide Answer

A) 3,085,000 grams

Incorrect. Grams are larger than milligrams, so girlfriend would expect the number of grams in 3,085 milligrams come be less than 3,085. The correct answer is 3.085 grams.

B) 308.5 grams

Incorrect. One gram is an ext than 10 times larger than a milligram, so you would expect the number of grams come be less than 308.5. The correct answer is 3.085 grams.

C) 3.085 grams

Correct. One gram is 1,000 times bigger than a milligram, so you can move the decimal allude in 3,085 three locations to the left.

D) 0.3085 grams

Incorrect. This is too small; one gram is 1,000, no 10,000, times bigger than a milligram. The exactly answer is 3.085 grams.

Factor label Method


There is however another technique that you can use to convert metric measurements—the factor label method. You supplied this method when you to be converting measurement devices within the U.S. Customary system.

The element label method works the very same in the metric system; it relies on the usage of unit fractions and also the cancelling of intermediate units. The table below shows some of the unit equivalents and A portion where the numerator and also denominator room equal amounts, together in

*
 or
*
. Unit fractions serve to help with switch in the variable Label method.


")">unit fractions
for length in the metric system. (You should notification that every one of the unit fractions contain a aspect of 10. Remember the the metric system is based upon the id that every unit is 10 times larger than the one the came before it.)

Also, an alert that two brand-new prefixes have actually been included here: mega- (which is really big) and also micro- (which is very small).


Unit Equivalents

Conversion Factors

1 meter = 1,000,000 micrometers

*

*

1 meter = 1,000 millimeters

*

*

1 meter = 100 centimeters

*

*

1 meter = 10 decimeters

*

*

1 dekameter = 10 meters

*

*

1 hectometer = 100 meters

*

*

1 kilometre = 1,000 meters

*

*

1 megameter = 1,000,000 meters

*

*


When applying the aspect label an approach in the metric system, be sure to check that you space not omitted over any intermediate systems of measurement!


Example

Problem

Convert 7,225 centimeters come meters.

7,225 cm = ___ m

Meters is larger than centimeters, for this reason you expect your answer come be much less than 7,225.

*

Using the element label method, create 7,225 cm as a portion and use unit fountain to transform it to m.

*

*

*

Cancel comparable units, multiply, and also simplify.

Answer

7,225 centimeters =

*
 meters


Using whichever method you prefer, transform 32.5 kilometers come meters.

A) 32,500 m

B) 325 m

C) 0.325 m

D) 0.00325 m


Show/Hide Answer

A) 32,500 m

Correct. To discover the variety of m in 32.5 km, girlfriend can set up the adhering to equation:

*
. The km units cancel, leaving the prize in m.

B) 325 m

Incorrect. A km is an ext than 10 time the dimension of a m; look at the unit fountain and shot your calculations again. The correct answer is 32,500 m.

C) 0.325 m

Incorrect. A kilometres is larger than a meter, so friend would expect the number of meters in 32.5 kilometres to be an ext than 32.5. Look at the unit fountain and try your calculations again. The exactly answer is 32,500 m.

D) 0.00325 m

Incorrect. A kilometres is bigger than a meter, so you would suppose the number of meters in 32.5 kilometres to be an ext than 32.5. Look at the unit fractions and shot your calculations again. The exactly answer is 32,500 m.

Now that you have seen how to convert among metric dimensions in multiple ways, let’s revisit the problem posed earlier.


Example

Problem

If you have a prescription for 5,000 mg that medicine, and also upon obtaining it filled, the dosage reads 5 g that medicine, walk the pharmacist do a mistake?

5,000 mg = ___ g?

Need to convert mg to g.

*

*

*

*

Answer

5 g = 5,000 mg, for this reason the pharmacist did not make a mistake.

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Summary


To convert among units in the metric system, determine the unit the you have, the unit the you want to convert to, and also then counting the variety of units in between them. If you space going indigenous a larger unit to a smaller unit, you main point by 10 successively. If you room going from a smaller sized unit come a bigger unit, you divide by 10 successively. The factor label technique can likewise be applied to conversions in ~ the metric system. To usage the variable label method, you main point the initial measurement by unit fractions; this enables you to represent the original measurement in a different measurement unit.