Is Grams Bigger Than Kilograms

The Metric System

Learning Objective(s)

· Draw the full general human relationship between the U.S. customary units and metric units of length, weight/mass, and volume.

· Define the metric prefixes and utilize them to perform bones conversions among metric units.

Introduction

In the United States, both the U.Due south. customary measurement organization and the metric arrangement are used, especially in medical, scientific, and technical fields. In well-nigh other countries, the metric organisation is the primary arrangement of measurement. If you travel to other countries, y'all will see that road signs list distances in kilometers and milk is sold in liters. People in many countries use words like "kilometer," "liter," and "milligram" to measure the length, volume, and weight of dissimilar objects. These measurement units are function of the metric system.

Unlike the U.S. customary organisation of measurement, the metric system is based on 10s. For example, a liter is 10 times larger than a deciliter, and a centigram is 10 times larger than a milligram. This thought of "10" is not present in the U.S. customary system—in that location are 12 inches in a foot, and 3 feet in a yard…and 5,280 feet in a mile!

So, what if you have to detect out how many milligrams are in a decigram? Or, what if you lot want to convert meters to kilometers? Understanding how the metric system works is a good first.

What is Metric?

The metric organisation uses units such equally meter, liter, and gram to measure length, liquid book, and mass, just as the U.South. customary system uses feet, quarts, and ounces to measure these.

In improver to the difference in the basic units, the metric organisation is based on 10s, and dissimilar measures for length include kilometer, meter, decimeter, centimeter, and millimeter. Notice that the discussion "meter" is part of all of these units.

The metric system also applies the idea that units within the system become larger or smaller past a power of x. This means that a meter is 100 times larger than a centimeter, and a kilogram is 1,000 times heavier than a gram. You lot will explore this idea a fleck after. For at present, find how this idea of "getting bigger or smaller past 10" is very different than the relationship betwixt units in the U.South. customary system, where 3 feet equals ane one thousand, and 16 ounces equals ane pound.

Length, Mass, and Book

The table beneath shows the basic units of the metric system. Note that the names of all metric units follow from these iii bones units.

Length	Mass	Volume
basic units
meter	gram	liter
other units y'all may meet
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 three feet.

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

Among scientists, one gram is defined as the mass of water that would fill up a 1-centimeter cube. You may notice that the give-and-take "mass" is used here instead of "weight." In the sciences and technical fields, a stardom is made betwixt weight and mass. Weight is a measure of the pull of gravity on an object. For this reason, an object'due south weight would be different if information technology was weighed on Globe or on the moon because of the difference in the gravitational forces. Withal, the object'due south mass would remain the aforementioned in both places because mass measures the corporeality of substance in an object. As long as you are planning on only measuring objects on Earth, yous can apply mass/weight fairly interchangeably—but it is worth noting that there is a difference!

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


The handle of a shovel is about i meter.	A paperclip weighs about i gram.	A medium-sized container of milk is about 1 liter.

Though information technology is rarely necessary to convert between the customary and metric systems, sometimes information technology helps to have a mental image of how large or small some units are. The table below shows the relationship between some mutual units in both systems.

	Common Measurements in Customary and Metric Systems
Length	1 centimeter is a piddling less than half an inch.
	1.vi kilometers is nigh 1 mile.
	1 meter is about 3 inches longer than 1 1000.
Mass	one kilogram is a little more than 2 pounds.
	28 grams is about the same as 1 ounce.
Book	one liter is a little more than 1 quart.
	4 liters is a little more than 1 gallon.

Prefixes in the Metric System

The metric system is a base 10 system. This ways that each successive unit of measurement is x times larger than the previous one.

The names of metric units are formed by adding a prefix to the bones unit of measurement of measurement. To tell how large or pocket-sized a unit is, y'all look at the prefix. To tell whether the unit is measuring length, mass, or volume, y'all 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 of operations unit

10 times larger than base of operations unit

base units

10 times smaller than base unit

100 times smaller than base unit

1,000 times smaller than base of operations unit

Using this table as a reference, you can see the following:

· A kilogram is ane,000 times larger than one gram (then 1 kilogram = 1,000 grams).

· A centimeter is 100 times smaller than one meter (so one meter = 100 centimeters).

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

Here is a similar table that merely shows the metric units of measurement for mass, along with their size relative to ane gram (the base of operations unit of measurement). The mutual abbreviations for these metric units have been included as well.

Measuring Mass in the Metric System

kilogram

(kg)

hectogram

(hg)

dekagram

(dag)

gram

(g)

decigram

(dg)

centigram

(cg)

milligram

(mg)

one,000 grams

100 grams

ten grams

gram

0.1 gram

0.01 gram

0.001 gram

Since the prefixes remain abiding through the metric system, y'all could create similar charts for length and volume. The prefixes have the same meanings whether they are attached to the units of length (meter), mass (gram), or volume (liter).

Which of the post-obit sets of three units are all metric measurements of length?

A) inch, foot, yard

B) kilometer, centimeter, millimeter

C) kilogram, gram, centigram

D) kilometer, human foot, decimeter

Show/Hibernate Answer

A) inch, foot, yard

Wrong. Although these units do measure out length, they are all units of measurement from the U.S. customary system. The right respond is kilometer, centimeter, millimeter.

B) kilometer, centimeter, millimeter

Correct. All of these measurements are from the metric arrangement. Yous tin tell they are measurements of length because they all contain the word "meter."

C) kilogram, gram, centigram

Incorrect. These measurements are from the metric system, but they are measurements of mass, non length. The correct answer is kilometer, centimeter, millimeter.

D) kilometer, human foot, decimeter

Incorrect. Kilometer and decimeter are metric units of length, but foot is not. The right reply is kilometer, centimeter, millimeter.

Converting Units Up and Down the Metric Calibration

Converting betwixt metric units of measure out requires knowledge of the metric prefixes and an understanding of the decimal system—that's well-nigh it.

For example, you lot tin effigy out how many centigrams are in ane dekagram by using the table higher up. Ane dekagram is larger than one centigram, and then you expect that one dekagram volition equal many centigrams.

In the tabular array, each unit is ten times larger than the 1 to its firsthand right. This ways that 1 dekagram = 10 grams; 10 grams = 100 decigrams; and 100 decigrams = ane,000 centigrams. So, 1 dekagram = 1,000 centigrams.

Case

Problem

How many milligrams are in one decigram?

kg	hg	dag	g	dg	cg	mg
				^		^

Identify locations of milligrams and decigrams.

Decigrams (dg) are larger than milligrams (mg), so you look there to be many mg in one dg.

				× ten		× 10
kg	hg	dag	g	dg	cg		mg
				^			^
				→ →

Dg is 10 times larger than a cg, and a cg is ten times larger than a mg.

Since you are going from a larger unit of measurement to a smaller unit, multiply.

1 dg · 10 · 10 = 100 mg

Multiply: ane · 10 · 10, to notice the number of milligrams in one decigram.

Reply

At that place are 100 milligrams (mg) in 1 decigram (dg).

Example

Problem

Convert 1 centimeter to kilometers.

km	hm	dam	m	dm	cm	mm
^					^

Identify locations of kilometers and centimeters.

Kilometers (km) are larger than centimeters (cm), so you expect there to be less than ane km in a cm.

÷10

÷ten

÷10

dam

← ← ← ← ←

Cm is x times smaller than a dm; a dm is ten times smaller than a one thousand, etc.

Since you are going from a smaller unit to a larger unit, split up.

1 cm ÷ x ÷ ten ÷ 10 ÷ 10 ÷ 10 = 0.00001 km

Divide: one ÷ 10 ÷ 10 ÷ 10 ÷ ten ÷ ten, to observe the number of kilometers in one centimeter.

Answer

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

One time you begin to understand the metric organisation, yous can employ a shortcut to catechumen amid unlike metric units. The size of metric units increases tenfold as you go up the metric calibration. The decimal system works the same way: a tenth is ten times larger than a hundredth; a hundredth is 10 times larger than a thousandth, etc. Past applying what yous know about decimals to the metric system, converting among units is as unproblematic as moving decimal points.

Hither is the start trouble from above: How many milligrams are in one decigram? You tin can recreate the order of the metric units every bit shown below:

This question asks you to start with 1 decigram and convert that to milligrams. As shown above, milligrams is two places to the right of decigrams. You lot can just motion the decimal point two places to the correct to convert decigrams to milligrams: .

The same method works when you are converting from a smaller to a larger unit of measurement, as in the trouble: Catechumen i centimeter to kilometers.

Note that instead of moving to the right, you are now moving to the left—so the decimal point must do the same: .

How many milliliters are in 1 liter?

A) 0.001

B) 0.1

C) 100

D) 1,000

Evidence/Hide Reply

A) 0.001

Incorrect. One liter is larger than one milliliter, and then you would look there to be more than than i milliliter in one liter. The correct respond is 1,000.

B) 0.1

Incorrect. One liter is larger than 1 milliliter, and so you lot would expect at that place to exist more one milliliter in 1 liter. The correct answer is 1,000.

C) 100

Incorrect. There are 100 milliliters in ane deciliter. The correct answer is ane,000.

D) 1,000

Correct. There are 10 milliliters in a centiliter, 10 centiliters in a deciliter, and 10 deciliters in a liter. Multiply: 10 · ten · 10, to find the number of milliliters in a liter, ane,000.

The metric system is an alternative system of measurement used in nearly countries, besides as in the United States. The metric system is based on joining one of a series of prefixes, including kilo-, hecto-, deka-, deci-, centi-, and milli-, with a base unit of measurement of measurement, such equally meter, liter, or gram. Units in the metric system are all related by a power of ten, which ways that each successive unit of measurement is 10 times larger than the previous 1. This makes converting ane metric measurement to some other a straightforward process, and is often as uncomplicated as moving a decimal point. Information technology is always important, though, to consider the direction of the conversion. If you are converting a smaller unit to a larger unit, so the decimal bespeak has to move to the left (making your number smaller); if you are converting a larger unit to a smaller unit, then the decimal point has to move to the right (making your number larger).