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Learning Objectives

- be more familiar with some of the advantages of the base ten number system
- know the prefixes of the metric measures
- be familiar with the metric system of measurement
- be able to convert from one unit of measure in the metric system to another unit of measure

## The Advantages of the Base Ten Number System

The metric system of measurement takes advantage of our base ten number system. The advantage of the metric system over the United States system is that in the metric system it is possible to convert from one unit of measure to another simply by multiplying or dividing the given number by a power of 10. This means we can make a conversion simply by moving the decimal point to the right or the left.

## Prefixes

Common units of measure in the metric system are the meter (for length), the liter (for volume), and the gram (for mass). To each of the units can be attached a prefix. The **metric prefixes** along with their meaning are listed below.

**Metric Prefixes**

kilo: thousand

deci: tenth

hecto: hundred

centi: hundredth

deka: ten

milli: thousandth

For example, if length is being measured,

1 kilometer is equivalent to 1000 meters.

1 centimeter is equivalent to one hundredth of a meter.

1 millimeter is equivalent to one thousandth of a meter.

## Conversion from One Unit to Another Unit

Let's note three characteristics of the metric system that occur in the metric table of measurements.

- In each category, the prefixes are the same.
- We can move from a
*larger to a smaller*unit of measure by moving the decimal point to the*right*. - We can move from a
*smaller to a larger unit*of measure by moving the decimal point to the*left*.

The following table provides a summary of the relationship between the basic unit of measure (meter, gram, liter) and each prefix, and how many places the decimal point is moved and in what direction.

*kilo hecto deka unit deci centi milli*

Basic Unit to Prefix | Move the Decimal Point | |

unit to deka | 1 to 10 | 1 place to the left |

unit to hector | 1 to 100 | 2 places to the left |

unit to kilo | 1 to 1,000 | 3 places to the left |

unit to deci | 1 to 0.1 | 1 place to the right |

unit to centi | 1 to 0.01 | 2 places to the right |

unit to milli | 1 to 0.001 | 3 places to the right |

## Conversion Table

Listed below, in the unit conversion table, are some of the common metric units of measure.

Unit Conversion Table | ||

Length | \(\text{1 kilometer (km) = 1,000 meters } (m)\) | \(1,000 \times 1\text{m}\) |

\(\text{1 hectometer (hm) = 100 meters}\) | \(100 \times 1 \text{m}\) | |

\(\text{1 dekameter (dam) = 10 meters}\) | \(10 \times 1 \text{m}\) | |

\(\text{1 meter (m)}\) | \(1 \times 1 \text{m}\) | |

\(\text{1 decimeter (dm) = } \dfrac{1}{10} \text{ meter}\) | \(.1 \times 1 \text{m}\) | |

\(\text{1 centimeter (cm) = } \dfrac{1}{100} \text{ meter}\) | \(.01 \times 1 \text{m}\) | |

\(\text{1 millimeter (mm) = } \dfrac{1}{1,000} \text{ meter}\) | \(.001 \times 1 \text{m}\) | |

Mass | \(\text{1 kilogram (kg) = 1,000 grams } (g)\) | \(1,000 \times 1\text{g}\) |

\(\text{1 hectogram (hg) = 100 grams}\) | \(100 \times 1 \text{g}\) | |

\(\text{1 dekagram (dag) = 10 grams}\) | \(10 \times 1 \text{g}\) | |

\(\text{1 gram (g)}\) | \(1 \times 1 \text{g}\) | |

\(\text{1 decigram (dg) = } \dfrac{1}{10} \text{ gram}\) | \(.1 \times 1 \text{g}\) | |

\(\text{1 centigram (cg) = } \dfrac{1}{100} \text{ gram}\) | \(.01 \times 1 \text{g}\) | |

\(\text{1 milligram (mg) = } \dfrac{1}{1,000} \text{ gram}\) | \(.001 \times 1 \text{g}\) | |

Volume | \(\text{1 kiloliter (kL) = 1,000 liters } (L)\) | \(1,000 \times 1\text{L}\) |

\(\text{1 hectoliter (hL) = 100 liters}\) | \(100 \times 1 \text{L}\) | |

\(\text{1 dekaliter (daL) = 10 liters}\) | \(10 \times 1 \text{L}\) | |

\(\text{1 liter (L)}\) | \(1 \times 1 \text{L}\) | |

\(\text{1 deciliter (dL) = } \dfrac{1}{10} \text{ liter}\) | \(.1 \times 1 \text{L}\) | |

\(\text{1 centiliter (cL) = } \dfrac{1}{100} \text{ liter}\) | \(.01 \times 1 \text{L}\) | |

\(\text{1 milliliter (mL) = } \dfrac{1}{1,000} \text{ liter}\) | \(.001 \times 1 \text{L}\) | |

Time | Same as the United States system |

**Distinction Between Mass and ****Weight**

There is a distinction between mass and weight. The **weight** of a body is related to gravity whereas the mass of a body is not. For example, your weight on the earth is different than it is on the moon, but your mass is the same in both places. **Mass** is a measure of a body's resistance to motion. The more massive a body, the more resistant it is to motion. Also, more massive bodies weigh more than less massive bodies.

**Converting Metric ****Units**

To convert from one metric unit to another metric unit:

- Determine the location of the original number on the metric scale (pictured in each of the following examples).
- Move the decimal point of the original number in the same direction and same number of places as is necessary to move to the metric unit you wish to go to.

We can also convert from one metric unit to another using unit fractions. Both methods are shown in Sample Set A.

Sample Set A

Convert 3 kilograms to grams.

**Solution**

a. 3 kg can be written as 3.0 kg. Then,

Thus, \(\text{3 kg = 3,000 g}\).

b. We can also use unit fractions to make this conversion.

Since we are converting to grams, and \(\text{1,000 g = 1 kg}\). we choose the unit fraction \(\dfrac{\text{1,000 g}}{\text{1 kg}}\) since grams is in the numerator.

\(\begin{array} {rcl} {\text{3 kg}} & = & {\text{3 kg} \cdot \dfrac{\text{1,000 g}}{\text{1 kg}}} \\ {} & = & {3 \cancel{\text{kg}} \cdot \dfrac{\text{1,000 g}}{1 \cancel{\text{kg}}}} \\ {} & = & {3 \cdot 1,000 \text{ g}} \\ {} & = & {3,000 \text{ g}} \end{array}\)

Sample Set A

Convert 67.2 hectoliters to milliliters.

**Solution**

Thus, \(\text{67.2 hL = 6,720,000 mL}\).

Sample Set A

Convert 100.07 centimeters to meters.

**Solution**

Thus, \(\text{100.07 cm = 1.0007m}\).

Sample Set A

Convert 0.16 milligrams to grams.

**Solution**

Thus, \(\text{0.16 mg = 0.00016}\).

Practice Set A

Convert 411 kilograms to grams.

**Answer**-
411,000 g

Practice Set A

Convert 5.626 liters to centiliters.

**Answer**-
562.6 cL

Practice Set A

Convert 80 milliliters to kiloliters.

**Answer**-
0.00008 kL

Practice Set A

Convert 150 milligrams to centigrams.

**Answer**-
15 cg

Practice Set A

Convert 2.5 centimeters to meters.

**Answer**-
0.025 m

## Exercises

Make each conversion.

Exercise \(\PageIndex{1}\)

87 m to cm

**Answer**-
8,700 cm

Exercise \(\PageIndex{2}\)

905 L to mL

Exercise \(\PageIndex{3}\)

16,005 mg to g

**Answer**-
16.005 g

Exercise \(\PageIndex{4}\)

48.66 L to dL

Exercise \(\PageIndex{5}\)

11.161 kL to L

**Answer**-
11,161 L

(Video) Measure: The Metric System Explained | Science Trek

Exercise \(\PageIndex{6}\)

521.85 cm to mm

Exercise \(\PageIndex{7}\)

1.26 dag to dg

**Answer**-
126 dg

Exercise \(\PageIndex{8}\)

99.04 dam to cm

Exercise \(\PageIndex{9}\)

0.51 kL to daL

**Answer**-
5.1 daL

Exercise \(\PageIndex{10}\)

0.17 kL to daL

Exercise \(\PageIndex{11}\)

0.05 m to dm

**Answer**-
0.5 dm

Exercise \(\PageIndex{12}\)

0.001 km to mm

Exercise \(\PageIndex{13}\)

8.106 hg to cg

**Answer**-
81,060 cg

Exercise \(\PageIndex{14}\)

17.0186 kL to mL

Exercise \(\PageIndex{15}\)

3 cm to m

**Answer**-
0.03 m

Exercise \(\PageIndex{16}\)

9 mm to m

Exercise \(\PageIndex{17}\)

4 g to mg

**Answer**-
4,000 mg

Exercise \(\PageIndex{18}\)

2 L to kL

Exercise \(\PageIndex{19}\)

6 kg to mg

**Answer**-
6,000,000 mg

Exercise \(\PageIndex{20}\)

7 daL to mL

#### Exercises for Review

Exercise \(\PageIndex{21}\)

Find the value of \(\dfrac{5}{8} - \dfrac{1}{3} + \dfrac{3}{4}\)

**Answer**-
\(\dfrac{25}{24} = 1 \dfrac{1}{24}\)

Exercise \(\PageIndex{22}\)

Solve the proportion: \(\dfrac{9}{x} = \dfrac{27}{60}\).

Exercise \(\PageIndex{23}\)

Use the method of rounding to estimate the sum: \(8,226 + 4,118\).

**Answer**-
12,300 (12,344)

Exercise \(\PageIndex{24}\)

Use the clustering method to estimate the sum: \(87 + 121 + 118 + 91 + 92\).

Exercise \(\PageIndex{25}\)

Convert 3 in. to yd.

**Answer**-
\(0.08\overline{3}\) yard.

## FAQs

### 9.2: The Metric System of Measurement? ›

The metric system of measurement **takes advantage of our base ten number system**. The advantage of the metric system over the United States system is that in the metric system it is possible to convert from one unit of measure to another simply by multiplying or dividing the given number by a power of 10.

**What is the metric system of measurement? ›**

The metric system is a system of measurement that **uses the meter, liter, and gram as base units of length (distance), capacity (volume), and weight (mass) respectively**. To measure smaller or larger quantities, we use units derived from the metric units.

**What are the 3 metric systems? ›**

Metric system basics

The three most common base units in the metric system are the **meter, gram, and liter**.

**How big is 1 metric? ›**

A meter is equal to **100 centimeters**. Meters can be used to measure the length of a house, or the size of a playground.

**Is metric in cm? ›**

Meters are denoted by m, whereas **centimeters are denoted by cm**. Both units meter and centimeters are used in the International System of Units, and a centimeter is considered as the current form of the metric system.

**Why is metric measurement? ›**

The metric system is a consistent and coherent system of units. In other words, **it fits together very well and calculations are easy because it is decimal**. This is a big advantage for use in the home, education, industry and science.

**Where is the metric system? ›**

Today, the metric system, which was created in **France**, is the official system of measurement for every country in the world except three: the United States, Liberia and Myanmar, also known as Burma. And even then, the metric system is still used for purposes such as global trade.

**What are all the metric types? ›**

**Below are the five types of metrics, along with the types of the inputs they take.**

- Class metrics (hard predictions) truth - factor. estimate - factor.
- Class probability metrics (soft predictions) truth - factor. ...
- Numeric metrics. truth - numeric. ...
- Static survival metircs. truth - Surv. ...
- dynamic survival metrics. turth - Surv.

**Is metric in inches? ›**

Standards for the exact length of an inch have varied in the past, but since the adoption of the international yard during the 1950s and 1960s **the inch has been based on the metric system and defined as exactly 25.4 mm**.

**How much is a metric? ›**

The metric ton used in most other countries is **1,000 kg**, equivalent to 2,204.6 pounds avoirdupois.

### How many feet is 10 metric? ›

For example, we know that 10 meters to feet is **32.8083 ft**.

**What is 100 meters called? ›**

**1 hectometer** (hm) = 100 m.

**What is metric table? ›**

The Metric Table **allows you to collect various metrics used to evaluate the current state of your model**. A Metric is an item of information about a specific aspect of the model.

**What metric is in ruler? ›**

The numbers on the ruler represent **centimeters (cm)**. There are 10 millimeters for each centimeter.

**Why is America not metric? ›**

The biggest reasons the U.S. hasn't adopted the metric system are simply **time and money**. When the Industrial Revolution began in the country, expensive manufacturing plants became a main source of American jobs and consumer products.

**Does America use the metric system? ›**

**The U.S. is one of the few countries globally which still uses the Imperial system of measurement**, where things are measured in feet, inches, pounds, ounces, etc.

**Do we use the metric? ›**

A metric system was first proposed in France in 1670. France adopted the metric standard in 1840 and many countries followed. Today, **the only developed nations which do not use the SI metric system are the United States, Liberia and Burma.**

**Which metric is bigger? ›**

The metric system also applies the idea that units within the system get larger or smaller by a power of 10. This means that **a meter is 100 times larger than a centimeter**, and a kilogram is 1,000 times heavier than a gram.

**What comes after cm? ›**

In the metric system of measurement, the most common units of distance are **millimeters**, centimeters, meters, and kilometers.

**Who invented the metric system? ›**

**The French** are widely credited with originating the metric system of measurement. The French government officially adopted the system in 1795, but only after more than a century of sometimes contentious bickering over its value and suspicion surrounding the intent of metric proponents.

### Is the metric system English? ›

Units in the English system are historical units of measurement used in medieval England which evolved from the Anglo-Saxon and Roman systems. **The metric system is a decimalized system of measurement developed in France in late 18th century**.

**Why the US uses the metric system? ›**

The effort toward national metrication is based on the premise that **the U.S. industrial and commercial productivity, mathematics and science education, and the competitiveness of its products and services in world markets would be enhanced** by adopting the metric system.

**What is metric system based on? ›**

metric system, international decimal system of weights and measures, based on **the metre for length and the kilogram for mass**, that was adopted in France in 1795 and is now used officially in almost all countries.

**How easy is the metric system? ›**

With the metric system, **it's quick and easy to convert one unit to another by multiplying or dividing by powers of ten**. Ten millimeters is one centimeter, and 10 centimeters equals one decimeter. In contrast, there isn't a straightforward to convert imperial units.

**What is the metric unit of volume? ›**

The SI unit of volume is the **cubic meter** (m^{3}), which is a derived unit. Liter (L) is a special name for the cubic decimeter (dm^{3}).

**What are metric examples? ›**

Key financial statement metrics include **sales, earnings before interest and tax (EBIT), net income, earnings per share, margins, efficiency ratios, liquidity ratios, leverage ratios, and rates of return**. Each of these metrics provides a different insight into the operational efficiency of a company.

**What are the metric symbols? ›**

prefix | symbol | decimal number |
---|---|---|

kilo | k | 1,000 |

mega | M | 1,000,000 |

giga | G | 1,000,000,000 |

tera | T | 1,000,000,000,000 |

**What is a process metric? ›**

Process metrics **define quantitative and qualitative measures related to a process, its performance and its evolution**. Process metrics are relevant to a process entity (i.e., activity, role, artifact, condition, asset) or combination of entities.

**What size is a mm? ›**

A millimeter is **one thousandth of a meter**. There are 25 millimeters in an inch.

**How big is 9 mm? ›**

9mm = **almost 3/8 inch**. 10mm = just over 3/8 inch. 11mm = almost 7/16 inch.

### How wide is a cm? ›

What size is a centimeter? A centimeter is a metric unit used to measure length. 1 centimeter is equal to **10 millimeters or 0.01 meter**. A cheerio is typically the size of 1 cm in diameter.

**What is metric to English? ›**

Metric to English | English to Metric |
---|---|

1 meter (m) | = 3.2808 feet |

= 1.09361 yards | |

1 sq. meter (m/to 2nd power) | = 10.7639 sq. feet |

= 1.196 sq. yards |

**How big is a 10mm? ›**

MM | Approximate Size In Inches | Exact Size In Inches |
---|---|---|

10mm | Little over 3/8 Inch | 0.39370 Inches |

11mm | 7/16 Inch | 0.43307 Inches |

12mm | Just short of 1/2 Inch | 0.47244 Inches |

13mm | Little over 1/2 Inch | 0.51181 Inches |

**What is 10 metric in inches? ›**

**What does 1 meter mean? ›**

A meter is **a standard metric unit equal to about 3 feet 3 inches**. This means that a meter is part of the metric system of measurement. Guitars, baseball bats, and yard sticks are examples of objects that are about one meter long. Meters are also used to measure distances in races, such as running and swimming.

**What is bigger than a mile? ›**

Kilometer | Mile |
---|---|

Yards | |

1 km = 3,280.84 ft | 1 mile = 5,280 ft |

Meters | |

1 km = 1,000 m | 1 mile = 1609.344 m |

**What is 1 cm equal to in mm? ›**

Answer: **10 millimeters** is equal to 1 centimeter.

**Which is longer km or miles? ›**

1.609 kilometers equal 1 mile. The kilometer is a unit of measurement, as is the mille. However, **a mile is longer than a kilometer**. "Mile" is a bigger unit.

**What is 10 meters called? ›**

**Is a metric in math? ›**

In mathematics, **a metric space is a set together with a notion of distance between its elements, usually called points**. The distance is measured by a function called a metric or distance function. Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry.

### What is the function of meter stick? ›

A meterstick, metrestick, or yardstick is either a straightedge or foldable ruler used **to measure length**, and is especially common in the construction industry. They are often made of wood or plastic, and often have metal or plastic joints so that they can be folded together.

**What's less than a pound? ›**

Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. **An ounce** is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit.

**What are the 4 metric measurements? ›**

In the metric system of measurement, the most common units of distance are **millimeters, centimeters, meters, and kilometers**.

**What is metric vs imperial? ›**

The metric system is decimal because it is always based on powers of 10. The Imperial system is based on the inch / foot / yard / mile (length), the ounce / pound / stone / hundredweight (weight / mass) and the fluid ounce / pint / quart / gallon (volume).

**Who uses metric system? ›**

The metric system is the most used measurement system in the world. Only three countries in the world don't use the metric system: the United States, Liberia, and Myanmar. **Every other country around the world** uses the metric system.

**What is America's metric system called? ›**

(Technically, the American system known as Imperial is called **United States customary units** or USCS.)

**Why is the US metric system different? ›**

The biggest reasons the U.S. hasn't adopted the metric system are simply **time and money**. When the Industrial Revolution began in the country, expensive manufacturing plants became a main source of American jobs and consumer products.

**Who made the metric system? ›**

**The French** are widely credited with originating the metric system of measurement. The French government officially adopted the system in 1795, but only after more than a century of sometimes contentious bickering over its value and suspicion surrounding the intent of metric proponents.

**Is the metric system used everywhere? ›**

It is often stated that only three countries in the world—the United States, Liberia, and Myanmar—do not use the metric system. However, this belief is incorrect. In truth, **every country in the world uses the metric system to some extent**.

**Who uses imperial system? ›**

Only three countries – **the U.S., Liberia and Myanmar** – still (mostly or officially) stick to the imperial system, which uses distances, weight, height or area measurements that can ultimately be traced back to body parts or everyday items.

### What is the use of English system? ›

The English system of measures is **a collection of measures for length, volume, weight, area, etc**. that have their roots in hundreds of years of history. They were standardized somewhat by the British Weights and Measures Act of 1824, which defined the Imperial Units to be used throughout the British Empire.

**Why is the metric system used in science? ›**

Scientists all over the world use the metric system. There's a very good reason for this—**it's so everyone is doing the measuring the same way, all over the world**. Most other countries already use the metric system for measuring everything.

**What is metric vs standard? ›**

Depending on the context, “standard” often refers to U.S. fasteners. This typically means we're talking about measuring units in inches, whereas metric is exactly that: **measurements based on metric units, such as millimeters**. Keep in mind, however, the U.S. is now producing fasteners using the metric system.

**Why is the imperial system? ›**

Imperial units are **more useful in day-to-day life**. The metric system may be more useful in scientific areas but those who make scientific measurements on a daily basis already know the metric system as a second nature. Contrary to popular opinion, America is very far from being the only nation to use imperial units.