Table of Contents
| 1. | Introduction |
| 2. | Metric System |
| 3. | Unit Conversion for Length |
| 4. | Unit Conversion for Area |
| 5. | Unit Conversion for Volume |
| 6. | Summary |
| 7. | About Cuemath |
| 8. | FAQs |
| 9. | External References |
07 October 2020
Reading time: 5 minutes
Introduction
In olden days, unscientific methods were used for measurement by keeping objects next to each other for comparing their length and pouring liquids and weighing in the hand to know which is heavier. In 1799, the French government introduced the decimal system of measurement and later the International system of measurement was introduced in 1939.
Measurements are used in data and statics calculations and in geometry where the different types of geometrical figures can be classified
Also read:
- Speed, Acceleration, and Time Unit Conversions
- Weight, Mass and Density Conversion
Downloadable PDF
If you ever want to read it again as many times as you want, here is a downloadable PDF to explore more.
| 📥 |
How to convert units of Length, Area and Volume? |
Metric System
It is a system of measurement derived from a decimal system of measurement. The basic units in this system are meter grams and litre for measuring length ,volume and Capacity respectively.
Difference between Metric system and Imperial system of measurement
|
Metric system |
Imperial system |
|
In metric system the basic unit of measurements are meter,grams and litre |
In metric system the basic unit of measurements are feet,pounds and inches |
|
It is a simple system where conversion from smaller and bigger units are easy |
Conversion of smaller and bigger units are complex |
|
It is used in all Europe countries and India |
It is used by british countries |
Length, Area, and Volume
They are the one, two and three-dimensional measurements of geometrical figures. The prefixes used are kilo, hecto, deka, deci, centi and milli. The base unit remains same for length, Area and Volume which is "meters "
Length
Length Unit Converter
It is a one dimensional scalar quantity used to measure a line segment. The basic unit of measuring length in the International system of units is "METER". Further, according to the length of the specimen units like millimeter, centimeter, decimeter, dekameter, hecto meter and kilometer are respectively used.
|
Bigger units |
BASE UNIT |
Smaller units |
||||
|---|---|---|---|---|---|---|
|
Kilo(k) |
Hecto (H) |
Deka(D) |
METER(m) |
Deci(d) |
Centi(c) |
Milli (m) |
|
1000 |
100 |
10 |
1 |
1/10 |
1/100 |
1/1000 |
|
Multiply by 10 \(\Rightarrow\) |
\(\Leftarrow\) Divide by 10 |
|||||
The above table gives the information about the basic unit 'METER' and its prefixes and how they are converted to smaller and larger units depending on the measurement of specimen to be measured
The rule of conversion is " multiplication is done for converting higher units to smaller units ,similarly when converting smaller units to higher units division is carried out "
Conversion Table For Measurement Of Length
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m to dm 1 meter = 10 dm |
Dm to m 1 deci meter = 0.1 meters |
|
m to cm 1 meter = 100 centimeter |
cm to m 1 centimeter = 0.01meter |
|
m to mm 1 meter = 1000 millimeter |
mm to m 1 millimeter = 0.001 meter |
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m to da m 1 meter = 0.1 da meter |
da m to m 1 decameter = 10 meter |
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m to hm 1 meter = 0.01 hecta meter |
hm to m 1 hecta meter = 100 meter |
|
m to km 1 meter = 0.001 kilometers |
Km to m 1 kilometer = 1000 meter |
| Example |
Convert the following:
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5 meter = _____deci meter 1 meter = 10 deci meter 5 meter = 5 × 10 = 50 decimeter |
45 deci meter = ___ m 1 deci meter = 0.1 m 45 deci meter = 45 × 0.1 = 4.5 m |
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10 m= _____cm 1 meter = 100 centimeter 10 meter = 10 × 100 = 1000 cm |
500 cm = ______ m 1 centimeter = 0.01 meter 500 cm = 500 × 0.01 = 5 m |
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16 m= _____mm 1 meter = 1000 milli meter 16 meter = 16 × 1000 = 16000 mm |
68 millimeter = _____m 1 millimeter = 0.001 meter 68 millimeter = 68 × 0.001 = 0.068 m |
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20 m= _____decka meter 1 meter = 0.1 decka meter 20 meter = 20 × 0.1 = 2 decameter |
35 decameter = ___ meter 1 decameter = 10 meter 35 deca meter = 35 × 10 = 350 m |
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35 m= _____hecta meter 1 meter = 0.01 hecta meter 35 meter = 35 × 0.01 = 0.35 hecta meter |
70 hecta meter = ___ meter 1 hecta meter = 100 meter 70 hecta meter = 70 × 100 = 7000 m |
|
50 m= _____kilo meter 1 meter = 0.001 kilo meter 50 meter = 50 × 0.001 = 0.05 kilometer |
500 kilometer = ____m 1 kilometer = 1000 m 500 kilometer = 500 × 1000 = 5, 00, 000 m |
Km to mile
1 km = 0.621 mile
mile to Km
1 mile = 1.609 km
|
Kilometer |
Miles |
|---|---|
|
5 |
5 × 0.621 = 3.105 |
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10 |
10 × 0.621 = 3.210 |
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40 |
40 × 0.621 = 24.84 |
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200 |
200 × 0.621 = 124.2 |
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500 |
500 × 0.621 = 310.5 |
Area
Area Unit Converter
It is a scalar quantity, which is used to measure the quantity of two dimensional geometric plane figures where length and breadth is taken into consideration.Since area is the two-dimensional plane, the basic unit used to measure is \(" mm^2" (Length \times Length)\). Depending on the size of the plane surface the measurement can as follows,
|
Bigger units |
BASE UNIT |
Smaller units |
|||||
|---|---|---|---|---|---|---|---|
|
kilo |
hecta |
deca |
meter |
deci |
centi |
milli |
|
| km2 | ham2 | dam2 | m2 | dm2 | cm2 | mm2 | |
|
1000 |
100 |
10 |
1 |
1/10 |
1/100 |
1/1000 |
|
|
Multiply by 10 \(\Rightarrow\) |
\(\Leftarrow\) Divide by 10 |
||||||
Conversion Table For Measurement Of Area
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m2 to dm2 1 meter = 10 decimeter 1 m2= 10 × 10 = 100 dm2 |
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m2 to cm2 1 meter = 10 centimeter 1 m2= 100 × 100 = 10000 cm2 |
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m2 to mm2 1 meter = 10 mm 1 m2= 1000 × 1000 = 1000000 mm2 |
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m2 to da m2 1 meter = 0.1 decameter 1 m2= 0.1 × 0.1 = 0.01 da m2 |
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m2 to hm2 1 meter = 0.01 hectameter 1 m2= 0.01 × 0.01 = 0.0001 hm2 |
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m2 to km2 1 meter = 0.01 kilometer 1 m2= 0.001 × 0.001 = 1 × 10 -6kilo m2 After multiplying the decimal, after point we get 6 numbers, so to convert it into simple form above answer can be written |
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dm2 to m2 1 dm= 0.1 m 1 dm2= 0.1 × 0.1 = 0.01 m2 |
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cm2 to m2 1 cm= 0.01 m 1 cm2= 0.01 × 0.01 = 0.0001 m2 |
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mm2 to m2 1 cm= 0.001 mm 1 mm2= 0.001 × 0.001 = 1 × 10 -6m2 |
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da m2 to m2 1 da m= 10 m 1 da m2= 10 × 10 = 100 m2 |
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hm2 to m2 1 hm= 100 m 1 hm2= 100 × 100 = 10000 m2 |
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km2 to m2 1 km= 100 m 1 km2= 1000 × 1000 = 1000000 m2 |
| Example |
Convert the following:
Acre is an imperial system of measuring a land whereas feet is a metric system of measurement.
Acre to square feet
1 acre = 43560 square feet.
Square feet to acre
1 square feet = 2.296 × 10-5 acre
|
Square feet |
Acres |
|
5000 |
5000 ÷ 43560 = 0.1147 |
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10,000 |
10,000 ÷ 43560 = 0.2295 |
|
Acres |
Square feet |
|
10 |
10 × 43560 = 435600 |
|
50 |
50 × 43560 = 2178000 |
Volume
Volume is a three dimensional measurement where length ,breadth and height of the geometrical solid figure are taken for the consideration .The unit used is " mm3 (length breadth height)”.The below table gives the conversion of smaller and bigger units.
Volume Unit Converter
|
Bigger units |
BASE UNIT |
Smaller units |
||||
|
kilo |
hecta |
deca |
meter |
deci |
centi |
milli |
| km3 | ham3 | dam3 | m3 | dm2 | cm3 | mm3 |
|
1000 |
100 |
10 |
1 |
1/10 |
1/100 |
1/1000 |
|
Multiply by 10 \(\Rightarrow\) |
\(\Leftarrow\) Divide by 10 |
|||||
Conversion Table For Measurement Of Volume In Terms Of Meter
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m3 to dm3 1 meter = 10 dmeter 1 m3 =10 × 10 × 10 = 1000 dm3 |
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m3 to cm3 1 meter = 10 cm 1m3 = 100 × 100 × 100 = We have 6 zeros after 1, the simplied answer will be 1m3 = 1 × 106cm3 |
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m3 to mm3 1 meter = 100 milli meter 1 m3= 1000 × 1000 × 1000 = 1 × 109 mm3 |
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m3 to da m3 1 meter = 0.1 deca meter 1 m3= 0. 1× 0.1 × 0.1 = 0.001 da m3 |
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m3 to hm3 1 meter = 0.01 hecta meter 1 m3= 0.01 × 0.01 × 0.01 = 1 × 10-6hm3 After multiplying the decimal, after point we get 6 numbers, so to convert it into simple form above answer can be written |
|
m3 to km3 1 meter = 0.01 kilo meter 1 m3= 0.001 × 0.001 × 0.001 = 1 × 10-9 km3 |
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dm3 to m3 1 dm= 0.1 m 1 dm3= 0. 1× 0.1 × 0.1 = 0.001 m3 |
|
cm3 to m3 1 cm= 0.01 m 1 cm3= 0.01 × 0.01 × 0.01 = 1 × 10-6 m3 |
|
mm3 to m3 1 cm= 0.001 mm 1mm3= 0.001 × 0.001 × 0.001 = 1 × 10-9 m3 After multiplying the decimal, after point we get 9 numbers, so to convert it into simple form above answer can be written |
|
da m3 to m3 1 da m= 10 m 1 da m3= 10 × 10 × 10 = 1000 m3 |
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hm3 to m3 1 hm= 100 m 1 hm3= 100 × 100 × 100 = 1 × 106m3 |
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km3 to m3 1 km= 100 m 1 km3= 1000 × 1000 × 1000 We have 9 zeros after 1, the simplied answer will be = 1 × 109 m3 |
| Examples |
Convert the following :
1. litre to m3
Answer : \(1 \rm{m}^3= 1000 \text{ litres}\) \(1 \text{litre} = \frac{1}{1000}\rm{m}^3\)
|
\(1 \text{ litre} = 0.001 \text{ m}^3\) |
2. m3 to cm3
Answer :
\(\begin{align}1 \text{m}^3&= 100 × 100 × 100 \text{ cm}^3\\1 \text{m}^3 &= 10,00,000 \text{ cm}^3\end{align}\)
we have 6 zeros after one so in the simplest form, it can be written as
|
\(1 \text{m}^3 = 1 \times 106 \text{ cm}^3\) |
3. cubic feet to \(\text{m}^3 \)
Answer :
1 feet \(= 0.305 \text{ m}\)
1 cubic feet \(=0.305 × 0.305 × 0.305 \text{m}^3\)
|
1 cubic feet\(= 0.0284 \text{m}^3\) |
4. km3 to mile3
Answer :
\(1 \text{ km} = 0.621\) mile
\(= 0.621 \times 0.621 \times 0.621\)
|
1 km3= 0.239 mile3 |
mile3 to km3
Answer : 1 mile \(= 1/ 0.621 \text{ km}\)
\(1 \text{ mile}^3 = (\frac{1}{0.621}) \times (\frac{1}{0.621}) \times (\frac{1}{ 0.621}) \text{ km}^3\)
|
\(1 \text{ mile}^3 = 0.0414 \text{ km}^3\) |
Summary
According to the international system of measurement "METER" is the unit used for measuring length anywhere in the world and it is known as the base unit. Length, Area and Volume uses meter as the base unit, depending on the size of the object to be measured prefixes like kilo, hecta, deka, deci, centi and milli are used.
When converting larger prefixes kilo, hecta and deka to smaller prefixes deci, centi and milli multiplication with 10 is carried respectively and for converting smaller prefix to higher prefix division by 10 are done.
Written by Nethravathi C, Cuemath Teacher
About Cuemath
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Frequently Asked Questions (FAQs)
What is the metric system?
It derived from a decimal system of measurement where the basic units like meter, grams and litre are used for measuring length ,volume and capacity
What is the imperial system?
It is a used in British countries, the basic units feet, inches and pounds are used for measuring length ,volume and capacity
What are the metric system prefixes?
Metric system of prefixes are kilo(1000),deca(100),hecta(10),deci(1/10),centi(1/100) and milli(1/1000)
How to convert cm to m?
To convert from centimeters to meters, simply divide the number of centimeters by 100 and change the units to m