Mathematics

How to convert units of Length, Area and Volume?

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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

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How to convert units of Length, Area and Volume?

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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, Area and Volume :


Length

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

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

m to da m

1 meter = 0.1 da meter

da m to m

1 decameter = 10 meter

 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:

    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

   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

   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

   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

   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

10

10 × 0.621 = 3.210

40

40 × 0.621 = 24.84

200

200 × 0.621 = 124.2

500

500 × 0.621 = 310.5


Area

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

m2 to dm2

1 meter = 10 decimeter

1 m2= 10 × 10 = 100 dm2

m2 to cm2

1 meter = 10 centimeter

1 m2= 100 × 100 = 10000 cm2

m2 to mm2

1 meter = 10 mm

1 m2= 1000 × 1000 = 1000000 mm2

m2 to da m2

1 meter = 0.1 decameter

1 m2= 0.1 × 0.1 = 0.01 da m2

m2 to hm2

1 meter = 0.01 hectameter

1 m2= 0.01 × 0.01 = 0.0001 hm2

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

dm2  to m2

1 dm= 0.1 m

1 dm2= 0.1 × 0.1 = 0.01 m2

cm2  to m2

1 cm= 0.01 m

1 cm2= 0.01 × 0.01 = 0.0001 m2

mm2 to m2

1 cm= 0.001 mm

1 mm2= 0.001 × 0.001 = 1 × 10 -6m2

da m2  to m2

1 da m= 10 m

1 da m2= 10 × 10 = 100 m2

hm2  to m2

1 hm= 100 m

1 hm2= 100 × 100 = 10000 m2

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

10,000

10,000 ÷ 43560 = 0.2295

 

Acres

Square feet

10

10 × 43560 = 435600

50

50 × 43560 = 2178000


Volume

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 " mm(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

Volume is a three dimensional measurement

Conversion Table For Measurement Of Volume In Terms Of Meter

m3 to dm3

1 meter = 10 dmeter

1 m3  =10 × 10 × 10 = 1000 dm3

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

m3 to mm3

1 meter = 100 milli meter

1 m3= 1000 × 1000 × 1000 = 1 × 109 mm3

m3 to da m3

1 meter = 0.1 deca meter

1 m3= 0. 1× 0.1 × 0.1 = 0.001 da m3

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

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

hm3  to m3

1 hm= 100 m

1 hm3= 100 × 100 × 100 = 1 × 106m3

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


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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


External References

To know more about conversions, please visit this blog:

Converting units for area and volume - Measures - KS3 Maths


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