Mathematics
How to convert units of Length, Area and Volume?
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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

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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

### 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 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 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

### 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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## 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