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# Unit Conversion

The unit is known as definite magnitude of a physical quantity. The physical quantities can be measured by using various units depending upon the quantities. For example the weight of the rice, sugar, wheat etc. can be calculated by using kilogram, gram, tons etc. A set of fundamental units is a set of units of measurement for physical quantities from which every other unit can be generated.
A system of weights and measures based on the principle that each and every quantity should have one unit whose multiples and sub multiples are all derived by multiplying or dividing by powers of ten. The standard unit is also called as metric system. In this section we will learn more about different units and its conversions.

## Volume Unit Conversion

In Volume we normally use liter to represent as the standard unit, and the other standard units are

In Volume we normally use liter to represent as the standard unit, and the other standard units are
1 milliliter = 0.001 liter
1 centiliter = 0.01 liter
1 deciliter = 0.1 liter
1 decaliter = 10 liters
1 hectoliter = 100 liters
1 kiloliter = 1000 liters
1 cubic inch = 1.639×10-2 liters
1 gallon = 3.785 liters
1 cubic foot = 28.316 liters

## Length Unit Conversion

In length, we normally use meter to represent as the standard unit, which is abbreviated as $m$. The other standard units are

1 millimeter = $0.001$ meter

1 centimeter = $0.01$ meter

1 decimeter = $0.1$ meter

1 decameter = $10$ meters

1 hectometer = $100$ meters

1 kilometer = $1000$ meters

1 inch = $2.54 \times 10^{-2}$ meters

1 foot = $0.3048$ meters

1 angstrom = $1 \times 10^{-10}$ meters

1 fermi = $1 \times 10^{-15}$ meters

1 light year = $0.946 \times 10^{16}$ meters

1 mile = $1.609344$ km

## Mass Unit Conversion

In Mass, we normally use gram to represent as the standard unit, and the other standard units are

1 milligram = $0.001$ gram

1 centigram = $0.01$ gram

1 decigram = $0.1$ gram

1 decagram = $10$ grams

1 hectogram = $100$ grams

1 kilogram = $1000$ grams

1 stone = $6350.29$ grams

1 pound = $453.592$ grams

1 ounce =  $28.3495$ grams

## Time Unit Conversion

The standard units in time are

1 minute = $60$ seconds

1 hour = $60$ minutes = $3600$ seconds

1 day = $24$ hours

1 week = $7$ days

1 year = $365 \frac{1}{4}$ days (for the Earth to travel once around the sun)

## Energy Unit Conversion

The basic units in which the energy measured is joule (J). The other units of energy are given below

1 BTU (British thermal unit) = $1055$ Joule

1 erg = $1 \times 10^{-7}$ Joule

1 foot pound = $1.356$ Joule

1 calorie = $4.186$ Joule

1 kilowatt hour = $3.6 \times 10^{6}$ Joule

1 electron volt = $1.602 \times 10^{-19}$ Joule

1 liter atmosphere = $101.13$ Joule

## Area Unit Conversion

The basic units in which the area measured is square meter ($m^{2}$). The other units of area are given below

1 sq. inch = $6.4516 \times 10^{-4}$  square meter

1 sq. Foot = $9.2903 \times 10^{-2}$  square meter

1 acre = $4.0468 \times 10^{3}$ square meter

1 hectare = $1 \times 10^{4}$ square meter

1 sq. mile = $2.5888 \times 10^{6}$ square meter

1 barn =  $1 \times 10^{-28}$ square meter

## Power Unit Conversion

The basic units in which the area measured is watt ($W$). The other units of pressure are given below

1 erg/sec = $1 \times 10^{-5}$ watt

1 BTU/hr = $0.2930$ watt

1 foot pound/sec = $1.356$ watt

1 horsepower = $745.7$ watt

1 calorie/sec = $4.186$ watt

## Force Unit Conversion

The basic units in which the force measured is Newton ($N$). The other units of force are given below

1 dyne = $1 \times 10^{-5}$ Newton

1 pound = $4.448$ Newton

## Density Unit Conversion

The basic units in which the density measured is kilogram/cube meter (kg/$m^{3}$). The other units of density are given below

1 slug/cu ft = $515.4$ kilogram/cube meter

1 pound / cu in = $2.768 \times 10^{4}$ kilogram/cube meter

## Viscosity Unit Conversion

In viscosity we normally use kg/m.s to represent as the standard unit, and the other standard units are

1 poise = $0.1$  kg/m.s

1 slug/ft . S = $4.79 \times 10^{1}$ kg/m.s

## Unit Conversion Problems

The following are the unit conversion problems.

### Solved Examples

Question 1: Convert the travelling distance in terms of meter, the distance traveled by the girl is 4 miles and 3 km.
Solution:
Given, girl travels 4 miles and 3 km.

We know that,

1 mile = $1.609344$ km

4 miles = $4 \times 1.609344$ km

= $6.437376$ km

Total travel distance = $6.437376$ km + $3$ km

= $9.437376$ km

We know that 1 km = $1000$ m

$9.437376$ km = $9.437376 \times 1000$ m

= $9437.376$ km

Question 2: Convert $5$ kilograms into grams.
Solution:
We knew that $1$ kg = $1000$ grams

We need to find $5$ kilogram into grams.

Multiply $5$ with $1000$ = $5000$ grams.

Therefore, $5$ kilograms = $5000$ grams

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