Explain Percentage Change Calculator

Introduction:
                  A percentage change is a way to express a change in a variable. It represents the relative change between the old value and the new one.
The formula used to calculate the percentage change is

Percentage change formula= `((V2 - V1) / (V1)) * 100` .

V_1- represents the old value

V_{2 -} the new one.                                                        

Example 1:
Chris bought 40 Compact disks last month.  He bought only 30 this year.  Calculate is the percent of change.
Solution:
Here,          V2 = new value =  35 Compact disks
                     V1 = old value = 40 Compact disks
Percentage of change =?
By plugging in the given values in to the formula we get
Percentage change =  `(35 -40) / (40)` * 100.
The difference between 35 and 40 is 5
By plugging in the given values in to the formula we get,
 = `5 / 40` * 100
The fraction 8/ 40 gives us  1/5.
`= 1/ 5 ` * 100.
= 20%
The percentage of change is 20 %

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Understanding Median Formula

Introduction:

                    The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first.

What is median:

Median (a): constituting the middle value of an ordered set of values is called median.
                     The set of values arranged in Lower value to higher value (increasing order).If the set of data has an odd number of entries, the median formula is the middle value of the set after sorting the list into increasing order.
                     If the set of data has an even number of means , the median is equal to the sum of the two middle value (after sorting) numbers  and divided by two.

The median is the middle value, so I'll have to rewrite the list in order:

13, 13, 13, 13, 14, 14, 16, 18, 21

There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number:

Formula for the Median,

                                     M=(n+1)/2

                                          here,

                                                  M - median,

                                                   n - total number of values present in the set.

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How to solve Proportions

Introduction:

A proportion means comparison or equality among two ratios. We can also say that it is used to compare two ratios or make an equivalent fraction. In proportions we have two groups, one is extreme and the other is mean. Extreme means the first and the last number and the mean is the second and the third number of a proportion of four parts.

Solving Proportions:

There are different ways of solving proportions
By doing equivalent fractions:
This works when the denominator and numerator of one fraction is multiple of the another one
By simplifying:
Numerator and denominator of one fraction is not a multiple of another one.
Cross multiplication:
It means multiplying the numerator of the first fraction to the denominator of the second fraction equals to the denominator of the first fraction to the numerator of the second fraction.
1.Solving proportions by finding equivalent fractions
`(4)/8=10/n`
so, to find the equivalent fractions we need to multiply and divide the numerator and the denominator by the same number. To solve this multiply the numerator by 8 to get 32 and the denominator by 5.
`(4xx8)/(8xx8)=10/n`
`(32)/64=10/n`
so, n=20

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Exponents Scientific Notation

Introduction:

                     The Scientific notation also known as standard form or as exponential notation. The scientific notation is a way of writing numbers that accommodates values too large or small to be expediently written in standard decimal notation.

                    The scientific or exponents notation has a number of useful properties, that often by mathematicians, engineering and scientists.

General Form of Scientific Notation:

The scientific notation are written by,
       A X 10^B (A times 10 to the power of B)
Here Exponents B is an integer and A is a coefficient that has a any real number called as the mantissa or significant. If the number is negative then put minus sign in ordinary decimal notation(A).
For Ex :         9 X 10 ³
Here 9 is a mantissa of significand and
3 is an Exponents.
Convert a number from normal form into scientific notation:
The main function of writing a number in scientific notation is to have a decimal number, with one digit to the left of the decimal point, followed by  A X 10 to Some power.
Step 1: First we divide the A by 10.B times making it A.
Step 2: Each division by 10 moves the decimal point to the left B digit.

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Arithmetic Progression

Introduction:

        It is a sequence of numbers in which each term except the first term can be calculated by adding constant number (common difference) to the immediately preceding number. Quantities are said to be in Arithmetic progression when they increase or decrease by a common difference.

The General form of the arithmetic sequence is,
     a, a+d, a+2d, a+3d………..
Here a is the first number and d is the common difference.
To find the nth term of an arithmetic progression we can use the following formula,
     a_n=a+ (n-1) d
Properties of Arithmetic Progression:

• When we add or subtract any constant number with all the terms of the sequence, the arithmetic sequence remains an arithmetic sequence.

     Example:
     5, 7, 9, 11, 13, 15, 17….. is an A.P with common difference 2.
     Add 3 with all the terms,
     8, 10, 12, 14, 16, 18, 20…. Is also an A.P with common difference 2.

• When we multiply or divide by a non-zero constant with all the terms of the sequence, the arithmetic progression sequence remains an arithmetic progression.

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