Question

How do you convert $$245\mathrm{\%}$$ into fraction and decimal?

Answer 1

Hint: The concept percentage is just the quantity out of 100. For example 2% means 2 out of 100 and 2% marks of x means if the score is 2 out of 100 then what is the score out of x.
The answer is ${\displaystyle \frac{2}{100}}x$ . So n% of m means ${\displaystyle \frac{n}{100}}\times m$ and n% simply means ${\displaystyle \frac{n}{100}}$ . We can use it to solve the question.

Complete step by step answer:
We have to convert 245% into fraction and decimal
We know that n% of m means ${\displaystyle \frac{n}{100}}\times m$ and n% means ${\displaystyle \frac{n}{100}}$
So the value of 245% is ${\displaystyle \frac{245}{100}}$
245 and 100 have a common factor 5 so by reducing the fraction we get
${\displaystyle \frac{245}{100}}$ = ${\displaystyle \frac{49}{20}}$
Now we have convert ${\displaystyle \frac{245}{100}}$ into decimal number
To convert the fraction which has a denominator in the form of ${10}^n$ where n is an integer we can put the decimal sign after n digits from the right of numerator
For example ${\displaystyle \frac{abcde}{1000}}=ab.cde$ where a, b, c, d and e are digits
If numerator has less than n digits we can put more zeros in the left of numerator to increase the digits
For example we can write ${\displaystyle \frac{ab}{10000}}=0.00ab$ where a and b are digits.
So now we can write ${\displaystyle \frac{245}{100}}$ is equal to 2.45
So the fraction form of 245% is ${\displaystyle \frac{49}{20}}$ and decimal form of 245% is 2.45

Note:
The fraction which does not have denominator in the form of ${10}^n$ to decimal, we convert the fraction to decimal by division for example we have to convert ${\displaystyle \frac{40}{18}}$ into decimal
First we have to divide and write the quotient
In this case it is 2
Reminder is 4 which is less than 18
Now place a decimal sign after quotient and multiply the reminder with 10 and divide it by 18 and write quotient
In this case it will be 2.2
Note the remainder and multiply the reminder with 10 and divide it by 18 and write quotient
In this case it will be 2.22
Repeat the above process until you get the remainder 0. Sometimes it will be never be 0 in that case some number will repeat, in the above 2 will repeat infinite times after decimal point we can put a bar sign above repeated digits
${\displaystyle \frac{40}{18}}=2.\bar{2}$