Question

How do you change 6.8% into a decimal and fraction?

Answer 1

Hint: This question is from the chapter of algebra. We have to convert the given number into decimal and fraction. First, we will change 6.8% into decimal. After changing into decimal we will change 6.8% into fraction. Before solving this question, let us know one thing that if a number is multiplied with the term %. Then, after removing that percentage symbol, we get the same number which is further divided by 100.

Complete step-by-step solution:
Let us solve this question.
In this question, we have to change the number 6.8% which is in percentage into a decimal number and fraction.
First, we will find the number or change 6.8% into decimal. After that, we will convert the same into fraction.
So, let us change 6.8% into a decimal.
For converting into decimal, we will first divide the number 6.8 by 100 after that we will write 68 in numerator and in denominator, we will write 10 multiplied by 100.
So, 6.8% can be written as \[6.8\%=\dfrac{6.8}{100}\] which can also be written as \[6.8\%=\dfrac{68}{100\times 10}\].
So, we can write \[6.8\%=\dfrac{68}{100\times 10}\] as \[6.8\%=\dfrac{68}{1000}\]
As we can see that in the fraction\[\dfrac{68}{1000}\], there is 1000 in the denominator which is a number 10 having power of 3. Therefore, in the decimal form we will write three numbers after decimal.
Hence, the term \[\dfrac{68}{1000}\] also can be written as 0.068.
Therefore, the term 6.8% can be written as decimal form is 0.068.
Now, we will convert 6.8% in fraction form.
As we have found that 6.8% can be written as\[\dfrac{68}{1000}\].
From here, we will find the prime factorization of 68 and 1000. After that, we will find the prime factors of them.
Prime factorization of 68:
\[\begin{align}
  & 2\left| \!{\underline {\,
  68 \,}} \right. \\
 & 2\left| \!{\underline {\,
  34 \,}} \right. \\
 & 17\left| \!{\underline {\,
  17 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}\]
Hence, prime factors of 68 will be
\[68=2\times 2\times 17\times 1\]
And prime factorization of 1000 is below:
\[\begin{align}
  & 2\left| \!{\underline {\,
  1000 \,}} \right. \\
 & 2\left| \!{\underline {\,
  500 \,}} \right. \\
 & 2\left| \!{\underline {\,
  250 \,}} \right. \\
 & 5\left| \!{\underline {\,
  125 \,}} \right. \\
 & 5\left| \!{\underline {\,
  25 \,}} \right. \\
 & 5\left| \!{\underline {\,
  5 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}\]
Hence, prime factors of 1000 will be:
\[1000=2\times 2\times 2\times 5\times 5\times 5\times 1\]
Hence,\[2\times 2\]will be cancelled out from the numerator and denominator. After that, we ill
Hence, we can write the fraction \[\dfrac{68}{1000}\] as
\[\dfrac{68}{1000}=\dfrac{17\times 1}{2\times 5\times 5\times 5\times 1}=\dfrac{17}{250}\]
Hence, the fractional form of 6.8% is \[\dfrac{17}{250}\].

Note: If we have solved this question and want to be sure that we are correct. Then, we have a method to check if we are correct.
As we have got that the fractional term is \[\dfrac{17}{250}\] and the decimal term is 0.068.
So, for cross checking, we will divide 17 by 250 and make that equal to 0.068.
As we know prime factors of 250 are 2, 5, 5, and 5. So, we will divide part by part.
\[\dfrac{17}{250}=\dfrac{17}{2\times 5\times 5\times 5}=\dfrac{17}{2}\times \dfrac{1}{5\times 5\times 5}=8.5\times \dfrac{1}{5\times 5\times 5}\]
Similarly, we will divide the numerator by all fives.
\[\Rightarrow \dfrac{17}{250}=\dfrac{8.5}{5\times 5\times 5}=\dfrac{8.5}{5}\times \dfrac{1}{5\times 5}=1.7\times \dfrac{1}{5\times 5}=\dfrac{1.7}{5}\times \dfrac{1}{5}=0.34\times \dfrac{1}{5}\]
Hence, we can write the above equation as
\[\Rightarrow \dfrac{17}{250}=0.34\times \dfrac{1}{5}=\dfrac{0.34}{5}=0.068\]
So, we have cross checked and we have got the same value.