Question

How do you simplify \[64\div 0.2\]?

Answer 1

Hint: A rational number is a number that can be expressed as a fraction, for instance \[\dfrac{1}{2}\] or \[\dfrac{11}{39}\]. To divide a rational number with another rational number which is in decimal form, we have to make the denominator as an integer by multiplying with multiples of 10 to both the numerator and denominator. If both numerator and denominator are integers then we can perform simple division.

Complete step by step answer:
As per the given question, we have to simplify the given expression which is the division of two rational numbers. And, the given expression is \[64\div 0.2\].
We can also write \[64\div 0.2\] as \[\dfrac{64}{0.2}\]. Here, we have a decimal number in the denominator. So, in order to get rid of that we multiply both the numerator and denominator by 10. Thus, we can rewrite the expression as
\[\Rightarrow \dfrac{64\times 10}{0.2\times 10}\]
Here, multiplication of 64 with 10 is 640 and that of 0.2 with 10 is 2. Hence, by substituting these values into the above expression, we get
\[\Rightarrow \dfrac{640}{2}\]
As the denominator is 2, we can write 640 as \[2\times 320\]. Here, we can eliminate 2 from the numerator and denominator. Then, we get
\[\Rightarrow \dfrac{640}{2}=\dfrac{2\times 320}{2}=320\]

\[\therefore 320\] is the simplified form of \[64\div 0.2\].

Note: A common mistake made while solving this question is by considering 0.2 as 0 multiplied by 2. This leads to wrong calculations thus; we get the wrong solution. We can also solve this problem by taking 64 as \[2\times 32\] and 0.2 as \[2\times {{10}^{-1}}\]. When we divide \[2\times 32\] with \[2\times {{10}^{-1}}\], we get \[32\times {{10}^{1}}\] which is equal to 320. We should avoid calculation mistakes to get the correct answer.