Question

How do you simplify \[1.4\div 9.8\]?

Answer 1

Hint: A rational number is a number that can be expressed as a fraction, for instance \[\dfrac{1}{3}\]or \[\dfrac{9}{37}\] . 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 \[1.4\div 9.8\].
We can also write \[1.4\div 9.8\] as \[\dfrac{1.4}{9.8}\]. Here, we have a decimal number in both numerator and 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
\[\Rightarrow \dfrac{1.4\times 10}{9.8\times 10}\]
Here, multiplication of \[1.4\] with 10 is 14 and that of \[9.8\] with 10 is 98. Hence, by substituting these values into the above expression, we get
\[\Rightarrow \dfrac{14}{98}\].
As the denominator is 98, we can write 98 as \[7\times 14\]. Here, we can eliminate 14 from the numerator and denominator. Then, we get
\[\Rightarrow \dfrac{14}{98}=\dfrac{14}{7\times 14}=\dfrac{1}{7}\]
\[\therefore \dfrac{1}{7}\] is the simplified form of \[1.4\div 9.8\].
We can write \[\dfrac{1}{7}\] in decimal form that is \[0.143\].

\[\therefore 0.143\] is also a simplified form of \[1.4\div 9.8\].

Note: We can also solve this problem by taking \[1.4\] as \[14\times {{10}^{-1}}\] and \[9.8\] as \[98\times {{10}^{-1}}\]. When we divide \[14\times {{10}^{-1}}\] with \[98\times {{10}^{-1}}\], we get \[\dfrac{14}{98}\] which is equal to \[\dfrac{1}{7}\]. Converting decimals into their exponents avoids confusion. We should avoid calculation mistakes to get the correct answer.