Question

How do you simplify\[\dfrac{2.82}{1.41}\]?

Answer 1

Hint: In the given question, we have been asked to solve\[\dfrac{2.82}{1.41}\]. In order to solve the given question, first we need to convert the decimals into fraction form and then evaluate further. A decimal converted into fraction form by observing the number of decimal places in a given number and putting that number to the power of 10. If there is a decimal number in the numerator then we check the decimal places and write 10 to that power in the denominator and vice-versa. In this way, we will simplify the given fraction.

Complete step-by-step solution:
We have given that,
\[\Rightarrow \dfrac{2.82}{1.41}\]
Converting the decimal number in the numerator into fraction form,
Therefore, in \[2.82\]there are two decimal places and hence we write 10 to the power 2 in the denominator.
\[\Rightarrow 2.82=\dfrac{282}{{{10}^{2}}}=\dfrac{282}{100}\]
Now,
In \[1.41\]there are two decimal places and hence we write 10 to the power 2 in the numerator as the number given is in the denominator.
\[\Rightarrow \dfrac{1}{1.41}=\dfrac{{{\left( 10 \right)}^{2}}}{141}=\dfrac{100}{141}\]
Combining both the fraction forms, we get
\[\Rightarrow \dfrac{2.82}{1.41}=\dfrac{282}{100}\times \dfrac{100}{141}\]
Simplifying the above, we get
\[\Rightarrow \dfrac{2.82}{1.41}=\dfrac{282}{141}\]
Converting the fraction into simplest form, we get
\[\Rightarrow \dfrac{282}{141}=2\]
Therefore,
\[\Rightarrow \dfrac{2.82}{1.41}=2\]
Hence, it is the required solution.

Note: Always count the number of decimal places that is the number of digits after the decimal for the conversion of decimal into fraction form. The number of digits that are in the decimal place is written to the power of 10 and then putting that in numerator and denominator according to the question and that number will be written as it is but without the decimal point.