Question

If $178\times 34=6052,$ then the value of $6.052\div 17.8$ is
$\left( a \right) 34$
$\left( b \right) 0.34$
$\left( c \right) 0.034$
$\left( d \right)$ None of these

Answer 1

Hint: We will write the decimal numbers as fraction in terms of the powers of ten. We know that the division of the factors can be changed to the multiplication by taking the reciprocal of the fraction which is the divisor. So, we will use this to find the quotient.

Complete step by step solution:
We are given with $178\times 34=6052.$
We are asked to find the value of $6.052\div 17.8.$
We know that $6.052$ is the dividend and $17.8$ is the divisor.
We need to write both the dividend and the divisor as fractions with denominator a power of ten.
We know that the denominator will contain $10$ to the power the number of digits after the decimal point.
We will get $6.052=\dfrac{6052}{1000}.$
And similarly, we will get $17.8=\dfrac{178}{10}.$
Now, we can write the quotient as $6.052\div 17.8=\dfrac{6052}{1000}\div \dfrac{178}{10}.$
We know that we need to take the reciprocal of the divisor when we need to find the quotient of two fractions. Then we can multiply the fractions.
We know that the reciprocal of the divisor is $\dfrac{10}{178}.$
Now we will change the operation to multiplication to get $6.052\div 17.8=\dfrac{6052}{1000}\times \dfrac{10}{178}.$
We know that $178\times 34=6052.$
Also, we know that $100\times 10=1000.$
Therefore, we will substitute for the numerator and the denominator of the first fraction.
Then, we will get $6.052\div 17.8=\dfrac{178\times 34}{100\times 10}\times \dfrac{10}{178}.$
We will cancel $178$ and $10$ form both fractions to get $6.052\div 17.8=\dfrac{34}{100}.$
Since the denominator contains $10$ to the second power, to write the fraction as a decimal number we need to count the digits of the numerator from the right and put the decimal point after two digits.
Then, we will get $6.052\div 17.8=0.34.$
Hence the answer is $6.052\div 17.8=0.34.$

So, the correct answer is “Option b”.

Note: Instead of taking the reciprocal of the divisor, we can directly write the quotient in the fraction form as $\dfrac{6.052}{17.8}.$ Since $178\times 34=6052,$ we will get $\dfrac{6052}{178}=34.$ Since the numerator has $3$ digits after the decimal point, we can write $0.034$ and since the denominator has a digit after the decimal point, the position of decimal point will be shifted to one position to the right and we will get $0.34.$