Question

How do you find the quotient of \[5.8\] divided by $30.8$?

Answer 1

Hint: Quotient is the number that we get by dividing one number by another number. A quotient is related to both the given numbers by,
$Dividend = (Quotient \times Divisor) + Remainder$
When we divide two decimal numbers we don’t get any remainder, i.e. for decimal numbers we have,
$Dividend = Quotient \times Divisor$
For dividing two decimal numbers we first try to get rid of the decimal by multiplying by $10$ and then we divide the numbers or fractions that we get.

Complete step-by-step solution:
We have to divide the number \[4\] by another number $38$, i.e. we have to evaluate $4 \div 38$.
We observe that we are given two whole numbers to divide where the dividend is less than the divisor. In case where dividend is less than divisor we get the quotient as $0$ and the dividend itself is the remainder. So we can write,
$4 = (0 \times 38) + 4$
But here we will try to find the quotient in decimal numbers such that we are left with no remainder.
We will find the quotient up to 3 decimal places. So we multiply the dividend by ${10^3}$. We can write,
$4 = \dfrac{{4 \times {{10}^3}}}{{{{10}^3}}} = \dfrac{{4000}}{{1000}}$
So now we have to evaluate,
$\dfrac{{4000}}{{1000}} \div 38$
We can solve this as follows,
$ \dfrac{{4000}}{{1000}} \div 38 \\
   = \dfrac{{4000}}{{1000}} \times \dfrac{1}{{38}} \\
   = \dfrac{{4000}}{{38}} \times \dfrac{1}{{1000}} \\
$
We can write $4000$ as,
$4000 = (105 \times 38) + 10$
We can observe that $4000$ divided by $38$ gives $105$ as quotient and $10$ as remainder. We can ignore the remainder term from this.
We can write,
$
  \dfrac{{4000}}{{38}} \times \dfrac{1}{{1000}} \\
   = \dfrac{{(105 \times 38) + 10}}{{38}} \times \dfrac{1}{{1000}} \\
   \approx \left( {\dfrac{{105 \times 38}}{{38}}} \right) \times \dfrac{1}{{1000}} \\
   = 105 \times \dfrac{1}{{1000}} \\
   = \dfrac{{105}}{{1000}} \\
   = 0.105 \\
$
Thus, we get the quotient as $0.105$
We can write,
$4 = 0.105 \times 38$

Hence, the quotient of \[4\] divided by $38$ is $0.105$ when rounded to $3$ decimal places.

Note: We converted dividend into fraction using $10$ raised to some powers as the dividend is less than the divisor. We may not get an exact answer in decimals in some cases in which case we can round up the result to \[2\]- $3$ decimal places.