Question

What is \[\dfrac{{30}}{8}\] as a decimal?

Answer 1

Hint: We use the concept of decimals to solve this sum. We will also know about the whole part and the fractional part of a decimal number in this problem. And we shall know about types of decimal numbers that are present.

Complete step by step answer:
There are different kinds of numbers namely natural numbers, whole numbers and so on. And decimals are one among them. In algebra, decimals are a kind of numbers, which consists of a whole number and a fractional part, which are separated by a decimal point. A decimal point is represented by . In other words, a decimal number is a number in which the fractional part consists of a denominator which is in the terms of powers of 10.
There are two types of decimal numbers. They are,
Recurring decimal number: a decimal number in which the fractional part gets repeated.
For example, \[56.787878\] , in which “ \[78\] ” is repeated. (This is a finite value)
Or take the number, \[6.343434....\] , in which “ \[34\] ” is repeating. (And this is an infinite value)
Non-recurring decimal number: a decimal number in which the fractional part does not repeat.
For example, \[4.0237\] which is a finite value and \[7.394....\] , which is an infinite value.
Before the decimal point, the place values are called as ones, tens, hundreds, and so on from right to left.
After decimal points, the place values are called as tenth’s, hundredths, and so on from left to right.
So, here we need to find the value of \[\dfrac{{30}}{8}\] in decimal form.
If we do actual division, i.e., if 30 is divided by 8, we get the value 3 as quotient and 6 in the remainder.
So, we can conclude that \[\dfrac{{30}}{8} = 3 + \dfrac{6}{8}\]
And when the fraction \[\dfrac{6}{8}\] is simplified, we get \[\dfrac{3}{4}\]
So, \[\dfrac{{30}}{8} = 3 + \dfrac{3}{4}\]
Here, \[3\] can be written as \[3.00\] .
And \[\dfrac{3}{4} = 3{\text{ times }}\dfrac{1}{4}\]
And when a whole is divided into four equal parts, each part is a quarter and which implies that, \[\dfrac{1}{4} = 0.25\]
So, \[\dfrac{3}{4} = 3{\text{ times }}0.25\]
\[ \Rightarrow \dfrac{3}{4} = 0.75\]
So, we get, \[\dfrac{{30}}{8} = 3.00 + 0.75\]
\[ \Rightarrow \dfrac{{30}}{8} = 3.75\]
So, we have written the value \[\dfrac{{30}}{8}\] as decimal.

Note:
There is a tip or a short method to calculate the decimal values. If there is a term, which contains powers of 10 in the denominator, then this method is very useful. And the rule or method is, if a number is divided by powers of 10, then the decimal in that number is moved the number of times present as the power of 10, towards left.
For example, consider, \[\dfrac{{3487}}{{100}}\] which is equal to \[\dfrac{{3487}}{{{{10}^2}}}\]
So, the decimal is moved two times towards the left and the answer we get will be \[34.87\] .