Question

Write each of the following as decimals-
\[70 + \dfrac{8}{{10}}\]

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 solution:
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.
For example, take \[17.29\] .
It can be written as \[17 + 0.29\] which is also equal to \[17 + \dfrac{{29}}{{100}}\]
This have another way of representation, which is \[\dfrac{{1729}}{{100}}\]
Every whole number is also a decimal number, with fractional parts equal to zero. That means, for example, \[9\] can be written as \[9.0\] .(zero can be repeated many number of times)
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, in the question, it is given as, \[70 + \dfrac{8}{{10}}\] , where \[70\] is called as whole part and \[\dfrac{8}{{10}}\] is called as fractional part. And the value of \[\dfrac{8}{{10}}\] has value as \[0.8\] .
So, the value is written as \[70 + 0.8\] .
So, the final value is \[70.8\] .

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 \[34.87\] .