Question

Write the decimal of the expression, \[200 + 60 + 5 + \dfrac{1}{{10}}\].

Answer 1

Hint:
We are required to convert the sum of a few numbers into the decimal form. To do this we add similar kinds of numbers. We then take the LCM and write it in the mathematical or the fractional form. We then convert the fraction into a decimal by dividing.

Complete step by step solution:
Decimal numbers are those numbers in which the whole part and the fractional part is separated by a decimal point. The part that is to the left side of the decimal is called the whole part. The naming of this part is done in the same way as for the whole numbers. However, the part that is to the right side of the decimal is known as the decimal part. This part has its own rules and systems and it does not follow all the rules of the whole numbers exactly. For example – The nomenclature of the decimal part is different from the whole numbers. To name decimal parts we just spell out the words without taking into consideration their place values etc. But this does not mean that they do not have place values.
To solve this question, we first have to add similar terms.
As 200, 60 and 5 are similar because they are whole numbers, we will add them together.
\[200 + 60 + 5 = 265\]
Now, we can express \[200 + 60 + 5 + \dfrac{1}{{10}}\] as
\[200 + 60 + 5 + \dfrac{1}{{10}} = 265 + \dfrac{1}{{10}}\]
We will now take the LCM of the denominators. In this case, the denominators are 1 and 10, so the LCM of 1 and 10 is 10. So, we will multiply the denominators of both the terms with suitable numbers to make them 10. Subsequently, we will be multiplying the numerators with the same number too, so that the fraction does not get altered.
\[200 + 60 + 5 + \dfrac{1}{{10}} = \dfrac{{265 \times 10}}{{1 \times 10}} + \dfrac{{1 \times 1}}{{10 \times 1}}\]
Simplifying the above expression, we get
\[200 + 60 + 5 + \dfrac{1}{{10}} = \dfrac{{2650}}{{10}} + \dfrac{1}{{10}}\]
Now, as our denominators are equal, we will add the numerators to get the required improper fraction.
\[200 + 60 + 5 + \dfrac{1}{{10}} = \dfrac{{2651}}{{10}}\]
Now, we have to convert \[\dfrac{{2651}}{{10}}\] to the decimal form. For this, we will divide 2651 by 10.
\[\dfrac{{2651}}{{10}} = 265.1\]

The decimal form of \[200 + 60 + 5 + \dfrac{1}{{10}}\] is \[265.1\].

Note:
We can solve this question with another method also just as shown below.
We know that
\[200 + 60 + 5 + \dfrac{1}{{10}} = 265 + \dfrac{1}{{10}}\]
Now, dividing 1 by 10, we get
\[200 + 60 + 5 + \dfrac{1}{{10}} = 265 + 0.1\]
Now, adding the terms, we get
\[200 + 60 + 5 + \dfrac{1}{{10}} = 265.1\]
 The required answer is \[265.1\].