Question

Write in the short form: $600 + 300 + 10 + 1 + \dfrac{1}{{10}} + \dfrac{2}{{100}}$.

Answer 1

Hint: For this problem we need to convert the fraction into decimals. If the denominator has a value of 10, Then, the single zero terms in the denominator, the decimal will be placed before the single digit. Then, similarly, for the actual question given, the term in the denominator is 100, which gives the final answer by using the same concept. After that substitute the decimal value in place of the fraction part and add all the numbers to get the desired result.

Complete step-by-step answer:
Here the terms in the fractional form are $\dfrac{1}{{10}}$ and $\dfrac{2}{{100}}$.
To get the decimal form of fractions we divide the numerator by the denominator.
So, to get the decimal form of $\dfrac{1}{{10}}$, we divide 1 by 10 to get 0.1.
$ \Rightarrow \dfrac{1}{{10}} = 0.1$
So, to get the decimal form of $\dfrac{2}{{100}}$, we divide 2 by 100 to get 0.02.
$ \Rightarrow \dfrac{2}{{100}} = 0.02$
Substitute the value in an expression,
$ \Rightarrow 600 + 300 + 10 + 1 + \dfrac{1}{{10}} + \dfrac{2}{{100}} = 600 + 300 + 10 + 1 + 0.1 + 0.02$
Now add the terms on the right side,
$\therefore 600 + 300 + 10 + 1 + \dfrac{1}{{10}} + \dfrac{2}{{100}} = 911.12$

Hence, the short form of $600 + 300 + 10 + 1 + \dfrac{1}{{10}} + \dfrac{2}{{100}}$ is 911.12

Note: Our decimal system of numbers lets us write numbers as large or as small as we want, using a symbol called the decimal point. In our number system, digits can be placed to the left and right of a decimal point, to indicate numbers greater than one or less than one. The decimal point helps us to keep track of where the "ones" place is. It's placed just to the right of the one's place. As we move right from the decimal point, each number place is divided by 10.