Question

Find the number from the following expanded form
 $ 8\times {{10}^{4}}+6\times {{10}^{3}}+0\times {{10}^{2}}+4\times {{10}^{1}}+5\times {{10}^{0}} $

Answer 1

Hint: There are two ways to solve this problem but we will solve it by simple operations like multiplication and addition. Group the numbers with their respective exponential power to the 10 and once you get the multiplication, add them all together to find the final value. The indices rule, $ {{a}^{0}}=1 $ will also help you in the last group.

Complete step-by-step answer:
We have an expanded form of a number, so let us find out the number which has been expanded.
Let us group the numbers with their exponential of the number 10 and solve them separately and later add them all together in the end.
For, $ 8\times {{10}^{4}} $ , convert the $ {{10}^{4}} $ from exponential to a simple number and multiply with the number 8.
 $ \begin{align}
  & 8\times {{10}^{4}}=8\times 10000 \\
 & =80000
\end{align} $
Similarly, do it for all the other groups,
 $ \begin{align}
  & 6\times {{10}^{3}}=6\times 1000 \\
 & =6000
\end{align} $
 $ 0\times {{10}^{2}}=0 $ (anything multiplied by 0 is equal to 0)
 $ \begin{align}
  & 4\times {{10}^{1}}=4\times 10 \\
 & =40
\end{align} $
Now, for the last one, $ 5\times {{10}^{0}} $ , here the power to the 10 is zero.
 $ \begin{align}
  & 5\times {{10}^{0}}=5\times 1 \\
 & =5
\end{align} $
In the last step, add all the obtained numbers to find the result.
80000 + 6000 + 0 + 40 + 5 = 86045
Hence, the number from the expanded form is 86045.

Note: In this question, you need to remember the indices formula, $ {{a}^{0}}=1 $ . Also, you can’t add the numbers first and then multiply. The mathematics rule clearly states that the multiplication should be done before addition in order to get the correct answer. Another way to solve this is to take the highest exponential of 10 as a common and get the separated values in decimal and add them up and later in the end multiply by the highest exponential of 10 which is taken as common.