Question

expand the given number to decimal for by expanding in powers and by using the calculator short cut. 82104nine in powers, write the calculator shortcut extension for 82104nine, convert 82104nine to decimal form.

Answer 1

We have a number expressed in a base of 9, instead of the most common decimal base.

Then, is we have the number 82104 in 9-base, it means that we can expand it as:

`82104_{\text{nine}}=8\cdot9^4+2\cdot9^3+1\cdot9^2+0\cdot9^1+4\cdot9^0`

We then can expand this as:

`82104_{\text{nine}}=8\cdot6561+2\cdot729+1\cdot81+0\cdot9^{}+4\cdot1`

We can finally calculate what this number is in decimal form by finishing simplyfing the expression above:

`\begin{gathered} 82104_{\text{nine}}=8\cdot6561+2\cdot729+1\cdot81+0\cdot9^{}+4\cdot1 \\ 82104_{\text{nine}}=52488+1458+81+4 \\ 82104_{\text{nine}}=54031 \end{gathered}`

Answer:

If we decompose this number given the base 9, we get the following terms:

`82104_{\text{nine}}=8\cdot9^4+2\cdot9^3+1\cdot9^2+0\cdot9^1+4\cdot9^0`

The decimal form of 82104(nine) is 54031.