Sure! Let's break down the solution step-by-step to find the standard form of the given expression [tex]\( 80,000 + 4,000 + 500 + 90 + 2 \)[/tex].
1. Add the values together:
[tex]\[
80,000 + 4,000 + 500 + 90 + 2 = 84,592
\][/tex]
Therefore, the sum of the values is [tex]\( 84,592 \)[/tex].
2. Express [tex]\( 84,592 \)[/tex] in standard form:
- The standard form of a number is expressed as [tex]\( a \times 10^n \)[/tex] where [tex]\( 1 \leq a < 10 \)[/tex] and [tex]\( n \)[/tex] is an integer.
- To convert [tex]\( 84,592 \)[/tex] to standard form, we need to place the decimal point after the first digit and count the number of places the decimal point has moved.
[tex]\[
84,592 = 8.4592 \times 10^4
\][/tex]
Here, [tex]\( a = 8.4592 \)[/tex] and [tex]\( n = 4 \)[/tex].
3. Match with the given options:
[tex]\[
\begin{align*}
A & : 8 \times 10^4+4 \times 10^3+5 \times 10^2+9 \times 10^1+2 \times 10^0 \quad \text{(not a standard form)} \\
B & : 2^4 \times 17 \times 311 \quad \text{(not applicable here)} \\
C & : 84,592 \quad \text{(this is the sum, but not in standard form)} \\
D & : 8.4592 \times 10^4 \quad \text{(this matches our standard form)}
\end{align*}
\][/tex]
Hence, the standard form of [tex]\( 80,000 + 4,000 + 500 + 90 + 2 \)[/tex] is:
[tex]\[ \boxed{8.4592 \times 10^4} \][/tex]
And the correct answer is option [tex]\( D \)[/tex].
