Question

type the correct answer in the box. use numbers instead of words.
an equation is shown.
$5.8 \times 10^4 - 5 \times 10^3 = k \times 10^4$
what is the value of $k$?
$k = \square$

Explanation:

Step1: Convert \(5\times10^{3}\) to \(10^{4}\) form

We know that \(5\times10^{3}=5\times10^{3}\times\frac{10}{10}= 0.5\times10^{4}\) (since \(\frac{10^{3}\times10}{10^{4}} = 1\), so multiplying by \(\frac{10}{10}\) is equivalent to multiplying by 1, and \(5\times10^{3}\times10 = 5\times10^{4}\), then dividing by 10 gives \(0.5\times10^{4}\)).

Step2: Subtract the two terms with \(10^{4}\)

The left - hand side of the equation \(5.8\times10^{4}-5\times10^{3}\) becomes \(5.8\times10^{4}-0.5\times10^{4}\). Using the distributive property \(a\times c - b\times c=(a - b)\times c\) (where \(a = 5.8\), \(b = 0.5\), and \(c = 10^{4}\)), we have \((5.8 - 0.5)\times10^{4}=5.3\times10^{4}\).
Since \(5.8\times10^{4}-5\times10^{3}=k\times10^{4}\), then \(k\times10^{4}=5.3\times10^{4}\). Dividing both sides by \(10^{4}\) (since \(10^{4}
eq0\)), we get \(k = 5.3\).

Answer:

\(5.3\)