Question

directions: drag each expression to the correct location in the table. not all expressions will be used. evaluate the expressions given in the table and place the equivalent expression in the appropriate boxes. $2 \times 10^3$ $15 \times 10^{11}$ $6.9 \times 10^6$ $2 \times 10^5$ $(9 \times 10^5) + (6 \times 10^6)$ $\frac{6 \times 10^4}{3 \times 10^{-1}}$

Explanation:

Step1: Evaluate the first expression

First, simplify \((9 \times 10^{5})+(6 \times 10^{6})\). Rewrite \(9\times 10^{5}\) as \(0.9\times 10^{6}\) (since \(9\times 10^{5}=9\times10^{5}\times\frac{10}{10}=0.9\times 10^{6}\)). Then add: \(0.9\times 10^{6}+6\times 10^{6}=(0.9 + 6)\times 10^{6}=6.9\times 10^{6}\).

Step2: Evaluate the second expression

Simplify \(\frac{6\times 10^{4}}{3\times 10^{-1}}\). Divide the coefficients and subtract the exponents of 10: \(\frac{6}{3}\times 10^{4-(-1)} = 2\times 10^{5}\) (because \(a^{m}\div a^{n}=a^{m - n}\), so \(10^{4}\div10^{-1}=10^{4+1}=10^{5}\)).

Answer:

For \((9 \times 10^{5})+(6 \times 10^{6})\), the equivalent expression is \(6.9 \times 10^{6}\).
For \(\frac{6 \times 10^{4}}{3 \times 10^{-1}}\), the equivalent expression is \(2 \times 10^{5}\).