Question

e. compare. use <, >, or =. \\(\frac{4.56 \times 10^9}{3 \times 10^5} \bigcirc \frac{5.2 \times 10^8}{1.3 \times 10^3}\\)

Explanation:

Step1: Simplify left fraction

For \(\frac{4.56\times10^{9}}{3\times10^{5}}\), use exponent rule \(\frac{a^m}{a^n}=a^{m - n}\) and \(\frac{a\times10^m}{b\times10^n}=\frac{a}{b}\times10^{m - n}\).
\(\frac{4.56}{3}=1.52\), \(10^{9-5}=10^{4}\), so left is \(1.52\times10^{4}=15200\).

Step2: Simplify right fraction

For \(\frac{5.2\times10^{8}}{1.3\times10^{5}}\), \(\frac{5.2}{1.3}=4\), \(10^{8 - 5}=10^{3}\), so right is \(4\times10^{3}=4000\).

Step3: Compare values

\(15200>4000\), so \(\frac{4.56\times10^{9}}{3\times10^{5}}>\frac{5.2\times10^{8}}{1.3\times10^{5}}\).

Answer:

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