Question

which of the numbers below is greater than 1? 7.7 × 10⁻⁵ 6.2 × 10³ 8.0 × 10⁻⁹

Explanation:

Step1: Analyze \(7.7 \times 10^{-5}\)

Recall that \(10^{-n}=\frac{1}{10^{n}}\). So \(10^{-5}=\frac{1}{10^{5}} = 0.00001\). Then \(7.7\times10^{-5}=7.7\times0.00001 = 0.000077\), which is less than 1.

Step2: Analyze \(6.2 \times 10^{3}\)

Recall that \(10^{n}\) is 1 followed by \(n\) zeros. So \(10^{3}=1000\). Then \(6.2\times10^{3}=6.2\times1000 = 6200\), which is greater than 1.

Step3: Analyze \(8.0 \times 10^{-9}\)

\(10^{-9}=\frac{1}{10^{9}}=0.000000001\). Then \(8.0\times10^{-9}=8.0\times0.000000001 = 0.000000008\), which is less than 1.

Answer:

\(6.2 \times 10^{3}\)