Question

which of the numbers below is less than 1? 3.9×10⁻⁴ 4.0×10⁰ 6.2×10¹

Explanation:

Step1: Analyze \(3.9\times10^{-4}\)

Recall that \(10^{-n}=\frac{1}{10^{n}}\) for positive integer \(n\). So \(10^{-4}=\frac{1}{10^{4}} = 0.0001\). Then \(3.9\times10^{-4}=3.9\times0.0001 = 0.00039\), which is less than 1.

Step2: Analyze \(4.0\times10^{0}\)

Recall that any non - zero number to the power of 0 is 1, so \(10^{0}=1\). Then \(4.0\times10^{0}=4.0\times1 = 4.0\), which is greater than 1.

Step3: Analyze \(6.2\times10^{1}\)

Recall that \(10^{1}=10\). Then \(6.2\times10^{1}=6.2\times10 = 62\), which is greater than 1.

Answer:

\(3.9\times10^{-4}\)