Question

1. order the following numbers from greatest to least: $6.03 \times 10^{-5}$, $6.26 \times 10^{-4}$, $6.38 \times 10^{-6}$, $6.55 \times 10^{-3}$ $\square > \square > \square > \square$

Explanation:

Step1: Convert to standard form

To compare numbers in scientific notation, we can convert them to standard form or compare the exponents and coefficients. Let's first look at the exponents:

• For \(6.03\times10^{-5}\), the exponent is \(-5\), so \(6.03\times10^{-5}=0.0000603\)
• For \(6.26\times10^{-4}\), the exponent is \(-4\), so \(6.26\times10^{-4}=0.000626\)
• For \(6.38\times10^{-6}\), the exponent is \(-6\), so \(6.38\times10^{-6}=0.00000638\)
• For \(6.55\times10^{-3}\), the exponent is \(-3\), so \(6.55\times10^{-3}=0.00655\)

Step2: Compare the standard form numbers

Now we compare the standard form numbers:

• \(0.00655\) (from \(6.55\times10^{-3}\))
• \(0.000626\) (from \(6.26\times10^{-4}\))
• \(0.0000603\) (from \(6.03\times10^{-5}\))
• \(0.00000638\) (from \(6.38\times10^{-6}\))

We can see that \(0.00655>0.000626>0.0000603>0.00000638\)

Answer:

\(6.55\times10^{-3} > 6.26\times10^{-4} > 6.03\times10^{-5} > 6.38\times10^{-6}\)