Scientific notation — operations and applications

$0.000045$ is less than 1, so we expect a negative exponent.

Move the decimal point right until we get a number between 1 and 10: $0.000045\to 4.5$

We moved the decimal 5 places to the right, so the exponent is $-5$.

$0.000045=4.5\times 10^{-5}$

$4.5\times 10^5=450,000$, which is large, not small. Eliminate this option.

$45\times 10^{-6}$ has coefficient 45, which is not between 1 and 10 — not proper scientific notation. Eliminate.

$0.45\times 10^{-4}$ has coefficient 0.45, which is less than 1 — not proper scientific notation. Eliminate.

$4.5\times 10^{-5}=0.000045$ ✓ Coefficient is between 1 and 10, and exponent is negative as expected.

$6.0\times 3.0=18.0$

$4+5=9$, giving $18.0\times 10^9$

$18.0$ is not between 1 and 10. Rewrite: $18.0=1.8\times 10^1$

$1.8\times 10^1\times 10^9=1.8\times 10^{10}$

$18\times 10^9$ is not proper scientific notation since 18 > 10. Eliminate.

$6.0\times 3.0=18$ and $4+5=9$, so the base result is $18\times 10^9$, not involving exponent 20. Eliminate $9.0\times 10^{20}$.

$1.8\times 10^9$ vs $1.8\times 10^{10}$: after adjusting $18\times 10^9=1.8\times 10^{10}$, exponent 9 is too small. Eliminate $1.8\times 10^9$.

$1.8\times 10^{10}$ is in proper scientific notation and equals $18,000,000,000$. ✓