Question

Express your answer in scientific notation.
\[1.8 \cdot 10^{-2} - 3.9 \cdot 10^{-3} = \]

Answer 1

To solve the expression \(1.8 \cdot 10^{-2} - 3.9 \cdot 10^{-3}\), we first need to express both terms with the same exponent for the powers of ten.

The first term is \(1.8 \cdot 10^{-2}\) and the second term is \(3.9 \cdot 10^{-3}\). We can convert \(3.9 \cdot 10^{-3}\) to have the same exponent as the first term:

\[
3.9 \cdot 10^{-3} = 3.9 \cdot 10^{-3} \times \frac{10^{-2}}{10^{-2}} = 3.9 \cdot 10^{-3} \cdot 0.1 = 0.39 \cdot 10^{-2}
\]

Now we can rewrite the subtraction:

\[
1.8 \cdot 10^{-2} - 0.39 \cdot 10^{-2}
\]

Combining these two terms gives:

\[
(1.8 - 0.39) \cdot 10^{-2}
\]

Calculating \(1.8 - 0.39\):

\[
1.8 - 0.39 = 1.41
\]

Thus, we have:

\[
1.41 \cdot 10^{-2}
\]

Finally, we express \(1.41 \cdot 10^{-2}\) in scientific notation. The number \(1.41\) is already between \(1\) and \(10\), so it is properly expressed as:

\[
\boxed{1.41 \cdot 10^{-2}}
\]