Question

In this problem, you will practice adding, subtracting, multiplying, and dividing numbers written in scientific notation. For each part, use the following numbers.
3.2×104
1.95×106
8.03×10−8
2.56×10−2
4.82×1012

Choose one of the scientific numbers from the list and divide it by 0.3 (or
divide 0.3 by the number you choose). Show your work.

Answer 1

Let's choose the number \( 1.95 \times 10^6 \) and divide it by \( 0.3 \).

We start with the expression:

\[
\frac{1.95 \times 10^6}{0.3}
\]

First, we can rewrite \( 0.3 \) in scientific notation:

\[
0.3 = 3.0 \times 10^{-1}
\]

Now we substitute:

\[
\frac{1.95 \times 10^6}{3.0 \times 10^{-1}}
\]

Next, we can divide the coefficients (the numbers in front) and then subtract the exponents (according to the rules of exponents):

\[
= \frac{1.95}{3.0} \times 10^{6 - (-1)}
\]

Calculating \( \frac{1.95}{3.0} \):

\[
1.95 \div 3.0 = 0.65
\]

Now we simplify the exponent:

\[
= 0.65 \times 10^{6 + 1} = 0.65 \times 10^7
\]

Next, we want to express \( 0.65 \) in scientific notation:

\[
0.65 = 6.5 \times 10^{-1}
\]

So we can substitute that back into our expression:

\[
0.65 \times 10^7 = 6.5 \times 10^{-1} \times 10^7
\]

Finally, we combine the powers of 10:

\[
= 6.5 \times 10^{7 - 1} = 6.5 \times 10^6
\]

Thus, the final result of dividing \( 1.95 \times 10^6 \) by \( 0.3 \) is:

\[
\boxed{6.5 \times 10^6}
\]