Question

In this problem, you will practice adding, subtracting, multiplying, and dividing numbers written in scientific notation. For each part, use the following numbers. 
  3.2×10^4       1.95×10^6        8.03×10^−8         2.56×10^−2         4.82×10^12
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 \( 1.95 \times 10^6 \) from the list and divide it by \( 0.3 \).

### Step 1: Write the division in mathematical form
\[
\frac{1.95 \times 10^6}{0.3}
\]

### Step 2: Convert \( 0.3 \) to scientific notation
0.3 can be written as:
\[
0.3 = 3.0 \times 10^{-1}
\]

### Step 3: Rewrite the division using scientific notation
Now, we can rewrite the division:
\[
\frac{1.95 \times 10^6}{3.0 \times 10^{-1}}
\]

### Step 4: Divide the coefficients and subtract the exponents
When dividing numbers in scientific notation, divide the coefficients and subtract the exponents:
\[
\frac{1.95}{3.0} \times 10^{6 - (-1)}
\]

Calculating the coefficient:
\[
\frac{1.95}{3.0} = 0.65
\]

Now, for the exponent:
\[
6 - (-1) = 6 + 1 = 7
\]

### Step 5: Combine the results
Putting it all together:
\[
0.65 \times 10^{7}
\]

### Step 6: Convert back to proper scientific notation
To convert \( 0.65 \times 10^{7} \) to proper scientific notation, we need the coefficient to be between 1 and 10. We can rewrite it as:
\[
6.5 \times 10^{6}
\]

### Final Result
Thus, the final result of dividing \( 1.95 \times 10^{6} \) by \( 0.3 \) is:
\[
6.5 \times 10^{6}
\]