In this problem, you will practice adding, subtracting, multiplying, and dividing numbers written in scientific notation. For each part, use the following numbers.

Question

  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: \[ 6.5 \times 10^{6} \]