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 multiply it by 256.7. Show your work.

Answer 1

Let's choose the scientific number \( 2.56 \times 10^{-2} \) and multiply it by 256.7.

**Step 1: Convert 256.7 into scientific notation.**
256.7 can be written in scientific notation as \( 2.567 \times 10^2 \).

**Step 2: Multiply the numbers in scientific notation.**
We can perform the multiplication as follows:

\[
(2.56 \times 10^{-2}) \times (2.567 \times 10^2)
\]

**Step 3: Multiply the coefficients (the numbers before the \( \times 10 \)).**
\[
2.56 \times 2.567 = 6.56432
\]

**Step 4: Add the exponents of the \( 10 \) terms.**
\[
10^{-2} \times 10^{2} = 10^{0}
\]

**Step 5: Combine the results.**
Now, we can write this as:
\[
6.56432 \times 10^{0}
\]

Since \( 10^{0} = 1 \), we can simplify it to just:
\[
6.56432
\]

**Step 6: Convert to scientific notation (if necessary).**
Since \( 6.56432 \) is greater than 1, we can express it in scientific notation:
\[
6.56432 \times 10^{0}
\]

However, for standard scientific notation, this is appropriate as it is already simplified.

**Final result:**
\[
2.56 \times 10^{-2} \times 256.7 = 6.56432
\]

In scientific notation, it can also be presented as:
\[
6.56432 \times 10^0
\]