Evaluate 6.4x10^5 / 8.0x10^3 to 3 significant figures.

Steps to Solve

1. Divide the coefficients

To start, we divide the coefficients (the numbers in front of the powers of ten) of the two scientific notation numbers. This means we will divide $6.4$ by $8.0$.

[ \frac{6.4}{8.0} = 0.8 ]

2. Subtract the exponents

Next, we subtract the exponents of the powers of ten. We take the exponent of the first number ($10^5$) and subtract the exponent of the second number ($10^3$).

[ 5 - 3 = 2 ]

3. Combine the results

Now we combine our results from the previous two steps. We multiply the coefficient we got from step 1 by $10$ raised to the power we got from step 2.

[ 0.8 \times 10^2 ]

4. Convert to proper scientific notation

The next step is to express the result in scientific notation. We need to adjust $0.8$ to be a single digit left of the decimal, which gives us $8.0 \times 10^1$. However, since we have $10^2$, we combine them properly.

[ 8.0 \times 10^{1 + 2} = 8.0 \times 10^2 ]

5. Round to three significant figures

Finally, we check if our answer is in three significant figures. Since $8.0 \times 10^2$ already has three significant figures, it is already in the correct format.