Question

Adding in subtracting numbers in scientific notation. 8.5×10 to the -1st+5.9×10 to the -4th

Answer 1

To add or subtract numbers in scientific notation, we first need to express them with the same exponent. Let's look at the two numbers you've provided:

1. \( 8.5 \times 10^{-1} \)
2. \( 5.9 \times 10^{-4} \)

We can convert \( 8.5 \times 10^{-1} \) to have the same exponent as \( 5.9 \times 10^{-4} \).

\[
8.5 \times 10^{-1} = 8.5 \times 10^{-1} \times \frac{10^{-3}}{10^{-3}} = 8.5 \times 10^{-4} \times 10^{2} = 850 \times 10^{-4}
\]

Now we can add the two numbers:

\[
850 \times 10^{-4} + 5.9 \times 10^{-4} = (850 + 5.9) \times 10^{-4} = 855.9 \times 10^{-4}
\]

Now, we can convert this back to proper scientific notation:

\[
855.9 \times 10^{-4} = 8.559 \times 10^{-2}
\]

So, the final result of \( 8.5 \times 10^{-1} + 5.9 \times 10^{-4} \) is:

\[
\boxed{8.559 \times 10^{-2}}
\]