Question

Adding Exponentials
Add 5.00 × 10^−5 and 3.00 × 10^−3

Answer 1

To add 5.00 × 10^{-5} and 3.00 × 10^{-3}, we convert them to the same exponent, resulting in 0.05 × 10^{-3} and 3.00 × 10^{-3}, and then sum them to get 3.05 × 10^{-3}.

Step-by-step explanation:

To add the numbers 5.00 × 10^{-5} and 3.00 × 10^{-3}, we need to have exponents of the same value. We convert the exponents so that they match, doing this by expressing the smaller exponent number in terms of the larger exponent. In this case, we express 5.00 × 10^{-5} as 0.05 × 10^{-3} which makes it easier to combine with 3.00 × 10^{-3}.

Now we can add the numbers:

• (0.05 × 10^{-3}) + (3.00 × 10^{-3}) = (0.05 + 3.00) × 10^{-3}
• This simplifies to 3.05 × 10^{-3}.

The process of aligning exponents is fundamental when adding scientific notations, ensuring we work with like terms.

To add exponential numbers, you need to have the same exponent. In this case, both numbers have exponents of -5 and -3. Therefore, we can add the numbers directly and keep the exponent the same.

5.00 × 10-5 + 3.00 × 10-3 = (5.00 + 3.00) × 10-5 = 8.00 × 10-5.