Solve this problem , Make sure that it is in scientific notation format prior to solving. 32.8 + (8.03 x 10^-8)

1 answer

To solve \( 32.8 + (8.03 \times 10^{-8}) \), we first need to express \( 32.8 \) in scientific notation.

The number \( 32.8 \) can be expressed in scientific notation as: \[ 32.8 = 3.28 \times 10^1 \]

Now, we can rewrite the expression: \[ 3.28 \times 10^1 + 8.03 \times 10^{-8} \]

To add these two numbers, we need to have the same exponent. We can convert \( 3.28 \times 10^1 \) to an equivalent form with the exponent \( 10^{-8} \): \[ 3.28 \times 10^1 = 3.28 \times 10^{1 - 8} = 3.28 \times 10^{-7} \]

Now we can rewrite our expression as: \[ 3.28 \times 10^{-7} + 8.03 \times 10^{-8} \]

Next, we need to express \( 3.28 \times 10^{-7} \) in terms of \( 10^{-8} \): \[ 3.28 \times 10^{-7} = 32.8 \times 10^{-8} \]

Now, our expression becomes: \[ 32.8 \times 10^{-8} + 8.03 \times 10^{-8} \]

Now we can add the coefficients: \[ (32.8 + 8.03) \times 10^{-8} = 40.83 \times 10^{-8} \]

Finally, we can convert \( 40.83 \) into proper scientific notation: \[ 40.83 = 4.083 \times 10^1 \]

Thus: \[ 40.83 \times 10^{-8} = 4.083 \times 10^{-7} \]

Therefore, the final answer is: \[ \boxed{4.083 \times 10^{-7}} \]