Find 0.078−(5.2×10^−3) Express your answer in scientific notation. Do not round your answer.

Answer 1

To solve \( 0.078 - (5.2 \times 10^{-3}) \), we first need to convert the numbers into the same format before performing the subtraction.

1. Convert \( 0.078 \) into scientific notation: \[ 0.078 = 7.8 \times 10^{-2} \]

2. Convert \( 5.2 \times 10^{-3} \) into a form with a common exponent of \( 10^{-2} \): \[ 5.2 \times 10^{-3} = 0.052 \times 10^{-2} \]

3. Now we have: \[ 7.8 \times 10^{-2} - 0.052 \times 10^{-2} \]

   We can combine these since they are now both in terms of \( 10^{-2} \): \[ (7.8 - 0.052) \times 10^{-2} \]

4. Perform the subtraction: \[ 7.8 - 0.052 = 7.748 \]

5. Therefore, we have: \[ 7.748 \times 10^{-2} \]

6. Finally, express it in scientific notation: \[ 7.748 \times 10^{-2} \]

So, the final answer in scientific notation is: \[ \boxed{7.748 \times 10^{-2}} \]