Find 0.078−(5.2×10^−3) . Express your answer in scientific notation. Do not round your answer.(1 point)

Answer 1

To calculate $0.078-(5.2\times {10}^{-3})$, we first express $0.078$ in scientific notation.

$$0.078=7.8\times {10}^{-2}$$

Now, we need to perform the subtraction. To do this easily, we can express both numbers in terms of the same exponent. We will convert $7.8\times {10}^{-2}$ to have the same exponent as $5.2\times {10}^{-3}$.

To express $7.8\times {10}^{-2}$ in terms of ${10}^{-3}$:

$$7.8\times {10}^{-2}=7.8\times {10}^{-2}\times \frac{{10}^1}{{10}^1}=78\times {10}^{-3}$$

Now we can perform the subtraction:

$$78\times {10}^{-3}-5.2\times {10}^{-3}=(78-5.2)\times {10}^{-3}=72.8\times {10}^{-3}$$

Next, we need to express $72.8\times {10}^{-3}$ back into proper scientific notation (which requires the coefficient to be between 1 and 10):

$$72.8\times {10}^{-3}=7.28\times {10}^{-2}$$

Thus, the final answer in scientific notation is:

$$\boxed{{\displaystyle 7.28\times {10}^{-2}}}$$