find 0.078-(5.2x10^-3)express your answer in scientific notation

Answer 1

To find $0.078-(5.2\times {10}^{-3})$, we first convert $0.078$ to scientific notation.

$0.078$ can be expressed as: $$0.078=7.8\times {10}^{-2}$$

Now we have: $$7.8\times {10}^{-2}-5.2\times {10}^{-3}$$

Next, we need to express both terms with the same exponent. The term $5.2\times {10}^{-3}$ can be converted to the same exponent as $7.8\times {10}^{-2}$:

To do this, we can convert $5.2\times {10}^{-3}$ to an equivalent expression with ${10}^{-2}$: $$5.2\times {10}^{-3}=0.052\times {10}^{-2}$$

Now we can subtract: $$(7.8\times {10}^{-2})-(0.052\times {10}^{-2})=(7.8-0.052)\times {10}^{-2}$$

Calculating $7.8-0.052$: $$7.8-0.052=7.748$$

Now we can write our result: $$7.748\times {10}^{-2}$$

In scientific notation, this is best expressed as: $$7.748\times {10}^{-2}$$

Thus, the final answer is: $$\boxed{{\displaystyle 7.748\times {10}^{-2}}}$$