Question

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

Answer 1

To solve the expression \(0.078 - (5.2 \times 10^{-3})\), we first need to express \(0.078\) in scientific notation.

We can write \(0.078\) as:
\[
0.078 = 7.8 \times 10^{-2}
\]

Now, we will align the exponents to perform the subtraction. The term \((5.2 \times 10^{-3})\) can be kept as is.

Since \(10^{-2}\) and \(10^{-3}\) have different exponents, we can express \(7.8 \times 10^{-2}\) in terms of \(10^{-3}\):
\[
7.8 \times 10^{-2} = 7.8 \times 10^{-2} \cdot \frac{10^{-1}}{10^{-1}} = 78 \times 10^{-3}
\]

So now, we rewrite the original expression with a common exponent:
\[
0.078 - (5.2 \times 10^{-3}) = (78 \times 10^{-3}) - (5.2 \times 10^{-3})
\]
Next, we can subtract the coefficients:
\[
78 - 5.2 = 72.8
\]

Thus, we have:
\[
72.8 \times 10^{-3}
\]

Now, we express \(72.8\) in scientific notation:
\[
72.8 = 7.28 \times 10^{1}
\]

Combining this with \(10^{-3}\):
\[
72.8 \times 10^{-3} = 7.28 \times 10^{1} \times 10^{-3} = 7.28 \times 10^{-2}
\]

Therefore, the final answer in scientific notation is:
\[
\boxed{7.28 \times 10^{-2}}
\]