Question

calculate.
$(4.45 \times 10^6) - (1.9 \times 10^4)$
write your answer in scientific notation.

Explanation:

Step1: Convert to same exponent

To subtract numbers in scientific notation, we first convert them to have the same exponent. We know that \(10^{6}=10^{2}\times10^{4}\), so we can rewrite \(4.45\times 10^{6}\) as \(4.45\times10^{2}\times10^{4}=445\times 10^{4}\).
The expression becomes \((445\times 10^{4})-(1.9\times 10^{4})\).

Step2: Subtract the coefficients

Now we subtract the coefficients (the numbers in front of \(10^{4}\)): \(445 - 1.9 = 443.1\).
So the result is \(443.1\times 10^{4}\).

Step3: Convert back to scientific notation

We need to express \(443.1\times 10^{4}\) in proper scientific notation (where the coefficient is between 1 and 10). We know that \(443.1 = 4.431\times 10^{2}\), so \(443.1\times 10^{4}=4.431\times 10^{2}\times 10^{4}\).
Using the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\), we get \(4.431\times 10^{2+4}=4.431\times 10^{6}\).

Answer:

\(4.431\times 10^{6}\)