Question

evaluate the expression without using a calculator. (enter your answer in scientific notation.) \\(\frac{2.5 \times 10^{-4}}{5 \times 10^{2}}\\) \\(\times 10\\) resources read it submit answer 2. - / 2 points write the number in scientific notation. 89,800,000,000 \\(\times 10\\) resources read it

Explanation:

First Sub - Question: Evaluate \(\frac{2.5\times10^{-4}}{5\times10^{2}}\times10\)

Step 1: Divide the coefficients and the powers of 10 separately

First, divide the coefficients: \(\frac{2.5}{5}=0.5\). Then, for the powers of 10, use the rule \(a^{m}\div a^{n}=a^{m - n}\), so \(\frac{10^{-4}}{10^{2}}=10^{-4-2}=10^{-6}\). So the fraction \(\frac{2.5\times10^{-4}}{5\times10^{2}}\) simplifies to \(0.5\times10^{-6}\).

Step 2: Multiply by 10

Now multiply \(0.5\times10^{-6}\) by 10. Using the rule \(a^{m}\times a^{n}=a^{m + n}\), we have \(0.5\times10^{-6}\times10 = 0.5\times10^{-6 + 1}=0.5\times10^{-5}\).

Step 3: Convert to proper scientific notation

In scientific notation, the coefficient should be between 1 and 10. So we rewrite \(0.5\times10^{-5}\) as \(5\times10^{-1}\times10^{-5}\). Using the rule of exponents for multiplication, \(10^{-1}\times10^{-5}=10^{-1-5}=10^{-6}\). So the result is \(5\times10^{-6}\).

To write a number in scientific notation \(a\times10^{n}\), where \(1\leqslant|a|\lt10\) and \(n\) is an integer, we move the decimal point to the left until there is only one non - zero digit to the left of the decimal point. For 89,800,000,000, we move the decimal point 10 places to the left, so \(a = 8.98\) and \(n=10\).

Answer:

\(5\times10^{-6}\)

Second Sub - Question: Write 89,800,000,000 in scientific notation