Question

a biologist estimated the number of cells in a culture sample as 1.3 × 10². one week later, he looked at the same culture sample and estimated that the number of cells had grown to 3.9 × 10⁵. determine how many times larger the culture sample was compared to a week earlier.
complete the quotient in scientific notation and find the solution in standard notation.
\frac{(3.9 \times 10^{5})}{(1.3 \times 10^{2})} = \times =

Explanation:

Step1: Divide the coefficients

Divide \(3.9\) by \(1.3\): \(\frac{3.9}{1.3}=3\)

Step2: Divide the powers of 10

Use the rule \(\frac{10^{a}}{10^{b}} = 10^{a - b}\). Here \(a = 5\) and \(b=2\), so \(\frac{10^{5}}{10^{2}}=10^{5 - 2}=10^{3}\)

Step3: Combine the results

Multiply the results from step 1 and step 2. In scientific notation: \(3\times10^{3}\)

Step4: Convert to standard notation

For \(3\times10^{3}\), since the exponent is \(3\), we move the decimal point 3 places to the right. \(3\times10^{3}=3000\)

Answer:

In scientific notation: \(3\times10^{3}\)
In standard notation: \(3000\)