A culture of 1.75×1018 bacteria is in petri dish A. A culture of 6.25×1015 bacteria is in petri dish B.

How many times greater is the number of bacteria in petri dish A than petri dish B?

Enter your answer, in standard notation, in the box.

1 answer

To find how many times greater the number of bacteria in petri dish A is compared to petri dish B, we divide the number of bacteria in petri dish A by the number of bacteria in petri dish B.

Let:

  • \( A = 1.75 \times 10^{18} \) (bacteria in dish A)
  • \( B = 6.25 \times 10^{15} \) (bacteria in dish B)

Now, calculate the ratio:

\[ \frac{A}{B} = \frac{1.75 \times 10^{18}}{6.25 \times 10^{15}} \]

We can simplify this expression:

\[ \frac{A}{B} = \frac{1.75}{6.25} \times \frac{10^{18}}{10^{15}} = \frac{1.75}{6.25} \times 10^{18 - 15} = \frac{1.75}{6.25} \times 10^{3} \]

Now, calculate \( \frac{1.75}{6.25} \):

\[ \frac{1.75}{6.25} = 0.28 \]

Thus, we have:

\[ \frac{A}{B} = 0.28 \times 10^{3} \]

Converting \( 0.28 \times 10^{3} \) into standard notation:

\[ 0.28 \times 10^{3} = 2.8 \times 10^{2} \]

Therefore, the number of bacteria in petri dish A is \( 2.8 \times 10^{2} \) times greater than that in petri dish B.

The final answer is:

\[ \boxed{2.8 \times 10^{2}} \]