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.

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

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:

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