What is the total length of the line of bacteria in scientific notation with 3 significant figures?

Steps to Solve

1. Identify the values in scientific notation

The diameter of a single bacterium is given as $2.5 \times 10^{-8}$ meters. The total number of bacteria is 50,000, which can be expressed in scientific notation as $5.0 \times 10^{4}$, since $50,000 = 5.0 \times 10^4$.

2. Multiply the values of a

Next, multiply the two values in scientific notation:

$$ (2.5 \times 10^{-8}) \times (5.0 \times 10^{4}) $$

3. Multiply the coefficients and add the exponents

To perform the multiplication, calculate the coefficients and add the exponents:

• Coefficients: $2.5 \times 5.0 = 12.5$
• Exponents: $-8 + 4 = -4$

Thus,

$$ 12.5 \times 10^{-4} $$

4. Adjust the result to proper scientific notation

The coefficient $12.5$ is greater than $10$. To express this in proper scientific notation, convert $12.5$ to $1.25 \times 10^{1}$:

$$ 12.5 \times 10^{-4} = (1.25 \times 10^{1}) \times 10^{-4} = 1.25 \times 10^{-3} $$

5. Final result

Therefore, the total length of the line of bacteria is:

$$ 1.25 \times 10^{-3} \text{ meters} $$