Question

The table below shows the approximate masses of a dust particle and a grain of pollen.

Dust Particle 0.000000778 g
Grain of Pollen 0.00000000155 g
The mass of a dust particle can be estimated and written in the form a × 10b, where a = 8 and b =
.

The mass of a grain of pollen can be estimated and written in the form a × 10b, where a = 2 and b =
.

Based on the estimates, the mass of a dust particle is approximately
times larger than the mass of a grain of pollen.

Answer 1

To express the mass of a dust particle and a grain of pollen in scientific notation:

1. **Dust Particle:**
\[
0.000000778 \, \text{g} = 7.78 \times 10^{-7} \, \text{g}
\]
Here, \( a = 7.78 \) and \( b = -7 \).

2. **Grain of Pollen:**
\[
0.00000000155 \, \text{g} = 1.55 \times 10^{-9} \, \text{g}
\]
Here, \( a = 1.55 \) and \( b = -9 \).

Now, to determine how many times larger the mass of a dust particle is compared to the mass of a grain of pollen, we can calculate the ratio of their masses:

\[
\text{Ratio} = \frac{7.78 \times 10^{-7}}{1.55 \times 10^{-9}}
\]

Calculating this step-by-step:

1. Divide the coefficients:
\[
\frac{7.78}{1.55} \approx 5.02
\]

2. Subtract the exponents:
\[
10^{-7 - (-9)} = 10^{-7 + 9} = 10^{2}
\]

Putting this together:
\[
\text{Ratio} = 5.02 \times 10^{2} = 502
\]

Thus, the mass of a dust particle is approximately **502 times larger** than the mass of a grain of pollen.