To find out how much heavier a grain of rice is than a strand of hair, we need to subtract the mass of the strand of hair from the mass of the grain of rice.
- Mass of a strand of hair = \( 2.17 \times 10^{-5} \) ounces
- Mass of a grain of rice = \( 0.002 \) ounces = \( 2.00 \times 10^{-3} \) ounces (in scientific notation)
Now we can subtract the two masses:
\[ \text{Difference} = \text{Mass of grain of rice} - \text{Mass of strand of hair} \] \[ \text{Difference} = 2.00 \times 10^{-3} - 2.17 \times 10^{-5} \]
To perform the subtraction, it's easier to express both numbers with the same exponent. We can convert \( 2.00 \times 10^{-3} \) to a form with \( 10^{-5} \): \[ 2.00 \times 10^{-3} = 200 \times 10^{-5} \]
Now we can perform the subtraction: \[ \text{Difference} = 200 \times 10^{-5} - 2.17 \times 10^{-5} = (200 - 2.17) \times 10^{-5} = 197.83 \times 10^{-5} \]
Now we need to convert \( 197.83 \times 10^{-5} \) into proper scientific notation. To do this, we move the decimal point two places to the left, which increases the exponent by 2: \[ 197.83 \times 10^{-5} = 1.9783 \times 10^{-3} \]
Thus, the difference in mass, with the grain of rice being heavier than the strand of hair, is: \[ \boxed{1.9783 \times 10^{-3}} \text{ ounces} \]