To find out how much heavier a grain of rice is than a strand of hair, you can subtract the mass of the hair from the mass of the grain of rice.
- Mass of a grain of rice = \( 0.002 \) ounces
- Mass of a strand of hair = \( 2.17 \times 10^{-5} \) ounces
Next, we need to convert the mass of the grain of rice into scientific notation:
\[ 0.002 \text{ ounces} = 2 \times 10^{-3} \text{ ounces} \]
Now, we can perform the subtraction:
\[ \text{Difference} = \text{Mass of grain of rice} - \text{Mass of strand of hair} \] \[ \text{Difference} = (2 \times 10^{-3}) - (2.17 \times 10^{-5}) \]
Before subtracting, we convert \( 2 \times 10^{-3} \) into an equivalent form that has the same exponent as \( 2.17 \times 10^{-5} \):
\[ 2 \times 10^{-3} = 200 \times 10^{-5} \]
Now we subtract:
\[ \text{Difference} = (200 \times 10^{-5}) - (2.17 \times 10^{-5}) = (200 - 2.17) \times 10^{-5} \] \[ \text{Difference} = 197.83 \times 10^{-5} \]
To express \( 197.83 \) in proper scientific notation, we rewrite it:
\[ 197.83 = 1.9783 \times 10^{2} \]
Thus, we can combine the terms:
\[ 197.83 \times 10^{-5} = 1.9783 \times 10^{2} \times 10^{-5} = 1.9783 \times 10^{-3} \]
However, we keep it easier in the form of \( 1.9783 \) as \( 10^{1} \) (which gives it the correct final scientific notation since \( -3 + 2 \) equals \( -1 \)).
Therefore, the final answer in scientific notation is:
\[ \text{The difference in mass is approximately } 1.9783 \times 10^{-3} \text{ ounces}. \]
To ensure our answer is just as a simple decimal value, we round based on precision if that is required.
Thus, a grain of rice is approximately \( 1.9783 \times 10^{-3} \) ounces heavier than a strand of hair.