To find out how much heavier a grain of rice is compared to a strand of hair, we can subtract the mass of the hair from the mass of the grain of rice.
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The mass of a strand of hair: \[ m_{\text{hair}} = 2.17 \times 10^{-3} \text{ ounces} \] (Note: The average mass of hair is \[ 2.17 \text{ ounces} \] is likely a typo; it should actually be \[ 2.17 \times 10^{-3} \text{ ounces} \])
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The mass of a grain of rice: \[ m_{\text{rice}} = 0.002 \text{ ounces} = 2.00 \times 10^{-3} \text{ ounces} \]
Now we can calculate the difference: \[ \text{Difference} = m_{\text{rice}} - m_{\text{hair}} \] \[ \text{Difference} = (2.00 \times 10^{-3}) - (2.17 \times 10^{-3}) \]
\[ \text{Difference} = -0.17 \times 10^{-3} \text{ ounces} \]
To express this in scientific notation: \[ -0.17 \times 10^{-3} = -1.7 \times 10^{-4} \text{ ounces} \]
Thus, since we are asked how much heavier a grain of rice is than a strand of hair, it seems we've made a mistake in the premise. A strand of hair is heavier than a grain of rice.
The grain of rice is actually lighter by \( 1.7 \times 10^{-4} \) ounces. If you want to express how much lighter the strand of hair is than a grain of rice, the answer remains the same but negated:
Final answer: \[ \text{The difference in weight (how much lighter the grain of rice is)} = 1.7 \times 10^{-4} \text{ ounces} \] (expressed positively).