To find out how much heavier a grain of rice is than a strand of hair, we can first convert the mass of both items to the same units. The mass of a strand of hair is given as \( 2.17 \times 10^{-5} \) ounces, and the mass of a grain of rice is \( 0.002 \) ounces.
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First, we can express the mass of the grain of rice in scientific notation: \[ 0.002 = 2.0 \times 10^{-3} \text{ ounces} \]
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Now we can find the difference in mass between a grain of rice and a strand of hair: \[ \text{Difference} = \text{mass of grain of rice} - \text{mass of strand of hair} \] \[ = (2.0 \times 10^{-3}) - (2.17 \times 10^{-5}) \]
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To perform this subtraction, we need to express \( 2.0 \times 10^{-3} \) in terms of \( 10^{-5} \): \[ 2.0 \times 10^{-3} = 200 \times 10^{-5} \]
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Now we can perform the subtraction: \[ 200 \times 10^{-5} - 2.17 \times 10^{-5} = (200 - 2.17) \times 10^{-5} = 197.83 \times 10^{-5} \]
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Finally, we express \( 197.83 \times 10^{-5} \) in scientific notation: \[ 197.83 = 1.9783 \times 10^{2} \] Thus, \[ 197.83 \times 10^{-5} = 1.9783 \times 10^{2} \times 10^{-5} = 1.9783 \times 10^{-3} \]
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Therefore, the final answer, representing how much heavier a grain of rice is than a strand of hair, is: \[ \boxed{1.9783 \times 10^{-3}} \text{ ounces} \]
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