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.
Given:
- Mass of a strand of hair: \(2.17 \times 10^{-5}\) ounces
- Mass of a grain of rice: \(0.002\) ounces
First, we need to express \(0.002\) ounces in scientific notation:
\[ 0.002 = 2.0 \times 10^{-3} \text{ ounces} \]
Now we can perform the subtraction:
\[ \text{Difference} = \text{mass of rice} - \text{mass of hair} \]
\[ \text{Difference} = 2.0 \times 10^{-3} - 2.17 \times 10^{-5} \]
To subtract these, we need to have a common exponent. We can rewrite \(2.0 \times 10^{-3}\) with the same exponent as \(2.17 \times 10^{-5}\):
\[ 2.0 \times 10^{-3} = 2.0 \times 10^{-3} \times \frac{100}{100} = 200 \times 10^{-5} \]
Now, the subtraction looks like this:
\[ \text{Difference} = 200 \times 10^{-5} - 2.17 \times 10^{-5} \]
\[ = (200 - 2.17) \times 10^{-5} = 197.83 \times 10^{-5} \]
Next, we express \(197.83\) in scientific notation:
\[ 197.83 = 1.9783 \times 10^{2} \]
So we combine this with \(10^{-5}\):
\[ = 1.9783 \times 10^{2} \times 10^{-5} = 1.9783 \times 10^{-3} \]
Thus, the result, expressed in scientific notation, is:
\[ \boxed{1.9783 \times 10^{-3}} \text{ ounces} \]
This is how much heavier a grain of rice is than a strand of hair.
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