To find out how much heavier a grain of rice is than a strand of hair, we first need to calculate the difference in their masses.
- Mass of hair: \( 2.17 \times 10^{-5} \) ounces
- Mass of rice: \( 0.002 \) ounces
Next, let's express the mass of rice in scientific notation:
\[ 0.002 \text{ ounces} = 2.0 \times 10^{-3} \text{ ounces} \]
Now, we can determine how much heavier the grain of rice is by subtracting the mass of hair from the mass of rice:
\[ \text{Difference} = \text{Mass of rice} - \text{Mass of hair} \] \[ \text{Difference} = (2.0 \times 10^{-3}) - (2.17 \times 10^{-5}) \]
To perform this calculation, we need to express both numbers with the same exponent. We'll convert \( 2.0 \times 10^{-3} \) to have \( 10^{-5} \):
\[ 2.0 \times 10^{-3} = 200.0 \times 10^{-5} \]
Now we can perform the subtraction:
\[ \text{Difference} = (200.0 \times 10^{-5}) - (2.17 \times 10^{-5}) = (200.0 - 2.17) \times 10^{-5} \] \[ \text{Difference} = 197.83 \times 10^{-5} \]
Next, we express \( 197.83 \times 10^{-5} \) in proper scientific notation by moving the decimal point two places to the left:
\[ 197.83 \times 10^{-5} = 1.9783 \times 10^{-3} \]
Thus, the grain of rice is \( \approx 1.9783 \times 10^{-3} \) ounces heavier than the hair.
In summary, the difference in mass, expressed in scientific notation, is:
\[ \text{The grain of rice is } 1.9783 \times 10^{-3} \text{ ounces heavier than the hair.} \]
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