A strand of hair has an avermass of 2.17x10 exponent -5 ounces. A grain of rice has an average mass of 0.002 ounces. How much heavier is agrain of ricd than a strand of hair. Express your answer in scientific notation.

Answer 1

To find out how much heavier a grain of rice is than a strand of hair, we 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 convert the mass of the grain of rice to scientific notation: \[ 0.002 = 2.0 \times 10^{-3} \text{ ounces} \]

Now we perform the subtraction, keeping in mind to express both values in the same form: \[ \text{Mass of grain of rice} - \text{Mass of strand of hair} = 2.0 \times 10^{-3} - 2.17 \times 10^{-5} \]

To subtract these two, we need a common exponent. Let's convert \( 2.0 \times 10^{-3} \) to have the same exponent as \( 2.17 \times 10^{-5} \): \[ 2.0 \times 10^{-3} = 200 \times 10^{-5} \]

Now we can perform the subtraction: \[ 200 \times 10^{-5} - 2.17 \times 10^{-5} = (200 - 2.17) \times 10^{-5} = 197.83 \times 10^{-5} \]

Now, we need to express \( 197.83 \times 10^{-5} \) in proper scientific notation. We shift the decimal point to the left by two places: \[ 197.83 \times 10^{-5} = 1.9783 \times 10^{-3} \]

Therefore, the amount by which a grain of rice is heavier than a strand of hair is: \[ \boxed{1.9783 \times 10^{-3}} \text{ ounces} \]