When we subtract with scientific notation,

Question

we need to first make sure they are both in
scientific notation and that their exponents
are the same. If they are, we simply subtract
the coefficients and keep the 10 and
exponent the same.
Example: 5.2 x 10 - 3.1 x 10 = 2.1 x 3 3 10
3
Two strands of hair have an average mass of
4.34 Two grains of rice have an
average mass of 0.00003 ounces. How much
heavier is the grain of rice than a strand of
hair?
*Remember, you can use your Desmos
calculator from the upper middle of your
screen.
<---Read first.
x 10
−5
.
3.9566 x 10
−5
1.34 x 10−5
3.9566 x 10
−3
4.336 x 10
−3

Answer 1

To determine how much heavier a grain of rice is than a strand of hair, we need to perform the subtraction of the two masses, ensuring they are both in the same scientific notation.

From your problem statement, we have:

1. The average mass of a strand of hair: \( 4.34 \times 10^{-3} \) ounces (this is \( 4.34 \) grams).
2. The average mass of two grains of rice: \( 0.00003 \) ounces. In scientific notation, this can be expressed as \( 3.0 \times 10^{-5} \) ounces.

Now, we need to compare them:

1. Convert both measured quantities into a compatible form for subtraction, ensuring the exponents match if possible. We will convert \( 4.34 \times 10^{-3} \) to have the same exponent as \( 3.0 \times 10^{-5} \).

To do this:

• Change the exponent of \( 4.34 \times 10^{-3} \) to \( 10^{-5} \):

  \[ 4.34 \times 10^{-3} = 4.34 \times 10^{-3} \times \frac{100}{100} = 434 \times 10^{-5} \]

Now we can subtract the coefficients of both quantities: \[ 434 \times 10^{-5} - 3.0 \times 10^{-5} = (434 - 3) \times 10^{-5} = 431 \times 10^{-5} \] To return to standard scientific notation, we can express \( 431 \times 10^{-5} \) as: \[ 4.31 \times 10^{-3} \]

Thus, the difference in mass between the strands of hair and the grains of rice is: \[ 4.31 \times 10^{-3} \text{ ounces} \]

So the strand of hair is heavier than the grains of rice by \( 4.31 \times 10^{-3} \) ounces.