Question

Question
A science class is comparing the average mass of very small objects.

A single strand of human hair has an average mass of 3 × 10⁻⁶ ounces.

A single grain of rice has an average mass of 0.002 ounces.

The students want to know how much heavier the grain of rice is than the strand of hair, in ounces.

Which of the following is the correct difference, expressed in scientific notation?

(1 point)
Responses

5 × 10⁻⁶

5 × 10⁻⁶

2.003 × 10⁻³

2.003 × 10⁻³

1.97 × 10⁻⁶

1.97 × 10⁻⁶

1.997 × 10⁻³

Answer 1

To find out how much heavier the grain of rice is than the strand of hair, we will subtract the mass of the strand of hair from the mass of the grain of rice.

1. The mass of a single strand of human hair: \( 3 \times 10^{-6} \) ounces
2. The mass of a single grain of rice: \( 0.002 \) ounces, which can also be expressed in scientific notation as \( 2 \times 10^{-3} \) ounces.

Now, we perform the subtraction:

\[
2 \times 10^{-3} - 3 \times 10^{-6}
\]

To subtract these two values, we need to express both values with the same exponent. Let's express \( 2 \times 10^{-3} \) in terms of \( 10^{-6} \):

\[
2 \times 10^{-3} = 2000 \times 10^{-6}
\]

Now we can perform the subtraction:

\[
2000 \times 10^{-6} - 3 \times 10^{-6} = 1997 \times 10^{-6}
\]

Now, we can express \( 1997 \times 10^{-6} \) in scientific notation:

\[
1997 \times 10^{-6} = 1.997 \times 10^{-3}
\]

Thus, the correct difference in scientific notation is:

\[
1.997 \times 10^{-3}
\]

So the answer is:

**1.997 × 10⁻³**