Question

A strand of hair has an average mass of 2.7 × 10−5
ounces. A grain of rice has an average mass of 0.002 ounces. How much heavier is a grain of rice than a strand of hair? Express your answer in scientific notation. (1 point)
a × 10b

a =

b =

Answer 1

To determine 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:
- Average mass of a strand of hair = \( 2.7 \times 10^{-5} \) ounces
- Average mass of a grain of rice = \( 0.002 \) ounces

First, we convert \( 0.002 \) ounces into scientific notation:
\[
0.002 = 2.0 \times 10^{-3} \text{ ounces}
\]

Now, we will subtract the mass of the strand of hair from the mass of the grain of rice:
\[
2.0 \times 10^{-3} - 2.7 \times 10^{-5}
\]

To perform this subtraction, we need a common exponent:

Convert \( 2.0 \times 10^{-3} \) to a form that includes \( 10^{-5} \):
\[
2.0 \times 10^{-3} = 2.0 \times 10^{-3} \times \frac{100}{100} = 200 \times 10^{-5}
\]

Now we can perform the subtraction:
\[
200 \times 10^{-5} - 2.7 \times 10^{-5} = (200 - 2.7) \times 10^{-5} = 197.3 \times 10^{-5}
\]

Next, we express \( 197.3 \) in proper scientific notation:
\[
197.3 \times 10^{-5} = 1.973 \times 10^{-3} \text{ ounces} \quad (\text{moving the decimal point left by 2 places increases the exponent by 2})
\]

Now we express the answer as \( a \times 10^b \):
- \( a = 1.973 \)
- \( b = -3 \)

Thus,
\[
a = 1.973, \quad b = -3
\]