Question

question 7
a mustard seed has a mass of about 0.002 gram. a glass jar contains about 4.3602 × 10⁴ seeds.
which is a reasonable estimate of the mass of the mustard seeds in the jar?
(2 × 10⁻²) × (4 × 10⁴) = 8 × 10⁶
(2 × 10⁻²) × (4 × 10⁴) = 8 × 10²
(2 × 10⁻³) × (4 × 10⁴) = 8 × 10¹
(2 × 10⁻³) × (4 × 10⁴) = 8 × 10⁷

Explanation:

Step1: Convert 0.002 to scientific notation

0.002 can be written as \(2\times10^{-3}\) because we move the decimal point 3 places to the right.

Step2: Approximate \(4.3602\times10^{4}\)

We can approximate \(4.3602\times10^{4}\) as \(4\times10^{4}\) for estimation.

Step3: Multiply the two scientific notations

To find the mass of the seeds in the jar, we multiply the mass of one seed by the number of seeds. So we calculate \((2\times10^{-3})\times(4\times10^{4})\). Using the rule of exponents \(a^m\times a^n=a^{m + n}\) and multiplying the coefficients: \(2\times4 = 8\) and \(10^{-3}\times10^{4}=10^{-3 + 4}=10^{1}\). So the result is \(8\times10^{1}\).

Answer:

\((2\times 10^{-3})\times(4\times 10^{4}) = 8\times 10^{1}\) (the option with this expression)