Question

a tomato has a mass of 100 grams. the mass of an ant is 4.0×10⁻³ gram. the mass of the tomato is how many times greater than the mass of the ant? 2.5×10⁻² 2.5×10⁻¹ 2.5×10³ 2.5×10⁴

Explanation:

Step1: Set up the division

To find out how many times the mass of the tomato is greater than the mass of the ant, we divide the mass of the tomato by the mass of the ant. The mass of the tomato is 100 grams which can be written as $1\times10^{2}$ grams, and the mass of the ant is $4.0\times 10^{-3}$ grams. So the calculation is $\frac{1\times 10^{2}}{4.0\times 10^{-3}}$.

Step2: Use the rule of exponents for division

When dividing numbers in scientific - notation $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$. Here, $a = 1$, $b = 4$, $m = 2$, and $n=-3$. First, $\frac{1}{4}=0.25$. Then, $m - n=2-(-3)=2 + 3=5$. So $\frac{1\times 10^{2}}{4.0\times 10^{-3}}=0.25\times10^{5}$.

Step3: Convert to proper scientific - notation

$0.25\times10^{5}$ can be rewritten as $2.5\times10^{-1}\times10^{5}$. Using the rule of exponents $a^{m}\times a^{n}=a^{m + n}$, we have $2.5\times10^{-1 + 5}=2.5\times10^{4}$.

Answer:

$2.5\times 10^{4}$