Question

a worker bee has a mass of 1 · 10^(-4) kg. there are 4 · 10^4 worker bees living in one hive. what is the mass of all the worker bees in the hive together? write your answer in scientific notation.

Explanation:

Step1: Recall mass - multiplication formula

To find the total mass of all worker bees, we multiply the mass of one worker bee by the number of worker bees. The mass of one worker bee is $m = 1\times10^{- 4}$ kg and the number of worker bees is $n=4\times10^{4}$.
The formula for the total mass $M$ is $M = m\times n$.

Step2: Substitute values and use exponent rules

Substitute $m = 1\times10^{-4}$ and $n = 4\times10^{4}$ into the formula:
$M=(1\times10^{-4})\times(4\times10^{4})$.
Using the rule of exponents $a^{m}\times a^{n}=a^{m + n}$ and the commutative - property of multiplication $(a\times b)\times(c\times d)=(a\times c)\times(b\times d)$, we have $M=(1\times4)\times(10^{-4}\times10^{4})$.
Since $a^{m}\times a^{n}=a^{m + n}$, then $10^{-4}\times10^{4}=10^{-4 + 4}=10^{0}=1$. And $1\times4 = 4$. So $M = 4\times1=4$ kg.
In scientific notation, $4$ kg can be written as $4\times10^{0}$ kg.

Answer:

$4\times10^{0}$ kg