Question

choose the best approximation of the mass of a worker bee. choose 1 answer: (a) $1cdot10^{-4}$ kg (b) $1cdot10^{-3}$ kg an african elephant has a mass of 8139 kg. choose the best approximation of the mass of an african elephant. choose 1 answer: (a) $8cdot10^{3}$ kg (b) $8cdot10^{4}$ kg approximately how many times as large is the mass of an african elephant as the mass of a worker bee? choose 1 answer: (a) $8cdot10^{6}$ (b) $8cdot10^{7}$

Explanation:

Step1: Approximate mass of worker - bee

Worker - bees are very small. Their mass is around $1\times10^{-4}$ kg. So for the mass of a worker - bee, the best approximation is $1\times10^{-4}$ kg.

Step2: Approximate mass of African elephant

The mass of an African elephant is 8139 kg. In scientific notation, $8139 = 8.139\times10^{3}\approx8\times10^{3}$ kg.

Step3: Calculate mass ratio

To find out how many times the mass of an African elephant is larger than that of a worker - bee, we divide the mass of the elephant by the mass of the bee. Let $m_{e}$ be the mass of the elephant and $m_{b}$ be the mass of the bee. $m_{e}=8\times 10^{3}$ kg and $m_{b}=1\times10^{-4}$ kg. Then $\frac{m_{e}}{m_{b}}=\frac{8\times 10^{3}}{1\times10^{-4}}=8\times10^{3 - (- 4)}=8\times10^{7}$.

Answer:

A. $1\times10^{-4}$ kg
A. $8\times10^{3}$ kg
B. $8\times10^{7}$