Question

The largest mammal, a blue whale, has a weight of \(1.3 \times 10^{5}\) kilograms. The smallest mammal, a pygmy shrew, has a weight of \(2.0 \times 10^{-3}\) kilogram. What is the ratio of the weight of a blue whale to the weight of a pygmy shrew?

Short answer

The ratio of the weight of a blue whale to a pygmy shrew is \(6.5 \times 10^{7}\).

Step-by-step solution

Identify the Given Values

The weight of the blue whale is \(1.3 \times 10^{5}\) kg and the weight of the pygmy shrew is \(2.0 \times 10^{-3}\) kg.

Set Up the Ratio

The ratio of the weight of a blue whale to a pygmy shrew is expressed as \(\frac{weight of blue whale}{weight of pygmy shrew}\).

Substitute the given values into the Ratio

Substitute the given weights into the ratio. This gives: \(\frac{1.3 \times 10^{5}}{2.0 \times 10^{-3}}\).

Perform the Calculation

Perform the division operation to obtain the ratio. When you divide \(1.3 \times 10^{5}\) by \(2.0 \times 10^{-3}\), you get \(6.5 \times 10^{7}\)