Question

mixed word problems scientific notation
question
at a certain lab, the average mass of one ant is measured to be $2.9 \times 10^{-6}$ kilograms. use scientific notation to express the mass of 60 ants.
answer
attempt 1 out of 2
answer: $\square \times 10^{\square}$ kilograms

Explanation:

Step1: Find total mass of 60 ants

To find the mass of 60 ants, we multiply the mass of one ant by 60. The mass of one ant is \(2.9\times10^{-6}\) kilograms. So we calculate \(2.9\times10^{-6}\times60\).
First, multiply the coefficients: \(2.9\times60 = 174\).
Then, keep the power of 10: \(174\times10^{-6}\).

Step2: Convert to proper scientific notation

Scientific notation requires the coefficient to be between 1 and 10. So we rewrite 174 as \(1.74\times10^{2}\).
Now substitute back into the expression: \(1.74\times10^{2}\times10^{-6}\).
When multiplying powers of 10, we add the exponents: \(10^{2 + (-6)}=10^{-4}\).
So the expression becomes \(1.74\times10^{-4}\).

Answer:

\(1.74\times10^{-4}\)