Question

a water desalination plant can produce $2 \times 10^6$ gallons of water in one day. how many gallons can it produce in 89 days? write your answer in scientific notation. \boxed{} gallons

Explanation:

Step1: Identify the daily production and number of days

Daily production: \(2 \times 10^{6}\) gallons, Number of days: \(89\)

Step2: Multiply daily production by number of days

Total production = \(2 \times 10^{6} \times 89\)
First, calculate \(2\times89 = 178\)
So, Total production = \(178\times 10^{6}\)

Step3: Convert to scientific notation

Scientific notation requires a number between \(1\) and \(10\) multiplied by a power of \(10\).
\(178\times 10^{6}=1.78\times 10^{2}\times 10^{6}\)
Using the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\), we get \(1.78\times 10^{2+6}=1.78\times 10^{8}\)

Answer:

\(1.78\times 10^{8}\)