Question

which is the most accurate way to estimate 34% of 605?
\\(\frac{1}{3} \times 600\\)
\\(\frac{3}{4} \times 600\\)
\\(\frac{2}{3} \times 600\\)
\\(\frac{19}{20} \times 600\\)

Explanation:

Step1: Convert percentage to fraction

We know that \(34\%=\frac{34}{100}=\frac{17}{50}\approx\frac{1}{3}\) (since \(\frac{1}{3}\approx0.333\) and \(34\% = 0.34\)), and \(605\approx600\).

Step2: Analyze each option

• For \(\frac{1}{3}\times600\):

Since \(34\%\approx\frac{1}{3}\) and \(605\approx600\), this is a reasonable estimate.

• For \(\frac{3}{4}\times600 = 450\), \(\frac{3}{4}=0.75\) and \(0.75\) is much larger than \(0.34\).
• For \(\frac{2}{3}\times600 = 400\), \(\frac{2}{3}\approx0.667\) which is larger than \(0.34\).
• For \(\frac{19}{20}\times600= 570\), \(\frac{19}{20}=0.95\) which is much larger than \(0.34\).

Answer:

\(\frac{1}{3}\times600\)