Question

which is the most accurate way to estimate 65% of 523?
\\(\frac{1}{4} \times 520\\) \\(\frac{2}{3} \times 510\\)
\\(\frac{1}{2} \times 520\\) \\(\frac{1}{3} \times 510\\)

Explanation:

Step1: Approximate percentage and number

• Approximate \(65\%\) to a fraction. \(65\%=\frac{65}{100}=\frac{13}{20}\approx\frac{2}{3}\) (since \(\frac{2}{3}\approx0.67\) and \(\frac{13}{20} = 0.65\)).
• Approximate \(523\) to \(510\) (a number that is divisible by \(3\)).

Step2: Calculate the estimate

• Using the approximation \(\frac{2}{3}\times510\).
• Calculate \(\frac{2}{3}\times510=2\times170 = 340\).
• If we calculate the actual value \(65\%\text{ of }523=0.65\times523=(0.6 + 0.05)\times523=0.6\times523+0.05\times523=313.8+26.15 = 339.95\approx340\)

Answer:

\(\frac{2}{3}\times510\)