Question

which number fits between 1/4 and 1/3? hint: change to decimals first! 3/5 33% √12

Explanation:

Step1: Convert \( \frac{1}{4} \) to decimal

To convert a fraction to a decimal, divide the numerator by the denominator. So, \( \frac{1}{4}=1\div4 = 0.25 \).

Step2: Convert \( \frac{1}{3} \) to decimal

\( \frac{1}{3}=1\div3\approx0.333\cdots \) (it is a repeating decimal).

Step3: Analyze the given options

• Option 1: \( \frac{3}{5}=3\div5 = 0.6 \). Since \( 0.6>0.333\cdots \), it is not between \( 0.25 \) and \( 0.333\cdots \).
• Option 2: \( 33\%=\frac{33}{100}=0.33 \). Now, compare \( 0.25 \), \( 0.33 \), and \( 0.333\cdots \). We have \( 0.25<0.33<0.333\cdots \), so \( 33\% \) is between \( \frac{1}{4} \) and \( \frac{1}{3} \).
• Option 3: \( \sqrt{2}\approx1.414 \). Since \( 1.414 > 0.333\cdots \), it is not between \( 0.25 \) and \( 0.333\cdots \).

Answer:

33%