Question

(from lesson 2.12) xenia converted 3/4 to a decimal and got 1.3. she thought this looked wrong. explain to her what she might have done wrong. then show the work she should have done and provide an answer. for additional support, refer to the methods & meanings box “fraction ⇨ decimal ⇨ percent” on page 230.

Explanation:

Step1: Recall fraction to decimal conversion

To convert a fraction \(\frac{a}{b}\) to a decimal, we perform the division \(a\div b\). Here, the fraction is \(\frac{3}{4}\) (assuming a typo and it's \(\frac{3}{4}\) instead of \(\frac{3}{}\) as the problem seems to have a formatting issue; likely \(\frac{3}{4}\) to decimal). So we do \(3\div4\).
\(3\div4 = 0.75\)

Step2: Analyze Xenia's mistake

If Xenia got \(1.3\), she likely misperformed the division. Maybe she did \(4\div3\) (which is approximately \(1.333\)) instead of \(3\div4\). The correct conversion of \(\frac{3}{4}\) is dividing 3 by 4, not 4 by 3.

Step3: Correct work

To correctly convert \(\frac{3}{4}\) to a decimal:
Divide 3 by 4. Since 4 goes into 3 zero times, we add a decimal point and a zero, making it 30. 4 goes into 30 seven times (\(4\times7 = 28\)), subtract 28 from 30 to get 2. Add another zero to make it 20. 4 goes into 20 five times (\(4\times5 = 20\)). So \(3\div4 = 0.75\).

Answer:

Xenia likely divided the numerator and denominator in the wrong order (did \(4\div3\) instead of \(3\div4\)). The correct decimal for \(\frac{3}{4}\) is \(0.75\).