Question

1. how do you write 3.53 as a fraction?

$3\frac{5}{13}$ $3\frac{11}{20}$ $3\frac{7}{10}$ $3\frac{8}{15}$
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Explanation:

Step1: Let \( x = 3.\overline{53} \)

Let the repeating decimal be \( x \), so \( x = 3.535353\cdots \)

Step2: Multiply by 100

Since there are 2 repeating digits, multiply \( x \) by 100: \( 100x = 353.535353\cdots \)

Step3: Subtract

Subtract \( x \) from \( 100x \): \( 100x - x = 353.5353\cdots - 3.5353\cdots \)
Which simplifies to \( 99x = 350 \)

Step4: Solve for \( x \)

Divide both sides by 99: \( x=\frac{350}{99}=3\frac{53}{99}\)? Wait, no, wait, let's check the options. Wait, maybe I made a mistake. Wait the options are \( 3\frac{5}{13} \), \( 3\frac{11}{20} \), \( 3\frac{7}{10} \), \( 3\frac{8}{15} \). Wait, maybe the decimal is \( 3.5\overline{3} \)? Wait the original problem is \( 3.5\overline{3} \)? Let's re - evaluate. Let \( x = 3.5\overline{3} \), so \( x = 3.5333\cdots \)
Multiply by 10: \( 10x = 35.333\cdots \)
Multiply by 100: \( 100x = 353.333\cdots \)
Subtract \( 10x \) from \( 100x \): \( 100x - 10x=353.333\cdots - 35.333\cdots \)
\( 90x = 318 \)
\( x=\frac{318}{90}=\frac{53}{15}=3\frac{8}{15} \)? Wait no, \( 318\div90 = \frac{318\div6}{90\div6}=\frac{53}{15}\approx3.5333 \), and \( 3\frac{8}{15}=\frac{3\times15 + 8}{15}=\frac{53}{15}\approx3.5333 \). Wait, maybe the original decimal is \( 3.5\overline{3} \). Let's check the options:

• \( 3\frac{5}{13}=\frac{3\times13 + 5}{13}=\frac{44}{13}\approx3.3846 \)
• \( 3\frac{11}{20}=\frac{3\times20+11}{20}=\frac{71}{20} = 3.55 \)
• \( 3\frac{7}{10}=\frac{37}{10}=3.7 \)
• \( 3\frac{8}{15}=\frac{53}{15}\approx3.5333 \)

Wait, maybe the problem is \( 3.5\overline{3} \). Let's do it again. Let \( x = 3.5\overline{3}=3.5333\cdots \)
\( 10x = 35.333\cdots \)
\( 100x = 353.333\cdots \)
\( 100x-10x = 353.333\cdots - 35.333\cdots=318 \)
\( 90x = 318 \)
\( x=\frac{318}{90}=\frac{53}{15}=3\frac{8}{15} \)

Wait, but let's check the options. The fourth option is \( 3\frac{8}{15} \). Alternatively, maybe the decimal is \( 3.53 \) (non - repeating). Wait \( 3.53=\frac{353}{100}=3\frac{53}{100} \), but that's not an option. So the correct approach for the repeating decimal \( 3.5\overline{3} \) gives \( 3\frac{8}{15} \). Wait, let's check \( 3\frac{8}{15} \): \( 8\div15 = 0.5333\cdots \), so \( 3 + 0.5333\cdots=3.5333\cdots=3.5\overline{3} \). So the correct option is \( 3\frac{8}{15} \) (the fourth option). Wait, but let's check the options again. The options are:

1. \( 3\frac{5}{13} \)
2. \( 3\frac{11}{20} \)
3. \( 3\frac{7}{10} \)
4. \( 3\frac{8}{15} \)

Let's calculate each:

• \( 3\frac{5}{13}=\frac{44}{13}\approx3.3846 \)
• \( 3\frac{11}{20}=\frac{71}{20}=3.55 \)
• \( 3\frac{7}{10}=3.7 \)
• \( 3\frac{8}{15}=\frac{53}{15}\approx3.5333 \)

If the number is \( 3.5\overline{3} \) (3.5333...), then \( 3\frac{8}{15} \) is correct.

Answer:

\( 3\frac{8}{15} \) (the fourth option, i.e., the option with \( 3\frac{8}{15} \))