Which fraction is equivalent to 4.05? Write 0.24 as a fraction.
Understand the Problem
The questions are asking us to identify equivalent fractions for the decimal 4.05 and to convert the decimal 0.24 into a fraction. These involve understanding the relationship between decimals and fractions.
Answer
1. None 2. $\frac{24}{100}$
Answer for screen readers

None of the options are equivalent to $4.05$ in simplified form.

Option b) $\frac{24}{100}$ is the correct representation of $0.24$ as a fraction.
Steps to Solve

Convert Decimal 4.05 to Fraction
To convert the decimal $4.05$ into a fraction, write it as $\frac{405}{100}$. This is because $4.05$ has two decimal places, so we multiply both the numerator and denominator by $100$.
$$ 4.05 = \frac{405}{100} $$

Simplify the Fraction for 4.05
Now simplify $\frac{405}{100}$. First, find the greatest common divisor (GCD) of $405$ and $100$.
The GCD is $5$, so we divide both the numerator and denominator by $5$:
$$ \frac{405 \div 5}{100 \div 5} = \frac{81}{20} $$

Identifying Equivalent Fractions
From the options given, we need to check if $\frac{81}{20}$ is equivalent to any of the given fractions. The options are:
 a) $\frac{4}{99}$
 b) $\frac{81}{33}$
 c) $\frac{405}{99}$
Calculate each fraction to see if any equal $\frac{81}{20}$:
 For a) $\frac{4}{99}$: $4 \div 99 \approx 0.0404$ (not equivalent)
 For b) $\frac{81}{33}$: $81 \div 33 \approx 2.4545$ (not equivalent)
 For c) $\frac{405}{99}$: $405 \div 99 \approx 4.0909$ (not equivalent)
Upon checking, only option c) can be further evaluated, but it doesn't equal $4.05$. Thus, none are equivalent to $4.05$ in the simplified form.

Convert Decimal 0.24 to Fraction
To convert $0.24$ to a fraction, write it as $\frac{24}{100}$.
$$ 0.24 = \frac{24}{100} $$

Simplify the Fraction for 0.24
We simplify $\frac{24}{100}$ by finding the GCD, which is $4$:
$$ \frac{24 \div 4}{100 \div 4} = \frac{6}{25} $$
Checking the options given now:
 a) $\frac{8}{33}$
 b) $\frac{24}{100}$
 c) $\frac{2}{9}$
Only option b) is the nonsimplified form of $0.24$.

None of the options are equivalent to $4.05$ in simplified form.

Option b) $\frac{24}{100}$ is the correct representation of $0.24$ as a fraction.
More Information
The decimal $4.05$ can be expressed accurately as $\frac{81}{20}$. While the fraction $\frac{24}{100}$ for $0.24$ can be simplified to $\frac{6}{25}$, it still correctly represents the decimal.
Tips
 Failing to simplify fractions properly after converting from decimals.
 Not properly checking if the alternatives are equivalent, often leading to incorrect selections.