Which fraction is equivalent to 4.05? Write 0.24 as a fraction.

Steps to Solve

1. 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 $100$.

   $$ 4.05 = \frac{405}{100} $$

2. 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 $5$:

   $$ \frac{405 \div 5}{100 \div 5} = \frac{81}{20} $$

3. 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.

4. Convert Decimal 0.24 to Fraction

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

   $$ 0.24 = \frac{24}{100} $$

5. 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 non-simplified form of $0.24$.