Converting Decimal Fractions to Simple Fractions and Mixed Numbers: Converting to a fraction in its simplest form

To convert the decimal 0.4 to a fraction, follow these steps:

• Step 1: Write the decimal as a fraction.

0.4 as a fraction is $\frac{4}{10}$ because there is one digit after the decimal point.

• Step 2: Simplify the fraction.

To simplify $\frac{4}{10}$, find the greatest common divisor (GCD) of 4 and 10, which is 2.

Divide both the numerator and the denominator by their GCD:

$\frac{4 \div 2}{10 \div 2} = \frac{2}{5}$

Therefore, the fraction $\frac{4}{10}$ simplifies to $\frac{2}{5}$.

Thus, the decimal 0.4 can be expressed as the fraction $\frac{2}{5}$.

To write the decimal 4.6 as a fraction, follow these steps:

• Step 1: Recognize that 4.6 can be written as $\frac{4.6}{1}$.
• Step 2: Multiply both the numerator and the denominator by 10 to eliminate the decimal. This gives you $\frac{46}{10}$.
• Step 3: Simplify the fraction $\frac{46}{10}$ by finding the greatest common divisor (GCD) of 46 and 10, which is 2. Divide both the numerator and the denominator by 2.
• Step 4: Perform the division to simplify: $\frac{46 \div 2}{10 \div 2} = \frac{23}{5}$.

Thus, the decimal 4.6 expressed as a fraction in its simplest form is $\frac{23}{5}$.

To solve the problem of writing 0.04 as a fraction, we will follow these steps:

• Step 1: Identify the decimal and its place value.
• Step 2: Convert the decimal to an equivalent fraction.
• Step 3: Simplify the fraction to its simplest form.

Let's work through each step:

Step 1: The given decimal is 0.04. Recognizing that 0.04 is in the "hundredths" place, we can express it as:

$0.04 = \frac{4}{100}$

Step 2: Next, we simplify the fraction $\frac{4}{100}$. To do this, we find the greatest common divisor (GCD) of 4 and 100, which is 4.

Step 3: Divide the numerator and the denominator by their GCD:

$\frac{4}{100} = \frac{4 \div 4}{100 \div 4} = \frac{1}{25}$

Therefore, the fraction representation of the decimal 0.04, in simplest form, is $\frac{1}{25}$.

To solve the problem of expressing $20.5$ as a fraction and simplifying, we will follow these steps:

• Step 1: Recognize the whole number part: $20$.
• Step 2: Convert the decimal $0.5$ to a fraction. Since $0.5 = \frac{5}{10}$, and dividing the numerator and denominator by their GCD, 5, gives $\frac{1}{2}$.
• Step 3: Combine the whole number and the fraction: $20 \frac{1}{2}$, which is read as $20$ and $\frac{1}{2}$.

Hence, the number $20.5$ as a fraction is $20\frac{1}{2}$.

Therefore, the solution to the problem is $20\frac{1}{2}$.

To solve this problem, we need to convert the decimal $0.35$ into a fraction and simplify it:

• Step 1: Convert the decimal to a fraction. The decimal $0.35$ means that 35 is in the hundredths place. Thus, we write it as $\frac{35}{100}$.
• Step 2: Simplify the fraction $\frac{35}{100}$ by finding the greatest common divisor (GCD) of 35 and 100. The factors of 35 are 1, 5, 7, 35, and the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. The greatest common divisor is 5.
• Step 3: Divide both the numerator and the denominator by 5:
  $\frac{35}{100} = \frac{35 \div 5}{100 \div 5} = \frac{7}{20}$

Therefore, the simplified fraction of $0.35$ is $\frac{7}{20}$.

To convert the decimal 0.45 to a fraction, we follow these steps:

• Step 1: Express the Decimal as a Fraction
  The decimal 0.45 can be expressed as $\frac{45}{100}$ because moving the decimal two places to the right makes the numerator 45, with 100 as the denominator since there are two decimal places.
• Step 2: Simplify the Fraction
  Identify the greatest common divisor (GCD) of 45 and 100. The divisors of 45 are 1, 3, 5, 9, 15, 45, and the divisors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. The largest common divisor is 5.
• Step 3: Divide by the GCD
  Divide both the numerator and denominator by 5:
  $\frac{45}{100} = \frac{45 \div 5}{100 \div 5} = \frac{9}{20}$

Therefore, the simplified fraction corresponding to the decimal 0.45 is $\frac{9}{20}$.

The correct answer from the choices provided is $\frac{9}{20}$, which corresponds to choice 2.

To convert the decimal number 0.58 to a fraction:

• Step 1: Write 0.58 as a fraction with a power of 10 in the denominator. Since there are two decimal places, we write it as:
  $0.58 = \frac{58}{100}$
• Step 2: Simplify the fraction. Find the greatest common divisor (GCD) of 58 and 100. The GCD is 2.
• Step 3: Divide both the numerator and the denominator by their GCD to simplify:
  $\frac{58}{100} = \frac{58 \div 2}{100 \div 2} = \frac{29}{50}$

Therefore, the decimal 0.58 expressed as a fraction in its simplest form is $\frac{29}{50}$.

To solve this problem, let's convert the decimal number 0.66 to a fraction and then reduce it:

Step 1: Convert the decimal to a fraction.
The decimal 0.66 can be expressed as $\frac{66}{100}$ because it has two decimal places. This places the 66 over 100.

Step 2: Simplify the fraction $\frac{66}{100}$.
To simplify, we need to find the greatest common divisor (GCD) of the numerator 66 and the denominator 100.

The prime factorization of 66: $66 = 2 \times 3 \times 11$
The prime factorization of 100: $100 = 2 \times 2 \times 5 \times 5$

The common factor between them is 2. Thus, the GCD is 2.
Now, divide both the numerator and the denominator by the GCD, which is 2.

$\frac{66}{100} = \frac{66 \div 2}{100 \div 2} = \frac{33}{50}$

Therefore, the fraction $\frac{33}{50}$ is the simplest form of 0.66.

The final, reduced fraction is: $\frac{33}{50}$.

To convert the decimal number $0.72$ to a fraction, we need to consider the place value of the decimal.

The number $0.72$ has two decimal places. This means it can be expressed as $\frac{72}{100}$, because the 72 is situated in the hundredths place.

Next, we need to simplify this fraction by finding the greatest common divisor (GCD) of 72 and 100. The GCD of 72 and 100 is 4. We divide both the numerator and the denominator by this GCD:

$\frac{72}{100} = \frac{72 \div 4}{100 \div 4} = \frac{18}{25}$

Thus, the fraction $\frac{18}{25}$ is the simplest form of the decimal $0.72$.

Therefore, the solution to the problem is $\frac{18}{25}$.

To solve this problem, we'll take the following steps:

• Step 1: Convert the decimal to a fraction
• Step 2: Simplify the fraction

Let's work through each step:

Step 1: Convert the decimal to a fraction
The decimal 0.08 can be interpreted as eight hundredths, which means it can be written as the fraction $\frac{8}{100}$. This step uses the place value of the decimal where the hundredths place is equivalent to $\frac{1}{100}$.

Step 2: Simplify the fraction
To simplify $\frac{8}{100}$, we need to find the greatest common divisor (GCD) of 8 and 100. The factors of 8 are 1, 2, 4, 8, and the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. The greatest common factor shared by both is 4.
Divide the numerator and the denominator by the GCD, which is 4: $\frac{8 \div 4}{100 \div 4} = \frac{2}{25}$

Therefore, after converting 0.08 to a fraction and simplifying, the simplest form is $\frac{2}{25}$.