Converting Decimal Fractions to Simple Fractions and Mixed Numbers: Conversion from non-round denominator

To solve this problem, we'll follow these steps:

• Step 1: Convert the fraction by adjusting its denominator to a base of 100.
• Step 2: Scale the fraction accordingly and compute the equivalent decimal.
• Step 3: Compare to the given choices and confirm the result.

Let's work through these steps:
Step 1: We have the fraction $\frac{2}{5}$. To convert 5 to 100, multiply both the numerator and the denominator by 20, because $5 \times 20 = 100$.

Step 2: Multiply the numerator and denominator to get $\frac{40}{100}$.

Step 3: The fraction $\frac{40}{100}$ can be written as a decimal:
$40$ divided by $100$ is equal to $0.4$.

Therefore, the solution to the problem is 0.4.

To solve this problem, we'll express the fraction $\frac{1}{2}$ as a decimal following these steps:

• Step 1: Begin with the fraction $\frac{1}{2}$.
• Step 2: To convert this fraction to a denominator of 100, multiply the numerator and the denominator by 50:

$\frac{1 \times 50}{2 \times 50} = \frac{50}{100}$

This fraction is read as 50 hundredths, which converts directly to the decimal form:

$0.5$

Therefore, the decimal representation of the fraction $\frac{1}{2}$ is 0.5.

To solve this problem, we'll utilize multiplication to simplify the conversion process:

• Step 1: Begin with $\frac{3}{20}$.
• Step 2: Identify that multiplying $\frac{3}{20}$ by $\frac{5}{5}$ (which is 1, thus does not change the value) will yield a fraction with a denominator of 100: $\frac{3 \times 5}{20 \times 5} = \frac{15}{100}$.
• Step 3: A denominator of 100 allows straightforward conversion to decimal, with $\frac{15}{100} = 0.15$.

Therefore, the fraction $\frac{3}{20}$ converts to a decimal as 0.15.

This calculation aligns with the answer choice provided, making option : 0.15 the correct one.

To convert $\frac{4}{25}$ into a decimal, we can make the denominator a power of 10. Follow these steps:

• Step 1: Determine the conversion factor needed to change the denominator (25) to 100. Since $25 \times 4 = 100$, the conversion factor is 4.
• Step 2: Multiply both the numerator and the denominator of the fraction by this conversion factor.
  $\frac{4 \times 4}{25 \times 4} = \frac{16}{100}$
• Step 3: Convert the fraction $\frac{16}{100}$ directly into a decimal. Since 100 is the base of the decimal system, $\frac{16}{100} = 0.16$.

Therefore, the decimal representation of $\frac{4}{25}$ is 0.16.

To solve the problem of converting $\frac{11}{200}$ into a decimal, we will scale the fraction so the denominator becomes 1000, which facilitates easier conversion to a decimal number.

First, observe that:

• The given fraction is $\frac{11}{200}$.
• We want the denominator to be a power of 10, such as 1000.
• To do this, multiply both the numerator and the denominator by 5:

$\frac{11 \times 5}{200 \times 5} = \frac{55}{1000}$

Having the fraction $\frac{55}{1000}$, it is straightforward to convert it to a decimal by placing the decimal point three places from the right in the numerator, because 1000 has three zeros.

This results in the decimal number:

$0.055$

Therefore, the decimal representation of $\frac{11}{200}$ is 0.055.

To solve this problem, we'll follow these steps:

• Step 1: Directly divide the numerator by the denominator.
• Step 2: Perform long division to find the decimal equivalent.
• Step 3: Use equivalent fractions to line up the denominator with a power of 10, like 100.

Now, let's work through each step:

Step 1: The fraction given is $\frac{5}{4}$.

Step 2: Perform the long division:
Divide 5 by 4:

• 4 goes into 5 once, which gives us a whole number of 1. The remainder is 1.
• Bring down a 0 to make 10; 4 goes into 10 twice, giving a decimal value 2 (0.2) and a remainder of 2.
• Bring down another 0 to make 20; 4 goes into 20 exactly 5 times, completing the calculation with no remainder.

This results in a decimal value of 1.25.

Step 3: Convert it to a fraction with a denominator of 100:
- Multiply by 25 to make an equivalent fraction $\frac{5 \times 25}{4 \times 25} = \frac{125}{100}$, which directly converts to 1.25 in decimal.

Therefore, the solution to the problem is 1.25.

To convert the fraction $\frac{22}{20}$ into a decimal, we will perform the following steps:

• Step 1: Simplify the fraction.
  The fraction $\frac{22}{20}$ can be simplified by dividing both the numerator and the denominator by 2, the greatest common divisor.
  This results in $\frac{11}{10}$.
• Step 2: Convert the simplified fraction to a decimal.
  Since $\frac{11}{10}$ is the same as 11 divided by 10, we calculate $11 \div 10 = 1.1$.

Therefore, the decimal form of $\frac{22}{20}$ is $1.1$.

Based on the provided answer choices, the correct choice is 1.1 (Choice 1).

The solution to the problem is $1.1$.

To solve this problem, we'll follow this approach:

• Step 1: Identify the given fraction: $\frac{13}{2}$.
• Step 2: Perform long division to convert the fraction into a decimal.
• Step 3: Alternatively, understand it as $\frac{26}{4}$ or by direct interpretation gain conversion into a decimal.

Now, let's work through each step:

Step 1: We have the fraction $\frac{13}{2}$.

Step 2: Divide 13 by 2 using long division:

When you divide 13 by 2, 2 goes into 13 six times (since $6 \times 2 = 12$), leaving a remainder of 1. Bring down the decimal point and continue division. Hence, 10 divided by 2 gives 5. Therefore, the decimal equivalent of $\frac{13}{2}$ is $6.5$.

Step 3: Verification via mixed conversion: Recognizing $\frac{13}{2} = 6 \frac{1}{2} = 6.5$.

Therefore, the solution to convert $\frac{13}{2}$ into a decimal is $\textbf{6.5}$.

Hence, the correct choice among the given options is: \textbf{6.5}

To solve this problem, we'll focus on converting the fraction $\frac{8}{5}$ into a decimal. Let's follow these steps:

• Step 1: Direct division of the numerator by the denominator.
• Step 2: Alternative approach - adjusting the fraction to a denominator of 100.
• Step 3: Verification through comparison of methods.

Now, let's work through each step:

Step 1: Divide 8 by 5. Performing this division,

$\frac{8}{5} = 8 \div 5 = 1.6$.

Step 2: Alternatively, adjust to a denominator of 100. Multiply both the numerator and the denominator by 20:

$\frac{8}{5} = \frac{8 \times 20}{5 \times 20} = \frac{160}{100}$.

Converting $\frac{160}{100}$ to a decimal gives us 1.6.

Through both methods, we verify that the decimal representation of $\frac{8}{5}$ is 1.6.

Thus, the solution to the problem is 1.6.