Converting Decimal Fractions to Simple Fractions and Mixed Numbers: From a decimal to a denominator of 10

To solve this problem, we will convert the decimal $1.3$ into a fraction.

Step 1: Identify the whole number and decimal component. The number $1.3$ consists of the whole number $1$ and the decimal $0.3$.

Step 2: Convert the decimal $0.3$ to a fraction. The decimal $0.3$ means three-tenths, which is expressed as the fraction $\frac{3}{10}$.

Step 3: Combine the whole number and the fractional part into a mixed number. The number $0.3$ is converted to $\frac{3}{10}$, and adding the whole number $1$ gives us the mixed number $1 \frac{3}{10}$.

Therefore, when the decimal $1.3$ is expressed as a fraction, it is written as $1 \frac{3}{10}$.

To solve this problem, we'll convert the decimal $2.4$ into a mixed number:

• Step 1: Identify the integer part and the decimal part of $2.4$.
• The integer part is $2$, and the decimal part is $0.4$.
• Step 2: Convert the decimal $0.4$ to a fraction.
• Decimal $0.4$ is equivalent to $\frac{4}{10}$ because the digit $4$ is in the tenth position.
• Step 3: Combine the integer part with the fraction.
• The mixed number is $2\frac{4}{10}$.

Therefore, when $2.4$ is expressed as a mixed number, it is $2\frac{4}{10}$.

To convert the decimal $2.4$ to a mixed number, we need to follow these steps:

• Step 1: Identify the whole number part and the decimal part. Here, the whole number is $2$ and the decimal part is $0.4$.
• Step 2: Convert the decimal part $0.4$ to a fraction. To do this, recognize that $0.4$ can be written as $\frac{4}{10}$ since there is one digit after the decimal point, which implies the denominator is $10$.
• Step 3: Simplify the fraction $\frac{4}{10}$. Divide the numerator and the denominator by their greatest common divisor, which is $2$. Thus, $\frac{4}{10} = \frac{2}{5}$.
• Step 4: Combine the whole number and the simplified fraction to form the mixed number. The whole number $2$ and the fraction $\frac{2}{5}$ together give $2\frac{2}{5}$.

Therefore, the decimal $2.4$ is equivalent to the mixed number $2\frac{2}{5}$.

To solve this problem, we follow these steps:

• Step 1: Identify the given fraction $\frac{26}{10}$.
• Step 2: Perform the division of the numerator by the denominator.

Now, let's work through each step:
Step 1: We have the fraction $\frac{26}{10}$.
Step 2: Divide 26 by 10, which is the same as performing the calculation $26 \div 10$. The result of this operation is 2.6.

Therefore, the solution to the problem is $2.6$.

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

• Step 1: Recognize that the decimal number $1.3$ can be split into its whole number and decimal parts: $1$ and $0.3$.
• Step 2: Convert the decimal part $0.3$ to a fraction. Since $0.3$ is equivalent to $\frac{3}{10}$, we have converted the decimal to a fraction with a denominator of 10.
• Step 3: Combine the whole number part and the fractional part to form a mixed number. Thus, $1.3$ is equivalent to $1\frac{3}{10}$.

Therefore, the solution to the problem is $1\frac{3}{10}$.

To solve this problem, we need to convert the decimal number $8.1$ into a mixed number.

• Step 1: Recognize that the number $8.1$ can be broken into an integer part and a fractional part. The integer part is $8$ and the decimal part is $0.1$.
• Step 2: Convert the decimal part $0.1$ into a fraction. Since $0.1$ is equivalent to $\frac{1}{10}$, we write $0.1 = \frac{1}{10}$.
• Step 3: Combine the integer part and the fractional part to form a mixed number. Thus, $8.1$ can be rewritten as $8 + \frac{1}{10}$ which simplifies to the mixed number $8 \frac{1}{10}$.

Therefore, the solution to the problem is $8 \frac{1}{10}$.

To convert $2.3$ to a mixed number, follow these steps:

• Step 1: Identify the whole number part of the decimal. Here, the whole number is $2$.
• Step 2: Convert the decimal part $0.3$ into a fraction. The decimal $0.3$ can be viewed as $\frac{3}{10}$ because $0.3$ represents 3 tenths.
• Step 3: Combine the whole number and the fractional part to write the mixed number as $2\frac{3}{10}$.

This correctly converts the decimal $2.3$ into the mixed number $2\frac{3}{10}$.

Therefore, the correct answer is $2\frac{3}{10}$.

To solve this problem, we'll convert the decimal number 15.2 into a mixed number:

• Step 1: Identify the whole number: The number 15.2 has a whole part of 15.
• Step 2: Convert the decimal part to a fraction:
  The decimal 0.2 can be expressed as $\frac{2}{10}$.
• Step 3: Simplify the fraction:
  The fraction $\frac{2}{10}$ simplifies to $\frac{1}{5}$ (dividing both numerator and denominator by 2).
• Step 4: Form the mixed number:
  Combine the whole number 15 with the simplified fraction $\frac{1}{5}$ to obtain the mixed number $15\frac{1}{5}$.

Based on the provided choices, the correct answer is choice 2: $15\frac{1}{5}$.

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

• Step 1: Identify the whole number part and the decimal part of $1.2$.
• Step 2: Convert the decimal part $0.2$ into a fraction.
• Step 3: Combine the whole number and the fraction into a mixed number.

Now, let's work through each step:
Step 1: The whole number part is $1$, and the decimal part is $0.2$.
Step 2: Since $0.2 = \frac{2}{10}$, we convert the decimal into the fraction $\frac{2}{10}$.
Step 3: Combining these, we have the mixed number $1\frac{2}{10}$.

Therefore, the solution to converting $1.2$ is $1\frac{2}{10}$, which corresponds to option 3.

To convert the decimal $2.4$ into a mixed number, we'll follow these steps:

• Step 1: Convert the decimal part $0.4$ into a fraction.
• Step 2: Simplify the fraction.
• Step 3: Combine with the whole number.

Let's work through each step:
Step 1: Recognize that $0.4$ means $\frac{4}{10}$ because there is one digit after the decimal point, placing it into tenths.
Step 2: Simplify $\frac{4}{10}$ by dividing both the numerator and denominator by their GCD, which is 2. This gives us $\frac{2}{5}$.
Step 3: Combine the whole number $2$ with the fraction $\frac{2}{5}$ to form the mixed number $2\frac{2}{5}$.

Therefore, the conversion of $2.4$ to a mixed number is $2\frac{2}{5}$.

To convert the decimal $2.9$ to a mixed number, follow these steps:

• Step 1: Identify the whole number part. Here, the whole number is $2$.
• Step 2: Convert the decimal part to a fraction. The decimal part of $2.9$ is 0.9, which can be written as $\frac{9}{10}$ since the digit 9 is in the tenths place.
• Step 3: Combine the whole number and the fraction to form the mixed number.

Therefore, the decimal $2.9$ can be expressed as the mixed number $\mathbf{2\frac{9}{10}}$.

The correct choice from the given options is: $2\frac{9}{10}$.

We are tasked with converting the decimal number $1.9$ into a mixed number.

• Step 1: Identify the whole number part of $1.9$. The digit to the left of the decimal point is $1$.
• Step 2: Identify the fractional part of $1.9$. The digit to the right of the decimal point is $9$. This represents $\frac{9}{10}$.
• Step 3: Combine the whole number and the fractional part to form a mixed number. Therefore, $1.9 = 1\frac{9}{10}$.

Hence, the mixed number equivalent of the decimal $1.9$ is $1\frac{9}{10}$.

To solve this problem, we'll convert the decimal $6.2$ into a mixed number. Here's how:

• Step 1: Identify the whole number in the decimal. In $6.2$, the whole number is $6$.
• Step 2: Extract the decimal fraction. The fraction part is $0.2$.
• Step 3: Convert $0.2$ into a fraction. Since $0.2$ is 2 tenths, it is expressed as $\frac{2}{10}$.
• Step 4: Simplify $\frac{2}{10}$. This fraction can be simplified to $\frac{1}{5}$, but as we're asked for a denominator of 10, we will keep it as $\frac{2}{10}$.
• Step 5: Combine the whole number and the fractional part. The mixed number is $6 \frac{2}{10}$.

Therefore, the correct mixed number form of the decimal 6.2 is $6 \frac{2}{10}$.

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

• Step 1: Identify the parts of the decimal number $1.2$.
• Step 2: Convert the decimal part to a fraction.
• Step 3: Form a mixed number using the integer and the fractional parts.

Now, let's work through each step:
Step 1: The decimal number $1.2$ consists of an integer part $1$ and a decimal part $0.2$.
Step 2: The decimal $0.2$ translates to the fraction $\frac{2}{10}$, since the digit 2 is in the tenths place.
Step 3: Combine the integer part $1$ with the fractional part $\frac{2}{10}$ to form the mixed number $1\frac{2}{10}$.

Therefore, the solution to the problem is $1\frac{2}{10}$.

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

• Step 1: Identify the decimal and its components.
• Step 2: Convert the decimal part to a fraction.
• Step 3: Combine the whole number and fraction into a mixed number.

Now, let's work through each step:
Step 1: The given decimal is $7.3$. This can be separated into the whole number $7$ and the decimal fraction $.3$.
Step 2: To convert $.3$ into a fraction, we observe that it represents three tenths, which is $\frac{3}{10}$.
Step 3: Combine the whole number and the fractional part to form a mixed number. Thus, $7.3$ becomes $7\frac{3}{10}$ as a mixed number.

Therefore, the solution to the problem is $7\frac{3}{10}$.

To solve this problem, we need to convert the decimal $3.1$ into a mixed number:

• Step 1: Recognize the decimal number $3.1$ consists of a whole number part $3$ and a decimal part $0.1$.
• Step 2: Convert the decimal part $0.1$ to a fraction. The decimal $0.1$ is equivalent to $\frac{1}{10}$.
• Step 3: Combine the whole number part with the fractional part to form the mixed number, which gives us $3\frac{1}{10}$.

Therefore, the decimal $3.1$ is equivalent to the mixed number $3\frac{1}{10}$.

The correct choice is option 1: $3\frac{1}{10}$.

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

• Step 1: Identify the integer and decimal parts of $1.3$.
• Step 2: Convert the decimal $0.3$ to a fraction.
• Step 3: Combine the integer and fractional parts into a mixed number.

Let’s work through each step:
Step 1: The integer part of $1.3$ is $1$, and the decimal part is $0.3$.
Step 2: The decimal $0.3$ can be converted to the fraction $\frac{3}{10}$ because it signifies three-tenths.
Step 3: Combining the integer part with the fractional part, we get the mixed number $1\frac{3}{10}$.

Therefore, the solution to the problem is $1\frac{3}{10}$.

To convert the decimal $6.2$ into a fraction, follow these steps:

• Step 1: Separate $6.2$ into its whole number and decimal parts. Here, 6 is the whole number, and 0.2 is the decimal part.
• Step 2: Convert $0.2$ into a fraction. Since $0.2 = \frac{2}{10}$, simplify it to $\frac{1}{5}$.
• Step 3: Combine the whole number and the simplified fraction to create the mixed number $6 \frac{1}{5}$.
• Step 4: Convert the mixed number to an improper fraction. Multiply the whole number (6) by the denominator (5) and add the numerator (1):
$6 \times 5 + 1 = 31$
• Thus, $6 \frac{1}{5}$ as an improper fraction is $\frac{31}{5}$.

Thus, the decimal $6.2$ is equivalent to the fraction $\frac{31}{5}$. Comparing this with the provided choices, the correct choice is option 2: $\frac{31}{5}$.

To convert the decimal $1.1$ into a fraction, we will follow these steps:

• Step 1: Express $1.1$ as a sum: $1 + 0.1$.
• Step 2: Convert each part to a fraction.
• Step 3: Simplify and add the fractions.

Now, let's work through each step:

Step 1: Express $1.1$ as:

$1.1 = 1 + 0.1$

Step 2: Convert each part to a fraction:
$1$ can be written as $\frac{10}{10}$, and $0.1 = \frac{1}{10}$.

Step 3: Add the fractions:

$\frac{10}{10} + \frac{1}{10} = \frac{10 + 1}{10} = \frac{11}{10}$

Therefore, the decimal $1.1$ as a fraction is $\frac{11}{10}$.