Converting Decimal Fractions to Simple Fractions and Mixed Numbers: Convert a fraction with a denominator greater than 100 to a decimal

To solve the mixed number $2\frac{3}{300}$, we will convert the fractional part $\frac{3}{300}$ into a decimal:

• Step 1: Calculate the decimal equivalent of $\frac{3}{300}$. We do this by performing the division.
  $\frac{3}{300} = 3 \div 300 = 0.01$
• Step 2: Add the whole number to this result.
  The whole number component is $2$, and adding the fractional decimal gives $2 + 0.01 = 2.01$.

Therefore, the decimal representation of $2\frac{3}{300}$ is $2.01$.

Thus, the solution to the problem is $2.01$.

To solve this problem, follow these steps:

• Step 1: Simplify the fraction $\frac{15}{150}$.
• Step 2: Convert the simplified fraction to a decimal.
• Step 3: Add the decimal to the whole number $2$.

Now, let's work through each step in detail:

Step 1: Simplify the fraction $\frac{15}{150}$.
To simplify the fraction, divide both the numerator ($15$) and the denominator ($150$) by their greatest common divisor, which is $15$. Thus, we have:

Step 2: Convert the simplified fraction $\frac{1}{10}$ to a decimal.
The fraction $\frac{1}{10}$ is directly equivalent to the decimal $0.1$.

Step 3: Combine this decimal with the whole number $2$.
Add the decimal $0.1$ to the whole number $2$:

Therefore, the solution to the problem is $2.1$.

To convert the fraction $\frac{30}{150}$ into a decimal, let's follow these steps:

• Step 1: Simplify the fraction $\frac{30}{150}$ by finding the greatest common divisor (GCD) of 30 and 150, which is 30.
• Step 2: Divide both the numerator and the denominator by the GCD. So, $\frac{30}{150} = \frac{30 \div 30}{150 \div 30} = \frac{1}{5}$.
• Step 3: Convert the simplified fraction $\frac{1}{5}$ to a decimal by performing the division 1 divided by 5.

Now let's do the division:
Step 3: $\frac{1}{5} = 0.2$. Performing the division gives 0.2 as the result.

Therefore, the solution to the problem is $0.2$.

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

• Step 1: Simplify the fraction $\frac{54}{900}$.
• Step 2: Convert the simplified fraction to a decimal.
• Step 3: Add the decimal to the integer part of the mixed number.

Let's proceed with the solution:

Step 1: Simplify the fraction $\frac{54}{900}$.

To simplify, find the greatest common divisor (GCD) of 54 and 900. Here, $\text{GCD}(54, 900) = 18$. Therefore, we can divide both the numerator and the denominator by 18: $\frac{54}{900} = \frac{54 \div 18}{900 \div 18} = \frac{3}{50}$

Step 2: Convert $\frac{3}{50}$ to a decimal.

To do this, recognize that $\frac{3}{50}$ can be converted by first transforming the denominator 50 into 100, common for decimal representation: $\frac{3}{50} = \frac{3 \times 2}{50 \times 2} = \frac{6}{100} = 0.06$

Step 3: Add the decimal to the whole number.

Now add the decimal $0.06$ to the whole number $2$: $2 + 0.06 = 2.06$

Therefore, the conversion of the mixed fraction $2\frac{54}{900}$ to a decimal is $\mathbf{2.06}$.

To convert the fraction $\frac{25}{250}$ to a decimal, follow these steps:

• Step 1: Simplify the fraction. To simplify $\frac{25}{250}$, find the greatest common divisor (GCD) of 25 and 250, which is 25.
• Step 2: Divide both the numerator and denominator by their GCD.
  $\frac{25}{250} = \frac{25 \div 25}{250 \div 25} = \frac{1}{10}$
• Step 3: Convert the simplified fraction $\frac{1}{10}$ to a decimal. The decimal form of $\frac{1}{10}$ is 0.1.

Therefore, the decimal equivalent of the fraction $\frac{25}{250}$ is $0.1$.

Among the choices provided, $0.1$ matches the computed answer.

To convert the fraction $\frac{30}{1000}$ to a decimal:

• Step 1: Recognize the fraction $\frac{30}{1000}$ has a direct conversion due to the denominator being a power of ten, which makes it straightforward to convert directly to a decimal.
• Step 2: Divide the numerator by the denominator: $\frac{30}{1000} = 30 \div 1000$.
• Step 3: Perform the division: When dividing 30 by 1000, shift the decimal point in the numerator three places to the left (since 1000 is $10^3$): $30 \div 1000 = 0.03$.

Therefore, the solution to the problem is $0.03$.

Let's write the simple fraction as a decimal fraction:

$6.0$

Given that the fraction divides by 1000, we move the decimal point three places to the left:

$.0060$

We fill in the zero before the decimal point as follows:

$0.0060=0.006$

First we will divide both the numerator and denominator by 3 to get 100 in the denominator:

$\frac{12:3}{300:3}=\frac{4}{100}$

Now we'll rewrite the simple fraction as a decimal fraction:

$4.0$

Since the fraction divides by 100, we'll move the decimal point two places to the left:

$.040$

Now we will add the zero before the decimal point to get:

$0.040=0.04$

Let's write the simple fraction as a decimal fraction:

$11.0$

Since the fraction is divided by 1000, we move the decimal point three times to the left:

$.0110$

Now let's add the zero before the decimal point and we get:

$0.0110=0.011$

Let's write the simple fraction as a decimal fraction:

$300.0$

Since the fraction is divided by 1000, we move the decimal point three places to the left:

$.3000$

Now let's add the zero before the decimal point and we get:

$0.3000=0.3$

To solve this problem, we need to convert the fraction $\frac{20}{1000}$ into a decimal.

Step 1: Recognize that dividing by 1000 is equivalent to moving the decimal point three places to the left in the number 20.

Step 2: When we perform this division directly, we calculate $20 \div 1000$.

Since $20$ has effectively no decimal places to begin with, we must move three places left through zero to accommodate $1000$ as a divisor:

$20.0 \rightarrow 2.00 \rightarrow 0.200 \rightarrow 0.020$

Therefore, the decimal form of $\frac{20}{1000}$ is $\textbf{0.02}$.

Checking against the choices given, the correct answer is choice 2:

0.02

Therefore, the solution to this problem is $\textbf{0.02}$.

To solve the problem of converting the fraction $\frac{5}{500}$ into a decimal, we'll employ the following approach:

• Step 1: Simplify the fraction $\frac{5}{500}$.
• Step 2: Convert the simplified fraction to a decimal.
• Step 3: Verify the result through division.

Let's work through each step:

Step 1: Simplify the fraction:

The fraction $\frac{5}{500}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
$\frac{5 \div 5}{500 \div 5} = \frac{1}{100}$.

Step 2: Convert the simplified fraction to a decimal:

$\frac{1}{100}$ is equivalent to 0.01 in decimal form.

Step 3: Verify the result by division:

Dividing 5 by 500 gives:

$5 \div 500 = 0.01$.

The division confirms that the decimal conversion is correct.

Thus, the value of $\frac{5}{500}$ in decimal form is $\mathbf{0.01}$.

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

• Step 1: Assess the fraction, identifying the denominator as 1000.
• Step 2: Recognize that with the denominator as a power of 10, we move the decimal point a corresponding number of places in the numerator.
• Step 3: Execute the conversion to decimal form by moving the decimal point.

Now, let's work through each step:
Step 1: We're given the fraction $\frac{22}{1000}$.
Step 2: Since the denominator is 1000, which is $10^3$, we will move the decimal point in the numerator (22) three places to the left.
Step 3: Moving the decimal point three places to the left in 22, we get 0.022.

Therefore, the solution to the problem is $0.022$.

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

• Understand that $\frac{77}{1000}$ is a fraction where the denominator is a power of 10.
• Recognize that the decimal equivalent can be found directly by placing the decimal point three places to the left of the numerator (since the denominator is 1000).
• Write down the result.

Now, let's work through each step:

$\frac{77}{1000}$ means dividing 77 by 1000.

Step 1: Recognize that the denominator 1000 allows us to place the decimal point 3 positions to the left of the numerator.

Step 2: Start with 77, which can be viewed as 077 to ensure we can correctly place the decimal point.

Step 3: Move the decimal point three places left to get $0.077$.

Therefore, the solution to the problem is $0.077$.

Let's first multiply both the numerator and denominator by 2 to make the denominaor 1000:

$\frac{6\times2}{500\times2}=\frac{12}{1000}$

Now let's rewrite the simple fraction as a decimal:

$12.0$

Since the fraction divides by 1000, we'll move the decimal point three places to the left:

$.0120$

Finally we can add a zero before the decimal point to get our answer:

$0.0120=0.012$

Let's write the simple fraction as a decimal fraction:

$33.0$

Since the fraction is divided by 1000, we move the decimal point three places to the left:

$.0330$

Now let's add the zero before the decimal point and we get:

$0.0330=0.033$

Let's pay attention to where the decimal point is located in the number.

Remember:

One number after the decimal point represents tenths

Two numbers after the decimal point represent hundredths

Three numbers after the decimal point represent thousandths

And so on

In this case there are three numbers after the decimal point so the number is divided by 1000

Write the fraction in the following way:

$\frac{0171}{1000}$

We will remove the extra zeros and get:

$\frac{171}{1000}$

Let's pay attention to where the decimal point is located in the number.

Remember:

One number after the zero represents tens

Two numbers after the zero represent hundreds

Three numbers after the zero represent thousands

And so on

In this case, there are three numbers after the zero, so the number is divided by 1000

Let's write the fraction in the following way:

$\frac{0031}{1000}$

We'll then proceed to remove the unnecessary zeros as follows:

$\frac{31}{1000}$

Let's pay attention to where the decimal point is located in the number.

Remember:

One number after the zero represents tens

Two numbers after the zero represent hundreds

Three numbers after the zero represent thousands

And so on

In this case, there are three numbers after the zero, so the number is divided by 1000

Let's write the fraction in the following way:

$\frac{0079}{1000}$

We'll then proceed to remove the unnecessary zeros as follows:

$\frac{79}{1000}$

Let's pay attention to where the decimal point is located in the number.

Remember:

One number after the zero represents tens

Two numbers after the zero represent hundreds

Three numbers after the zero represent thousands

And so on

In this case, there are two numbers after the zero, so the number is divided by 100

Let's write the fraction in the following way:

$\frac{005}{100}$

Let's remove the unnecessary zeros as follows:

$\frac{5}{100}$

Let's then proceed to multiply both numerator and denominator by 4 and we obtain the following:

$\frac{5\times4}{100\times4}=\frac{20}{400}$