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

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 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 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:

$\frac{0012}{1000}$

We'll then proceed to remove the unnecessary zeros and obtain the following:

$\frac{12}{1000}$

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:

$\frac{0013}{1000}$

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

$\frac{13}{1000}$

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:

$\frac{0019}{1000}$

We'll then remove the unnecessary zeros as follows:

$\frac{19}{1000}$

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:

$\frac{0021}{1000}$

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

$\frac{21}{1000}$

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:

$\frac{0041}{1000}$

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

$\frac{41}{1000}$

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:

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

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:

$0.3000=0.3$

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 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:

$0.0060=0.006$

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 $0.03$.

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 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 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 $\mathbf{0.01}$.