Converting a decimal to a mixed number and an improper fraction without simplifying

Definition

To convert a decimal into a mixed number and an improper fraction without simplifying.

We can follow two methods.

Method 1

We read the decimal as whole number part, tenths, hundredths and so on and write it as a mixed number.
Using algorithm, we convert the mixed number to an improper fraction.

We read the decimal and write it as a mixed number and an improper fraction as shown in this example.

Convert 13.06 into a mixed number and an improper fraction without simplifying.

13.06 can be read as thirteen and six hundredths.
This can be written as mixed number $13\frac{6}{100}$ without simplifying
This can be further converted into improper fraction as follows. $\frac{[13 \times 100 + 6]}{100} = \frac{1306}{100}$.
So, $13\frac{6}{100} = \frac{1306}{100}$, an improper fraction. (without simplifying)

Method 2

Here, we drop the decimal point and write the number as the numerator of a fraction.
We count the number of digits after the decimal point.
Next, we write 1 followed by that many zeros as the denominator of same fraction.
We get an improper fraction by writing both the numerator and denominator.
This improper fraction can be converted into a mixed number by long division. (without simplifying)

Consider the same decimal number 13.06.

Here, we drop the decimal point and write the number 1306 as the numerator of a fraction.
We count the number of digits after the decimal point. Here, it is 2 digits.
Next, we write 1 followed by that many zeros as the denominator of same fraction.
So, we get $13.06 = \frac{1306}{100}$
This improper fraction can be converted into a mixed number by long division as $\frac{1306}{100} = 13\frac{6}{100}$ (without simplifying)

Example 1:

Convert 4.6 to a mixed number and improper fraction without simplifying.

Solution

Step 1:

The decimal 4.6 is read as 4 and 6 tenths.

Step 2:

So, it can be written as a mixed number $4\frac{6}{10}$. The mixed number has a whole number part 4 and a fractional part $\frac{6}{10}$ which can be reduced to lowest terms.

Step 3:

The same mixed number can be converted into an improper fraction as follows. The denominator 10 is multiplied with whole number 4 and the product is added to the numerator 6 to give 4 × 10 + 6 = 46.

Step 4:

This becomes the numerator of the improper fraction and 10 is retained as the denominator of the improper fraction.

Step 5:

So, $4.6 = 4\frac{6}{10}=\frac{46}{10}$ (without simplifying)

Example 2:

Convert 11.75 to a mixed number and improper fraction without simplifying

Solution

Step 1:

The decimal 11.75 is read as 11 and 75 hundredths.

Step 2:

So, it is written as a mixed number $11\frac{75}{100}$. The mixed number has a whole number part 11 and a fractional part $\frac{75}{100}$.

Step 3:

The same mixed number can be converted into an improper fraction as follows. The denominator 100 is multiplied with whole number 11 and the product is added to the numerator 75 to give 11 × 100 + 75 = 1175.

Step 4:

This becomes the numerator of the improper fraction and 100 is retained as the denominator of the improper fraction.

Step 5:

So, $11\frac{75}{100} = \frac{1175}{100}$ (without simplifying).