Converting Decimal Fractions to Simple and Mixed Fractions

First Stage - knowing how to read a decimal fraction correctly
A decimal fraction is actually a non-whole number that consists of digits and a decimal point.
The decimal point divides the fraction as follows:

All the part to the left of the decimal point - is called whole numbers.
All the part to the right of the decimal point - is divided this way:
The first digit after the point - represents tenths
The second digit after the point - represents hundredths
The third digit after the point represents thousandths

To read a decimal fraction correctly, we need to ask ourselves what the last digit in the decimal fraction represents.
When we understand what the digit represents, we say it like this:
___ wholes and "everything that appears after the decimal point" "what the digit represents".

For example-
How do we read the decimal fraction $40.23$?
First, let's understand what the last digit represents. It represents hundredths.
Therefore, we'll read the number as: $40$ wholes and $23$ hundredths.

The Second Stage - Constructing the Mixed Fraction
After we succeeded in reading the decimal number correctly, we can easily construct the mixed fraction.
When we read the decimal number
If we used the word tenths - we put $10$ in the denominator
If we used the word hundredths - we put $100$ in the denominator
If we used the word thousandths - we put $1000$ in the denominator

The number itself - everything that appears after the decimal point, we place in the numerator.
The whole number digit in the decimal fraction, we add to the mixed fraction as the whole number.

Worth remembering:
Thousandths - $1000$ in the denominator
Hundredths - $100$ in the denominator
Tenths - $10$ in the denominator

Let's practice converting a decimal fraction to a mixed number:
Convert the number $62.325$ to a mixed number

Solution
First, let's check how we read it correctly.
$62$ wholes and $325$ thousandths. Because $5$ the last digit represents thousandths.
Now that we used the word thousandths, it's simple to understand that the denominator in the mixed fraction will be $1000$. Everything after the decimal point will be in the numerator and $62$ wholes will be the wholes of course. So we get:
$62 \frac{325}{1000}$

Additional exercise:
Convert the number $2.1$ to a mixed fraction.

Solution
Let's check how we say it correctly - $2$ wholes and $1$ tenth.
Tenths clearly indicates that the denominator of the mixed fraction is $10$.
Therefore, the numerator will be $1$ and the whole number will be $2$.
We get that the mixed fraction is:
$2 \frac{1}{10}$

A simple fraction is a fraction composed of only a numerator and denominator and does not involve whole numbers and a fraction like a mixed fraction.
When we have a decimal number with $0$ in its whole number part - meaning there are no whole numbers, the fraction will be simple without our intervention.
We will act in the same way - we will see how we read the decimal fraction correctly and then check
If we used the word tenths - $10$ in the denominator
If we used the word hundredths - $100$ in the denominator
If we used the word thousandths - $1000$ in the denominator

Let's look at an example:
Convert the decimal fraction $0.824$ to a simple fraction

Solution
When we read the decimal number, we look at the last digit, see that it indicates thousandths, and therefore the denominator is $1000$. In the numerator will appear $824$.

We get:
$824\over1000$

If there are whole numbers, we will get a mixed fraction as we learned, and then we will need to convert the mixed fraction into a simple fraction according to the rules.