# Order of Decimals, Mixed Numbers and Fractions

You have to change all these numbers into a decimal format to make a comparison of mixed numbers and decimals.
To write the numbers in order, first, you must write the lowest number.
The highest number must be written as the last number.
Other numbers must be placed in between the lowest and highest numbers.

## A step-by-step guide to order Decimals, Mixed Numbers, and Fractions

Ordering decimals, mixed numbers, and fractions can be done by comparing the numbers’ values.

1. Ordering decimals: To order decimals, compare the numbers digit by digit starting from the left. The first number with a larger digit is greater. For example, 0.35 is greater than 0.3 because 5 is larger than 3.
2. Ordering mixed numbers: To order mixed numbers, first convert the mixed numbers to fractions. Then compare the fractions by comparing the numerator (top number) and the denominator (bottom number) separately. The fraction with the larger numerator or smaller denominator is greater. For example, 3 1/2 is greater than 2 3/4 because the numerator (7) is greater than the numerator (11) of the second fraction.
3. Ordering fractions: To order fractions, first, compare the numerators (top numbers) and then compare the denominators (bottom numbers). The fraction with the larger numerator or smaller denominator is greater. For example, 3/4 is greater than 1/2 because the numerator (3) is greater than the numerator (1) of the second fraction.

Note: If the fractions have different denominators, you must convert them to have a common denominator before comparing them.

When comparing decimals, mixed numbers, or fractions, it’s essential to have a clear understanding of what each number represents and how to work with them to be able to order them correctly.

### Order of Decimals, Mixed Numbers, and Fractions – Examples 1

Order this set of numbers from least to greatest. $$3 \frac{5}{9},\frac{6}{4},1.8,1.3$$
Solutions:
Step 1: The smallest number is 1.3 and the largest number is $$3 \frac{5}{9}$$.
Step 2: Change $$\frac{6}{4}$$ into a decimal. It is 1.5.
Step 3: Now order from least to greatest.
$$1.3<\frac{6}{4}<1.8<3 \frac{5}{9}$$

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