I. Comparing two decimal numbers
A. Where the numbers are written in decimal form
We can see that 34.97 < 35.2 because 34 < 35.
If two decimals do not have the same integer part, then the smaller one is the one with the smaller integer part.
Where two decimals have equal integer parts, we have to look at their decimal parts, digit by digit, starting with the digit just to the right of the decimal point and appending zeros as required.
Example 1: 56.24 > 56.239. Why?
The two integer parts are equal and the first figure after the decimal point is 2 in both numbers, but 4 > 3, which allows us to reach a conclusion.
Example 2: 3.5 < 3.54. Why?
Append a zero so that 3.5 = 3.50; 0 < 4, which allows us to reach a conclusion.
Note: Once we find two different digits in the same column of the decimals, we can reach a conclusion. So 6.4 > 6.398 (as 4 > 3). Be careful: The number of digits of the decimal part is irrelevant when comparing two decimals!
B. Where the numbers are written using decimal fractions
To compare two decimals written as fractions, write them in decimal form.
So we find that 34.2 > 34.173, which allows us to reach a conclusion.
II. Ordering decimals
Arranging numbers in ascending order means starting with the smallest and going up to the largest.Arranging numbers in descending order means starting with the largest and going down to the smallest.
Example 1: To arrange 5.6, 4.33, and 4.385 in ascending order, compare the numbers two by two; we can see that 4.33 < 4.385 and that 4.385 < 5.6. Therefore, we can write: 4.33 < 4.385 < 5.6.
Example 2: To arrange 41.667, 41.3, and 50.1 in descending order, compare the numbers two by two; we can see that 50.1 > 41.667 and that 41.667 > 41.3. Therefore, we can write: 50.1 > 41.667 > 41.3.
Read more:
Reading and Writing Decimal Numbers
Multiplying or Dividing a Decimal Number by 10, 100, or 1,000
Multiplying Decimal Numbers
Dividing Decimal Numbers
Converting Decimals to Fractions
The Effect of Addition and Multiplication on the Order of Numbers
Describing Different Types of Numbers
Dividing Whole Numbers with a Remainder
Adding and Subtracting Decimal Numbers