Compare and order decimals

In this lesson, we will learn:

• How to compare the value of two decimal numbers
• How to order a list of decimals in ascending and descending order

Notes:

• To compare two decimal numbers, we want to know how big or small the values are
• We use these symbols to compare numbers:

• We can compare using number lines:


• We can also compare using base ten (block) models:


• The steps for comparing two numbers:
1. Start with the biggest (left) place value.
2. Is the digit in this place value different between the two numbers?
1. YES: compare the digit (0 = smallest, 9 = biggest).
2. NO: move to the next smaller place value (right) and repeat step 2.
3. If all digits are the same in both numbers, they are equal.

• Once you have found a difference for a place value, it does not matter what numbers are in the places further on the right (smaller places)
• i.e. recall equivalent decimal tenths and hundredths 0.8=0.80
• ex. 8.9 > 8.79 (more decimal place values does not necessarily make the value greater)

• There are two ways to order a list of decimals:
• Ascending order: which means from least to greatest
• increasing; smallest to biggest (ex. 1.1 < 1.2 < 1.3 < 1.4)
• Descending order: which means from greatest to least
• decreasing; biggest to smallest (ex. 1.4 > 1.3 > 1.2 > 1.1)