Comparing and Ordering Decimals

Lesson Goal

By the end of this lesson your student should be able to compare two decimals with <, > or =, and put a list of decimals in order from least to greatest.

The method is to line up the decimal points and compare digits from the left, adding zeros to the end of a shorter decimal when that helps.

Where Students Get Stuck

🚨 The big misconception is that the decimal with more digits is bigger, so 19.875 looks bigger than 19.9. Annexing zeros fixes it: 19.9 is 19.900, and 900 thousandths beats 875.

Some students also mix up < and >. The open side faces the bigger number, and reading 19.837 < 19.875 aloud as 'is less than' helps it stick.

A tie is a real answer. Two decimals can be equal, and 0.4 and 0.40 are the same number written two ways.

Teaching Suggestion

Have the student write each pair in a stack with the decimal points lined up, one number above the other, before deciding. The stack does most of the work.

If you can, draw a number line from 19.8 to 20.0 and let the student mark the four scores. Seeing Silivas furthest right makes 'greater' something they can see, not just a rule.

Key Vocabulary

Decimal

A number with a decimal point, like 19.875, where digits to the right of the point are parts of a whole.

Compare

To decide whether one number is greater than, less than or equal to another.

Greater Than

The symbol whose open side faces the bigger number, as in 19.924 > 19.875.

Less Than

The symbol whose point faces the smaller number, as in 19.837 < 19.875.

Annex Zeros

To write zeros on the end of a decimal. It doesn't change the value: 19.9 = 19.900.