Comparing and Ordering Decimals

Comparing decimals works just like comparing whole numbers — compare digit by digit, starting from the left. The key step that prevents mistakes is adding trailing zeros so both numbers have the same number of decimal places before you compare.

The Method

1. Line up the decimal points
2. Add trailing zeros so both numbers have the same number of decimal places
3. Compare digit by digit from left to right

Example 1: Compare 0.7 and 0.65

Add a trailing zero to 0.7: $0.70$ vs $0.65$

Compare: $70$ hundredths vs $65$ hundredths.

$0.7 > 0.65$

Example 2: Compare 3.45 and 3.5

Add a trailing zero to 3.5: $3.45$ vs $3.50$

Compare digit by digit:

• Ones: $3 = 3$
• Tenths: $4 < 5$

$3.45 < 3.5$

Example 3: Compare 0.08 and 0.1

Add a trailing zero to 0.1: $0.08$ vs $0.10$

$8$ hundredths vs $10$ hundredths.

$0.08 < 0.1$

Common Mistake

Many people think $0.08$ is larger than $0.1$ because 8 is larger than 1. But $0.08$ is eight hundredths while $0.1$ is ten hundredths. Always compare by place value, not by the individual digits.

Ordering Multiple Decimals

Example 4: Order from least to greatest: 0.35, 0.4, 0.305, 0.045

Add trailing zeros to equalize decimal places (thousandths):

$0.350, \quad 0.400, \quad 0.305, \quad 0.045$

Now compare as whole numbers: 45, 305, 350, 400.

Answer: $0.045 < 0.305 < 0.35 < 0.4$

Example 5: Order from greatest to least: 2.1, 2.09, 2.15, 2.009

Equalize: $2.100, \; 2.090, \; 2.150, \; 2.009$

Compare: 2009, 2090, 2100, 2150 (treating as thousandths).

Answer: $2.15 > 2.1 > 2.09 > 2.009$

Using a Number Line

Decimals fit between whole numbers on the number line. Between 0 and 1, you can place tenths:

Practice Problems

Test your understanding with these problems. Click to reveal each answer.

Key Takeaways

• Add trailing zeros so decimals have the same number of places before comparing
• Compare digit by digit from left to right — the first difference determines the result
• $0.5 > 0.08$ even though $8 > 5$ — place value matters, not the digits alone
• This skill is essential for rounding decimals and ordering data

Return to Arithmetic for more foundational math topics.