Formula:

\[0.5 = 0.50 = 0.500 = \frac{5}{10} = \frac{50}{100} = \frac{500}{1000}\]

✅ Adding zeros to the RIGHT does NOT change the value

\(0.3 = 0.30 = 0.300\) (All Equal)
\(2.4 = 2.40 = 2.400\) (All Equal)

❌ Adding zeros to the LEFT changes the value

\(0.3 \neq 0.03\) (NOT Equal)
\(0.3 = \frac{3}{10}\) but \(0.03 = \frac{3}{100}\)

Example 1: Are \(0.6\) and \(0.60\) equivalent?

Method 1: Convert to fractions
\(0.6 = \frac{6}{10}\) and \(0.60 = \frac{60}{100} = \frac{6}{10}\)

✓ Yes! They are equivalent because they have the same value.

Example 2: Write three equivalent decimals for \(1.2\)

Add zeros to the right: \(1.20\), \(1.200\), \(1.2000\)

✓ Answer: \(1.2 = 1.20 = 1.200 = 1.2000\)

Example 1: Compare \(5.7\) and \(5.68\)

Step 1: Line up decimal points → 5.7 and 5.68
Step 2: Add trailing zeros → 5.70 and 5.68
Step 3: Compare whole numbers → 5 = 5 (equal)
Step 4: Compare tenths → 7 = 7 (equal)
Step 5: Compare hundredths → \(0 < 8\)

✓ Answer: \(5.68 < 5.7\) or \(5.7 > 5.68\)

Example 2: Compare \(12.45\) and \(8.99\)

Step 1: Compare whole numbers → \(12 > 8\)
Step 2: We can stop here! The whole number is greater.

✓ Answer: \(12.45 > 8.99\)

Example 3: Compare \(0.325\) and \(0.32\)

Step 1: Add trailing zeros → 0.325 and 0.320
Step 2: Compare ones → 0 = 0 (equal)
Step 3: Compare tenths → 3 = 3 (equal)
Step 4: Compare hundredths → 2 = 2 (equal)
Step 5: Compare thousandths → \(5 > 0\)

✓ Answer: \(0.325 > 0.32\)

📌 Basic Rule:

• Numbers to the RIGHT are GREATER
• Numbers to the LEFT are SMALLER

Example: Compare \(2.3\) and \(2.7\)

Since 2.7 is to the RIGHT of 2.3 → \(2.7 > 2.3\)

Ascending Order (Least to Greatest):

Arrange from smallest to largest
Example: \(0.2 < 0.5 < 0.8 < 1.1\)

Descending Order (Greatest to Least):

Arrange from largest to smallest
Example: \(5.7 > 4.2 > 3.8 > 1.1\)

Example 1: Order in ascending order: \(3.8\), \(3.08\), \(3.80\), \(0.38\)

Step 1: Add trailing zeros → 3.80, 3.08, 3.80, 0.38
Step 2: Compare whole numbers first:
    • \(0 < 3\), so 0.38 is smallest
    • For the three 3's, compare tenths: 0, 8, 8
    • 3.08 has 0 in tenths (smallest among 3's)
    • 3.8 = 3.80 (equivalent decimals)

✓ Answer: \(0.38 < 3.08 < 3.8 = 3.80\)

Example 2: Order in descending order: \(1.25\), \(1.52\), \(1.2\), \(1.5\)

Step 1: Add trailing zeros → 1.25, 1.52, 1.20, 1.50
Step 2: All whole numbers are 1 (equal)
Step 3: Compare tenths: 2, 5, 2, 5
    • 5 > 2, so decimals with 5 in tenths are larger
Step 4: For 1.52 and 1.50: compare hundredths → \(2 > 0\)
Step 5: For 1.25 and 1.20: compare hundredths → \(5 > 0\)

✓ Answer: \(1.52 > 1.5 > 1.25 > 1.2\)

Grid Values:

• 1 column (10 squares) = \(\frac{10}{100} = 0.1\) (one tenth)
• 1 row (10 squares) = \(\frac{10}{100} = 0.1\) (one tenth)
• 1 square = \(\frac{1}{100} = 0.01\) (one hundredth)
• Whole grid (100 squares) = \(\frac{100}{100} = 1.0\) (one whole)

Comparison Rule:

The decimal with more shaded squares is greater.

Sarah ran 3.45 kilometers and Tom ran 3.5 kilometers. Who ran farther?

Four students measured their heights: Alex = 1.42 m, Ben = 1.4 m, Clara = 1.38 m, Diana = 1.45 m. Arrange them from shortest to tallest.

A book costs $12.85 and a pen costs $12.78. Which is more expensive? Round both prices to the nearest dollar.

✅ Remember

Always line up decimal points when comparing!

✅ Tip

Use trailing zeros to make comparison easier!

✅ Warning

More digits doesn't mean greater! \(1.1 > 1.001\)

✅ Practice

Use place value charts for clarity!