Math Misconception Test

No, 9.11 is NOT greater than 9.9. In fact, 9.9 is greater than 9.11. Here's why:

Step-by-Step Comparison:

1. Compare the whole number part (left of the decimal):
   Both numbers have 9 as the whole number. → Equal so far.

2. Compare the tenths place (first digit after the decimal):

   • 9.11 → Tenths digit = 1
   • 9.9 → Tenths digit = 9
     → 9 > 1, so 9.9 is already larger.

Why the Confusion?

• A common mistake is to treat "9.11" as "nine point eleven" and assume it's larger than "nine point nine" because 11 > 9. This is incorrect.
• Decimals are compared digit-by-digit from left to right, not as whole numbers after the decimal.
• 9.9 is equivalent to 9.90 (adding a trailing zero doesn't change the value). Now compare:
  • 9.90 vs. 9.11
  • Tenths place: 9 > 1 → 9.90 > 9.11.

Visual Proof:

9.11 = 9 + 0.1 + 0.01  
9.9  = 9 + 0.9 + 0.00  
       = 9.90

Since 0.9 > 0.11 (because 0.9 = 0.90 and 0.90 > 0.11), 9.9 > 9.11.

Key Takeaway:

Always compare decimals place-by-place starting from the left.
9.9 > 9.11 is true because 9.9 = 9.90, and 90 hundredths > 11 hundredths.

💡 Remember: 9.9 is closer to 10, while 9.11 is closer to 9.
✅ Correct order: 9.11 < 9.9.