Common Mistakes
Learn
In this lesson, you will learn about common mistakes students make when working with decimals—and how to avoid them. Understanding these pitfalls will help you become more confident and accurate.
Top 5 Common Decimal Mistakes
- Thinking more digits means a bigger number: 0.125 is NOT bigger than 0.5
- Ignoring place value when comparing: Always line up decimal points
- Forgetting that 0.5 = 0.50 = 0.500: Trailing zeros don't change value
- Confusing tenths and hundredths: 0.7 (7 tenths) is different from 0.07 (7 hundredths)
- Reading decimals like whole numbers: 0.35 is NOT "zero point thirty-five" but "thirty-five hundredths"
Examples
See these common mistakes and learn the correct approach.
Mistake Example 1
Wrong thinking: "0.19 is bigger than 0.2 because 19 is bigger than 2"
Correct thinking: Write 0.2 as 0.20. Now compare 19 hundredths to 20 hundredths. 0.20 > 0.19.
Mistake Example 2
Wrong thinking: "0.8 and 0.80 are different numbers"
Correct thinking: They are equal! 0.8 = 0.80 = 8 tenths = 80 hundredths.
✏️ Practice
Test your understanding with these practice questions.
Practice Questions
0/4 correctIf y = 3x represents a proportional relationship, what is the constant of proportionality?
A recipe uses 2 cups of flour for every 3 cups of sugar. If you use 6 cups of flour, how many cups of sugar do you need?
Which equation represents a proportional relationship?
The table shows x: 2, 4, 6 and y: 8, 16, 24. What is the constant of proportionality?
Check Your Understanding
Test yourself with these 10 review questions. Click each question to reveal the answer.
Question 1: A student says 0.45 > 0.5 because 45 > 5. What is wrong with this reasoning?
Answer: The student compared digits without considering place value. Rewrite 0.5 as 0.50. Then 0.50 > 0.45. The correct answer is 0.5 > 0.45.
Question 2: True or False: 0.7 is the same as 0.07
Answer: False. 0.7 = 7 tenths = 0.70, while 0.07 = 7 hundredths. 0.7 is ten times larger than 0.07.
Question 3: A student writes that 0.30 is greater than 0.3. Is this correct?
Answer: No, this is incorrect. 0.30 = 0.3. They are equal values. Trailing zeros do not change the value.
Question 4: Which is the correct comparison: 0.9 ___ 0.89?
Answer: 0.9 > 0.89. Rewrite 0.9 as 0.90. Then 90 hundredths > 89 hundredths.
Question 5: A student says 0.099 > 0.1 because 99 > 1. Explain the error.
Answer: The student ignored place value. 0.1 = 0.100. Compare: 100 thousandths > 99 thousandths. So 0.1 > 0.099.
Question 6: What is wrong with saying "0.25 is twenty-five"?
Answer: 0.25 is not twenty-five. It is "twenty-five hundredths" or "zero point two five." The value 25 is a whole number, while 0.25 is less than 1.
Question 7: A student thinks 0.5 and 0.05 are equal because both have a 5. Is this correct?
Answer: No. 0.5 = 5 tenths = 0.50, while 0.05 = 5 hundredths. The position of the 5 matters: 0.5 is ten times larger than 0.05.
Question 8: Order from least to greatest: 0.6, 0.06, 0.66
Answer: 0.06, 0.6, 0.66. Rewrite as 0.06, 0.60, 0.66 to compare easily.
Question 9: A student says 1.5 < 1.45 because 1.45 has more digits. What is wrong?
Answer: More digits does not mean a larger value. Rewrite 1.5 as 1.50. Compare: 1.50 > 1.45. So 1.5 > 1.45.
Question 10: True or False: 0.40 = 0.4 = 0.400
Answer: True. All three represent the same value: 4 tenths. Adding trailing zeros after the last non-zero digit does not change the value.
Next Steps
- Review any concepts that felt challenging
- Move on to the next lesson when ready
- Return to practice problems periodically for review