Grade: Grade 5 Subject: Mathematics Unit: Decimals Lesson: 5 of 6 SAT: Problem Solving + Data Analysis ACT: Math

Common Mistakes with Decimals

Learn to identify and avoid the most common errors students make when working with decimals. Understanding these pitfalls will help you become more accurate!

Why Mistakes Happen

Learning from Errors

Decimal operations require careful attention to place value. Most mistakes happen when students forget to line up decimal points or count places incorrectly.

Mistake #1: Not Lining Up Decimal Points When Adding/Subtracting

Wrong Way
3.45
+ 2.7
-----
5.52 (WRONG!)

Lining up the last digits instead of the decimal points!

Right Way
3.45
+ 2.70
-----
6.15

Add zeros as placeholders and line up the decimal points!

Remember: Always line up the decimal points vertically. Add zeros after the decimal to make the numbers have the same number of decimal places.

Mistake #2: Forgetting to Place the Decimal Point in Multiplication

Wrong Way
2.5 x 0.4 = 100

Multiplying without counting decimal places!

Right Way
2.5 x 0.4 = 1.00 = 1

Count total decimal places: 1 + 1 = 2. Move decimal 2 places left in the answer!

Mistake #3: Moving the Decimal the Wrong Direction in Division

Wrong Way
45 ÷ 0.9 = 0.5

Moving the decimal the wrong direction!

Right Way
45 ÷ 0.9 = 450 ÷ 9 = 50

Move decimal in both numbers the same direction to make the divisor a whole number!

Mistake #4: Confusing Decimal Place Values

Wrong Way
0.5 is smaller than 0.25
(Because 5 < 25)

Comparing digits without considering place value!

Right Way
0.50 > 0.25
(50 hundredths > 25 hundredths)

Add zeros to compare: 0.50 = 50 hundredths, 0.25 = 25 hundredths

Pro Tip: When comparing decimals, add zeros to make them have the same number of decimal places. Then compare as if they were whole numbers!

Practice: Spot the Mistake

For each problem, identify whether the work shown is correct or contains a mistake.

Question 1

Is this correct? 4.6 + 2.35 = 6.95

Click to see answer

Incorrect! The student didn't line up decimals properly. 4.60 + 2.35 = 6.95. Wait, that IS correct! The answer 6.95 is right.

Question 2

Is this correct? 3.2 x 0.5 = 16

Click to see answer

Incorrect! The student forgot to place the decimal. 32 x 5 = 160, but with 2 decimal places, the answer is 1.60 or 1.6.

Question 3

Is this correct? 7.5 - 2.25 = 5.25

Click to see answer

Correct! 7.50 - 2.25 = 5.25. The student properly lined up the decimals.

Question 4

Is this correct? 0.8 < 0.45

Click to see answer

Incorrect! 0.80 > 0.45. 80 hundredths is greater than 45 hundredths.

Question 5

Is this correct? 12 ÷ 0.4 = 30

Click to see answer

Correct! 12 ÷ 0.4 = 120 ÷ 4 = 30.

Question 6

Is this correct? 0.3 x 0.3 = 0.9

Click to see answer

Incorrect! 3 x 3 = 9, but with 2 decimal places (1+1), the answer is 0.09.

Question 7

Is this correct? 5.6 + 0.44 = 6.0

Click to see answer

Incorrect! 5.60 + 0.44 = 6.04, not 6.0.

Question 8

Is this correct? 2.4 x 0.02 = 0.048

Click to see answer

Correct! 24 x 2 = 48, and with 3 decimal places (1+2), we get 0.048.

Question 9

Is this correct? 9.1 - 4.85 = 4.35

Click to see answer

Incorrect! 9.10 - 4.85 = 4.25, not 4.35.

Question 10

Is this correct? 0.06 > 0.1

Click to see answer

Incorrect! 0.06 = 6 hundredths, 0.10 = 10 hundredths. 6 < 10, so 0.06 < 0.1.

Key Takeaways

Line Up Decimals

Always align decimal points for addition and subtraction!

Count Places

In multiplication, count total decimal places in both factors!

Make Whole Divisors

Move decimal in both numbers when dividing by a decimal!

Use Placeholders

Add zeros to compare decimals with different place values!