Introduction
Comparing Decimals is an important Grade 4 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with comparing decimals.
What Is Comparing Decimals?
Comparing Decimals means choosing a model, naming what each number means, and explaining the strategy.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Comparing Decimals
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: Look at the number line below. What decimal is shown by the arrow?
- A. \(0.6\)
- B. \(0.65\)
- C. \(0.56\)
- D. \(0.68\)
Why it works: The arrow points exactly halfway between \(0.6\) and \(0.7\). The midpoint is \(0.65\).
Answer: \(0.65\)
Visual Model 2
Question: Look at the grid below with hundredths shaded. What decimal is shown?
- A. \(0.62\)
- B. \(0.72\)
- C. \(0.73\)
- D. \(0.82\)
Why it works: Count the shaded squares: \(7\) full columns (that's \(70\) squares) plus \(3\) extra squares make \(73\) squares total. So the decimal is \(73\) hundredths \(= 0.73\).
Answer: \(0.73\)
Worked Examples
Example 1
Question: Look at the place-value table below. What decimal has \(6\) tenths and \(2\) hundredths?
| Tenths | Hundredths | Decimal |
|---|---|---|
| \(6\) | \(0\) | \(0.60\) |
| \(6\) | \(2\) | ? |
- A. \(0.26\)
- B. \(0.62\)
- C. \(0.206\)
- D. \(6.02\)
- From the table: \(6\) tenths \(= 0.6\) and \(2\) hundredths \(= 0.02\).
- Add them: \(0.6 + 0.02 = 0.62\).
Answer: \(0.62\)
Example 2
Question: Look at the number line. What decimal is marked by the dot?
- A. \(0.38\)
- B. \(0.8\)
- C. \(0.3\)
- D. \(0.83\)
- This number line zooms in from \(0.30\) to \(0.40\), counting by hundredths.
- The dot lands on \(0.38\).
Answer: \(0.38\)
Example 3
Question: Look at these two hundredths grids side-by-side. Which decimal is greater?
- A. Grid 1 (\(0.43\))
- B. Grid 2 (\(0.34\))
- C. They are equal
- D. Cannot compare
- Count the shaded squares: Grid 1 has \(43\) hundredths and Grid 2 has \(34\) hundredths.
- Since \(43 > 34\), \(0.43 > 0.34\).
Answer: Grid 1 at \(0.43\) is greater
Real-World Word Problems
Problem 1
Question: Kai is at a lemonade stand. Pitcher A holds \(0.75\) liters. Pitcher B holds \(0.57\) liters. Which pitcher holds more lemonade?
- A. Pitcher A (\(0.75\) L)
- B. Pitcher B (\(0.57\) L)
- C. Both hold the same amount
- D. Pitcher B holds twice as much
Why it works: Compare the tenths place: \(7 > 5\), so \(0.75 > 0.57\). Pitcher A holds more lemonade.
Answer: Pitcher A holds more at \(0.75\) liters
Problem 2
Question: Mia is comparing two prices. Socks cost \($0.80\) and a pencil costs \($0.08\). Which item costs more?
- A. The socks (\($0.80\))
- B. The pencil (\($0.08\))
- C. Both cost the same
- D. The pencil costs 10 times more
Why it works: \(0.80\) has \(8\) tenths, while \(0.08\) has \(0\) tenths (just \(8\) hundredths). Since \(8\) tenths \(> 0\) tenths, \(0.80 > 0.08\). Socks cost more.
Answer: The socks cost more at \($0.80\)
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
Which comparison is true?
- A. \(0.6<0.59\)
- B. \(0.6=0.59\)
- C. \(0.6>0.59\)
- D. \(0.6<0.5\)
Question 2
Which decimal is the smallest?
- A. \(0.35\)
- B. \(0.53\)
- C. \(0.50\)
- D. \(0.55\)
Question 3
How does \(0.4\) compare to \(0.40\)?
- A. \(0.4<0.40\)
- B. \(0.4>0.40\)
- C. \(0.4=0.40\)
- D. \(0.4=0.04\)
Question 4
Order these decimals from least to greatest: \(0.72\), \(0.27\), \(0.70\), \(0.07\).
- A. \(0.07, 0.27, 0.70, 0.72\)
- B. \(0.72, 0.70, 0.27, 0.07\)
- C. \(0.27, 0.07, 0.70, 0.72\)
- D. \(0.07, 0.70, 0.27, 0.72\)
Question 5
Which shows the correct comparison?
- A. \(0.8>0.81\)
- B. \(0.8<0.81\)
- C. \(0.81<0.8\)
- D. \(0.81=0.8\)
Question 6
Which decimal is greatest?
- A. \(0.48\)
- B. \(0.84\)
- C. \(0.44\)
- D. \(0.41\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(0.6>0.59\)
Compare place by place: Write \(0.6\) as \(0.60\). Now both have the same number of decimal places. Since \(60 > 59\) hundredths, we have \(0.6 > 0.59\).
Question 2
Answer: \(0.35\) is the smallest
When comparing decimals, look at the tenths place first---it has the most weight. \(0.35\) has \(3\) tenths; the others (\(0.53, 0.50, 0.55\)) all have \(5\) tenths. Since \(3 < 5\), the number with fewer tenths is automatically the smallest, no matter what's in the hundredths place. So \(\mathbf{0.35}\) is the smallest. \checkmark
Question 3
Answer: \(0.4=0.40\)
A trailing zero doesn't change the value. Both \(0.4\) and \(0.40\) represent the same amount: \(4\) tenths, or \(40\) hundredths.
Question 4
Answer: \(0.07<0.27<0.70<0.72\)
Compare the tenths place first: \(0 < 2 < 7\). For the two decimals with tenths \(= 7\), compare hundredths: \(0 < 2\), so \(0.70 < 0.72\).
Question 5
Answer: \(0.8<0.81\)
Rewrite \(0.8\) as \(0.80\) to see it clearly. Comparing: \(80 < 81\) hundredths, so \(0.8 < 0.81\).
Question 6
Answer: \(0.84\) is the greatest
Look at the tenths place: \(0.84\) has \(8\) tenths while the others have \(4\) tenths. Since \(8 > 4\), \(0.84\) is the largest.
Connection to Standards
This lesson supports Grade 4 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Comparing Decimals becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
