Decimals are a fundamental part of mathematics and are used everywhere in daily life, from calculating grocery bills to measuring ingredients for a recipe. But what happens when you need to figure out which of two decimal numbers is larger or smaller? Understanding How To Compare Decimals is a crucial skill that builds a strong foundation in math.
This guide will break down the process of comparing decimals into simple, easy-to-follow steps. Whether you’re a student just learning about decimals, a parent helping with homework, or just brushing up on your math skills, this article will provide you with a clear and comprehensive understanding of decimal comparison. We’ll explore the concept of place value, walk through numerous examples, and even touch upon common mistakes to avoid, ensuring you become confident in comparing any decimal numbers you encounter.
What Does Comparing Decimals Mean?
Comparing decimals is the process of determining the relative size of two or more decimal numbers. Essentially, you’re figuring out if one decimal is greater than, less than, or equal to another. This skill is vital for understanding numerical values and is used in various mathematical operations and real-world scenarios.
To effectively compare decimals, we rely on the concept of place value. Just like whole numbers, each digit in a decimal number has a specific place value, which determines its contribution to the overall value of the number.
Let’s take two decimal numbers as an example: 0.78 and 0.783. To compare them, we can use a place value chart.
As you can see in the chart, we start comparing from the leftmost digit, which holds the largest place value – the tenths place in this case. Both 0.78 and 0.783 have ‘7’ in the tenths place. Since these are the same, we move to the next place value to the right, the hundredths place. Again, both have ‘8’.
Now we move to the thousandths place. 0.783 has ‘3’ in the thousandths place, while 0.78 effectively has a ‘0’ because we can add trailing zeros to decimals without changing their value. Since 3 is greater than 0, we can conclude that 0.783 is greater than 0.78.
This comparison can be written using mathematical symbols:
- 0.78 < 0.783 (0.78 is less than 0.783)
- 0.783 > 0.78 (0.783 is greater than 0.78)
This same method applies when comparing decimals with whole numbers or when ordering a series of decimals from least to greatest or greatest to least. You simply need to align the decimal points and compare digit by digit, starting from the largest place value.
What is Comparing Decimals? – Visual Explanation
How to Compare Decimals: Step-by-Step
Comparing decimals is straightforward once you understand the process. Here’s a simple, step-by-step guide:
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Align the Decimal Points: Write the decimals one below the other, making sure the decimal points are lined up vertically. This ensures that you are comparing digits in the same place value positions.
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Compare the Whole Number Parts (if any): If the decimals have whole number parts (the digits to the left of the decimal point), compare these first. If the whole number parts are different, the decimal with the larger whole number part is the larger decimal, regardless of the decimal portion.
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Compare Decimal Places from Left to Right: If the whole number parts are the same, or if there are no whole number parts (i.e., they are less than 1), start comparing the digits to the right of the decimal point, beginning with the tenths place, then the hundredths place, and so on. Continue comparing digits in each place value until you find a place where the digits are different.
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Determine Which Decimal is Larger: Once you find a place value where the digits differ, the decimal with the larger digit in that place value is the larger decimal. If you reach the end of the decimal numbers and all corresponding digits are the same, then the decimals are equal.
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Write the Comparison Statement: Use the symbols > (greater than), < (less than), or = (equal to) to write a comparison statement that accurately reflects the relationship between the decimals.
Examples of Comparing Decimals
Let’s work through some examples to solidify your understanding of how to compare decimals.
Example 1: Comparing Decimals in Tenths and Hundredths
Compare 0.65 and 0.46.
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Align the numbers by the decimal point:
0.65 0.46 -
Start with the largest place and compare numbers: Starting with the tenths place, compare ‘6’ and ‘4’.
Since 6 is greater than 4, 0.65 is greater than 0.46.
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Complete the comparison statement:
0.65 > 0.46
Example 2: Comparing Decimals in Thousandths
Compare 0.135 and 0.167.
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Align the numbers by the decimal point:
0.135 0.167 -
Start with the largest place and compare numbers: The tenths place digits are the same (both ‘1’). Move to the hundredths place.
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Continue until a difference is found: In the hundredths place, compare ‘3’ and ‘6’.
Since 3 is less than 6, 0.135 is less than 0.167.
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Complete the comparison statement:
0.135 < 0.167
Example 3: Comparing Decimals with Whole Numbers
Compare 3.456 and 3.018.
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Align the numbers by the decimal point:
3.456 3.018 -
Start with the largest place and compare numbers: The ones place digits are the same (both ‘3’). Move to the tenths place.
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Continue until a difference is found: In the tenths place, compare ‘4’ and ‘0’.
Since 4 is greater than 0, 3.456 is greater than 3.018.
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Complete the comparison statement:
3.456 > 3.018
Example 4: Comparing Decimals with Larger Whole Numbers
Compare 104.76 and 104.22.
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Align the numbers by the decimal point:
104.76 104.22 -
Start with the largest place and compare numbers: The hundreds, tens, and ones places are all the same (1, 0, and 4 respectively). Move to the tenths place.
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Continue until a difference is found: In the tenths place, compare ‘7’ and ‘2’.
Since 7 is greater than 2, 104.76 is greater than 104.22.
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Complete the comparison statement:
104.76 > 104.22
Example 5: Word Problem – Comparing Money
Frederick saved $27.98 and Samantha saved $27.89 for vacation. Who saved more?
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Align the numbers by the decimal point:
27.98 27.89 -
Start with the largest place and compare numbers: The tens and ones places are the same (2 and 7 respectively). Move to the tenths place.
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Continue until a difference is found: In the tenths place, compare ‘9’ and ‘8’.
Since 9 is greater than 8, $27.98 is greater than $27.89.
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Complete the comparison statement:
27.89 < 27.98
Frederick saved more money.
Example 6: Word Problem – Comparing Time
Peter swam 800m in 9.324 minutes in week 1 and 9.243 minutes in week 2. In which week was he faster? (Faster means less time).
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Align the numbers by the decimal point:
9.324 9.243 -
Start with the largest place and compare numbers: The ones place digits are the same (both ‘9’). Move to the tenths place.
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Continue until a difference is found: In the tenths place, compare ‘3’ and ‘2’.
Since 2 is less than 3, 9.243 is less than 9.324.
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Complete the comparison statement:
9.243 < 9.324
Peter swam faster in Week 2.
Teaching Tips for Comparing Decimals
- Visual Aids: Use place value charts, number lines, base-ten blocks, or decimal tiles to help students visualize the value of each decimal place.
- Hands-on Activities: Incorporate hands-on activities like using play money (dimes and pennies) to represent and compare decimals physically. This makes the concept more tangible.
- Real-World Connections: Relate decimal comparison to real-life scenarios like comparing prices in stores, measurements in cooking, or distances in sports.
Common Mistakes to Avoid
- Misaligning Decimal Points: A frequent error is not aligning decimal points correctly, leading to comparing digits in incorrect place values. Always ensure decimal points are vertically aligned before comparing.
- Ignoring Place Value: Some students may mistakenly compare decimals as if they were whole numbers, ignoring the significance of place value after the decimal point. Emphasize that the further to the right a digit is from the decimal point, the smaller its value.
- Confusion with Comparison Symbols: Students sometimes mix up the “greater than” (>), “less than” (<), and “equal to” (=) symbols. Practice using these symbols in context to reinforce their meaning.
Practice Questions: Test Your Knowledge
Let’s test your understanding with a few practice questions:
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Which comparison statement is correct for 0.76 and 1.23?
- 0.76 > 1.23
- 1.23 < 0.76
- 0.76 < 1.23
- 0.76 = 1.23
Explanation: Comparing the ones place, 0 is less than 1, therefore 0.76 < 1.23.
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Which comparison statement is correct for 0.882 and 0.9?
- 0.882 > 0.9
- 0.882 < 0.9
- 0.882 = 0.9
- 0.9 < 0.882
Explanation: Comparing the tenths place, 8 is less than 9, therefore 0.882 < 0.9.
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Which comparison statement is correct for 23.87 and 23.871?
- 23.87 > 23.871
- 23.87 = 23.871
- 23.871 < 23.87
- 23.87 < 23.871
Explanation: Adding a zero placeholder to 23.87 makes it 23.870. Comparing the thousandths place, 0 is less than 1, therefore 23.87 < 23.871.
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Which comparison statement is correct for 11.98 and 1.198?
- 11.98 = 1.198
- 11.98 > 1.198
- 11.98 < 1.198
- 1.198 > 11.98
Explanation: Comparing the tens place, 1 is greater than 0 (implicitly in 1.198), therefore 11.98 > 1.198.
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Ruby spent $23.17 and Cassie spent $32.71. Which statement correctly compares their spending?
- $32.71 < $23.17
- $32.71 = $23.17
- $32.71 > $23.17
- $23.17 > $32.71
Explanation: Comparing the tens place, 3 is greater than 2, therefore $32.71 > $23.17.
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Times of 4th graders running laps:
Student Time (seconds) Carlos 45.63 Nydia 49.14 Maria 44.23 Samuel 40.16 
Which comparison statement correctly compares Nydia’s and Carlos’s times?
- 49.14 < 45.63
- 44.23 < 45.63
- 40.16 > 45.63
- 49.14 > 45.63
Explanation: Comparing the ones place after the tens place are the same, 9 is greater than 5, therefore 49.14 > 45.63.
Comparing Decimals FAQs
What is the difference between comparing numbers and ordering numbers?
Comparing numbers typically involves determining the relationship between two numbers (greater than, less than, or equal to). Ordering numbers involves arranging three or more numbers in a sequence, either from least to greatest (ascending order) or greatest to least (descending order).
How can I compare decimals and fractions?
To compare decimals and fractions, you have two main options:
- Convert the fraction to a decimal: Divide the numerator of the fraction by the denominator to get its decimal equivalent. Then, compare the two decimals using the method described in this article.
- Convert the decimal to a fraction: Express the decimal as a fraction with a power of 10 as the denominator. Then, compare the two fractions by finding a common denominator or by comparing their numerators if they have the same denominator.
Take the Next Step
Mastering decimal comparison is a building block for more advanced math concepts. Continue practicing and exploring related topics to strengthen your understanding of decimals and numbers in general.
If you’re looking for more support, explore resources like worksheets and online tutorials to further enhance your skills in comparing and working with decimals.
