Comparing Decimal Numbers Practice Problems & Worksheets

Master decimal comparison with step-by-step practice problems. Learn digit-by-digit analysis to compare decimal fractions confidently using greater than, less than symbols.

📚Master Decimal Comparison with Interactive Practice
  • Apply digit-by-digit analysis to compare any decimal numbers accurately
  • Compare whole number parts first, then decimal places systematically
  • Use greater than, less than, and equal symbols correctly with decimals
  • Avoid common traps like comparing 0.2 vs 0.130 incorrectly
  • Find numbers between given decimal values using place value understanding
  • Build confidence with step-by-step solutions for decimal comparison problems

Understanding Comparing Decimal Fractions

Complete explanation with examples

Comparing decimal numbers is done using the system: Digit-by-digit analysis

First step:

Analyze the whole numbers: the decimal number with the larger whole number will be the greater of the two.

Second step:

Analyze the digits that come after the decimal point (only in the case where the whole numbers are equal)
We will move from digit to digit (starting with the tenths, then the hundredths, and so on)
If they continue to be equal, we will proceed with the comparison of the following digits.
If they are different, we will be able to determine which number is larger.

Detailed explanation

Practice Comparing Decimal Fractions

Test your knowledge with 21 quizzes

Choose the appropriate sign:

\( \frac{3}{5}~[?]~0.5 \)

Examples with solutions for Comparing Decimal Fractions

Step-by-step solutions included
Exercise #1

Which decimal number is greater?

Step-by-Step Solution

Let's convert the decimal numbers into simple fractions and compare them:

0.24 is divided by 100 because there are two digits after the decimal point, therefore:

0.24=24100 0.24=\frac{24}{100}

0.25 is divided by 100 because there are two digits after the decimal point, therefore:

0.25=25100 0.25=\frac{25}{100}

Let's now compare the numbers in the numerator:

25100>24100 \frac{25}{100}>\frac{24}{100}

Therefore, the larger number is 0.25.

Answer:

0.25 0.25

Video Solution
Exercise #2

Are they the same numbers?

0.23=?0.32 0.23\stackrel{?}{=}0.32

Step-by-Step Solution

Let's observe the numbers after the decimal point.

Due to the fact that 23 and 32 are not identical, the numbers cannot be considered as the same number.

Answer:

No

Video Solution
Exercise #3

Are they the same numbers?

0.1=?0.10 0.1\stackrel{?}{=}0.10

Step-by-Step Solution

We will add 0 to the number 0.1 in the following way:

0.1=0.10 0.1=0.10

And we will discover that the numbers are indeed identical

Answer:

Yes

Video Solution
Exercise #4

Are they the same numbers?

0.25=?0.250 0.25\stackrel{?}{=}0.250

Step-by-Step Solution

We will add 0 to the number 0.25 in the following way:

0.25=0.250 0.25=0.250

And we will discover that the numbers are identical

Answer:

Yes

Video Solution
Exercise #5

Are they the same numbers?

0.22=?0.2 0.22\stackrel{?}{=}0.2

Step-by-Step Solution

We will add 0 to the number 0.2 in the following way:

0.2=0.20 0.2=0.20

And we will discover that the numbers are not identical

Answer:

No

Video Solution

Frequently Asked Questions

Everything you need to know about Comparing Decimal Fractions

How do you compare decimal numbers step by step?

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Use the digit-by-digit analysis method: First, compare whole numbers - the larger whole number means the larger decimal. If whole numbers are equal, compare digits after the decimal point from left to right (tenths, hundredths, etc.) until you find a difference.

What is the easiest way to compare decimals with different lengths?

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Focus on place value, not the number of digits. For example, 0.2 is greater than 0.130 because 2 tenths is greater than 1 tenth. Missing digits are treated as zeros, so 0.2 = 0.200.

Why is 60.23 greater than 45.78 when comparing decimals?

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Because the whole number part (60) is greater than the whole number part (45). When comparing decimals, always start with the whole numbers first - if they're different, you don't need to look at the decimal places.

How do you compare 4.154 and 4.11 using place value?

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Step by step comparison: 1) Whole numbers are equal (4 = 4). 2) Tenths place is equal (1 = 1). 3) Hundredths place differs (5 > 1). Therefore, 4.154 > 4.11.

What does it mean when decimals like 0.50 and 0.5 are equal?

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Trailing zeros after the decimal point don't change the value. Both 0.50 and 0.5 represent exactly 5 tenths, so they are equal. The zero in the hundredths place in 0.50 doesn't add value.

How many numbers are between 1.7 and 1.8?

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There are infinite numbers between any two decimals. Examples include 1.71, 1.75, 1.702, 1.789, etc. Any decimal starting with 1.7 followed by digits other than 0, or 1.8 followed by digits, will fall between these values.

What are common mistakes when comparing decimal numbers?

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Common errors include: 1) Thinking more digits means a larger number (0.130 vs 0.2). 2) Not aligning decimal points mentally. 3) Forgetting that missing digits equal zero. 4) Comparing decimal parts like whole numbers without considering place value.

How do you use greater than and less than symbols with decimals?

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The symbol always points to the smaller number. For 60.23 > 45.78, the '>' points to 45.78 (smaller). For 0.003 < 0.03, the '<' points to 0.003 (smaller). Remember: the wide end faces the larger number.

More Comparing Decimal Fractions Questions

Click on any question to see the complete solution with step-by-step explanations

Comparing Decimal Fractions

Calculate the Sum: Adding £42.50 and £32.40 in British Currency Compare Fractions and Decimals: Is 2/4 = 0.5? Compare Fraction and Decimal: 1/5 ? 0.22 - Select the Correct Sign Compare 0.8 and 8/100: Choosing the Correct Mathematical Symbol Solve the Decimal Inequality: Finding a Number Between 0.45 and 0.5

Continue Your Math Journey

Master Comparing Decimal Fractions first, then advance to these related topics that build on your fraction skills

Suggested Topics to Practice in Advance

What is a Decimal Number?Decimal fraction remainderRemaindersDecimal FractionsReducing and Expanding Decimal NumbersConverting a Decimal Fraction to a Mixed NumberConverting a simple fraction to decimal - how to calculate?Addition and Subtraction of Decimal Numbers

Topics Learned in Later Sections

Converting Decimals to Fractions

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems
Comparison to simple fractions Find the missing number Identical numbers Identify the greater value Is the equality correct? Worded problems Write the suitable number