Solved Exercises on Comparing Decimals to Hundredths in Grade 4

Master comparing decimals to hundredths: place value understanding, comparison strategies, and practical applications through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic Decimal Comparison
Exercise 1
Compare 0.45 and 0.38. Which is greater?
Definition:

Comparing decimals: Determining which decimal number is greater, lesser, or equal to another

Place value: The value of a digit based on its position in a number

Comparison method:
  1. Align the decimal points vertically
  2. Compare digits from left to right (starting with the tenths place)
  3. If digits in the same place are equal, move to the next place value
  4. The first unequal digit determines which number is greater
Decimals
0.45 vs 0.38
Compare
4 > 3
Result
0.45 > 0.38
Step 1: Align the decimals

0.45

0.38

Step 2: Compare tenths place

Tenths in 0.45: 4

Tenths in 0.38: 3

Since 4 > 3, 0.45 is greater

Step 3: No need to compare hundredths

Since the tenths are different, we can stop here

Step 4: Write the comparison

0.45 > 0.38

0.45 > 0.38
Final answer:

0.45 is greater than 0.38

Applied rules:

• Left-to-Right Rule: Always compare from left to right (highest place value first)

• Place Value Rule: Higher place values have greater influence on the number's value

• Stop Rule: Stop comparing once you find different digits in the same place

Tip: Think of decimals like money: $0.45 is more than $0.38
2 Equal Decimals Comparison
Exercise 2
Compare 0.70 and 0.7. Are they equal?
Definition:

Equivalent decimals: Different decimal representations that represent the same value

Trailing zeros: Zeros at the end of a decimal that don't change the value

Decimals
0.70 vs 0.7
Comparison
Same value
Result
0.70 = 0.7
Step 1: Align the decimals

0.70

0.70 (adding a trailing zero to match places)

Step 2: Compare tenths place

Tenths in 0.70: 7

Tenths in 0.7: 7

They are equal, continue comparing

Step 3: Compare hundredths place

Hundredths in 0.70: 0

Hundredths in 0.7: 0 (since 0.7 = 0.70)

They are equal

Step 4: Conclusion

All corresponding digits are equal, so 0.70 = 0.7

0.70 = 0.7
Final answer:

0.70 is equal to 0.7

Applied rules:

• Equivalence Rule: Adding zeros after the last non-zero digit doesn't change the value

• Place Value Rule: 0.7 = 0.70 = 0.700 because they represent the same amount

• Comparison Rule: If all corresponding digits are equal, the numbers are equal

Tip: Think of 0.7 as 0.70 - they both represent 70 hundredths
3 Comparing with Different Whole Numbers
Exercise 3
Compare 1.23 and 0.98. Which is greater?
Definition:

Decimal with whole number: A number with both whole and decimal parts

Comparison rule: Whole number part is always compared first

Decimals
1.23 vs 0.98
Compare
1 > 0
Result
1.23 > 0.98
Step 1: Compare whole number parts first

Whole part of 1.23: 1

Whole part of 0.98: 0

Since 1 > 0, we can stop here

Step 2: Apply the whole number rule

Any number with a whole part of 1 is greater than any number with a whole part of 0

Step 3: No need to compare decimal parts

Since the whole numbers are different, the decimal parts don't matter

Step 4: Write the comparison

1.23 > 0.98

1.23 > 0.98
Final answer:

1.23 is greater than 0.98

Applied rules:

• Whole Number Priority: Always compare whole number parts first

• Place Value Hierarchy: Whole numbers have greater value than decimal fractions

• Stop Rule: If whole parts differ, decimal parts don't affect the comparison

Tip: Think of it like counting: 1 apple is always more than 0 apples, regardless of the decimal parts
Decimal Comparison Summary
0.45 > 0.38
Comparison Example
Greater Than
>
Symbol means "is greater than"
Less Than
<
Symbol means "is less than"
Equal To
=
Symbol means "is equal to"
Key definitions:

Decimal place value: Each position after the decimal represents a power of ten

Tenths place: First digit after decimal point (1/10)

Hundredths place: Second digit after decimal point (1/100)

Comparison: Determining which number is larger, smaller, or equal

Complete methodology:
  1. Align decimal points: Line up numbers by their decimal points
  2. Compare whole numbers first: If present, compare these first
  3. Compare tenths place: If whole numbers are equal, compare tenths
  4. Compare hundredths place: If tenths are equal, compare hundredths
  5. Write the result: Use appropriate comparison symbol
Tip 1: Always compare from left to right, starting with the highest place value.
Tip 2: Trailing zeros after the last non-zero digit don't change the value (0.5 = 0.50).
Tip 3: For easier comparison, add zeros to make all decimals have the same number of places.
Tip 4: Think of decimals as money to make comparison more intuitive.
Common errors: Comparing from right to left, forgetting to compare whole numbers first, ignoring place value.
Memory aid: "Look left to right, whole numbers first, then tenths, then hundredths."
Comparison rules:

• Compare whole number parts first (if any)

• Then compare tenths place: 4 tenths > 3 tenths

• If tenths are equal, compare hundredths place

• Equivalent decimals: 0.5 = 0.50 = 0.500

Solution: Exercises 4 to 5
4 Comparing Same Whole Numbers
Exercise 4
Compare 2.45 and 2.63. Which is greater?
Definition:

Same whole number comparison: When whole numbers are equal, compare decimal parts

Decimal part analysis: Focus on tenths and hundredths when whole numbers match

Decimals
2.45 vs 2.63
Compare
2 = 2
Compare tenths
4 < 6
Result
2.45 < 2.63
Step 1: Compare whole number parts

Whole part of 2.45: 2

Whole part of 2.63: 2

Since 2 = 2, continue comparing

Step 2: Compare tenths place

Tenths in 2.45: 4

Tenths in 2.63: 6

Since 4 < 6, 2.45 is less than 2.63

Step 3: No need to compare hundredths

Since the tenths are different, we can stop here

Step 4: Write the comparison

2.45 < 2.63

2.45 < 2.63
Final answer:

2.45 is less than 2.63

Applied rules:

• Whole Number Equality: When whole numbers are equal, compare decimal parts

• Place Value Hierarchy: Continue comparing from highest decimal place value

• Stop Rule: Stop when finding different digits in the same place

Tip: When whole numbers are the same, focus only on the decimal parts
5 Ordering Multiple Decimals
Exercise 5
Order these decimals from least to greatest: 0.56, 0.6, 0.506, 0.65
Definition:

Decimal ordering: Arranging decimals in ascending or descending order

Systematic comparison: Comparing multiple numbers using consistent method

Numbers
0.56, 0.6, 0.506, 0.65
Standardize
0.560, 0.600, 0.506, 0.650
Ordered
0.506, 0.560, 0.600, 0.650
Step 1: Standardize decimal places

Write each decimal with three decimal places: 0.560, 0.600, 0.506, 0.650

Step 2: Compare tenths place

0.506 (5 tenths), 0.560 (5 tenths), 0.600 (6 tenths), 0.650 (6 tenths)

Step 3: Among those with 5 tenths, compare hundredths

0.506 (0 hundredths), 0.560 (6 hundredths)

Step 4: Among those with 6 tenths, compare hundredths

0.600 (0 hundredths), 0.650 (5 hundredths)

Step 5: Arrange in order

0.506 < 0.560 < 0.600 < 0.650

Step 6: Return to original forms

0.506 < 0.56 < 0.6 < 0.65

0.506 < 0.56 < 0.6 < 0.65
Final answer:

From least to greatest: 0.506, 0.56, 0.6, 0.65

Applied rules:

• Standardization Rule: Make all decimals have same number of decimal places

• Grouping Rule: Group numbers with same whole/tenths/hundredths digits

• Sequential Comparison: Compare systematically from highest to lowest place value

Tip: Always standardize decimals by adding zeros to make comparison easier
Decimal Comparison Fundamentals and Practice
0.45 > 0.38 because 4 > 3 in tenths place
Comparison Example
Key definitions:

Decimal comparison: Determining the relative size of decimal numbers using place value

Place value system: Each position has a specific value based on powers of ten

Decimal places: Positions after the decimal point (tenths, hundredths, thousandths)

Complete methodology:
  1. Align decimals: Write numbers with decimal points aligned vertically
  2. Compare whole numbers: Start with the largest place value
  3. Compare decimal parts: Move to tenths, then hundredths if needed
  4. Use comparison symbols: > (greater than), < (less than), = (equal to)
Tip 1: Think of decimals as money ($0.45 vs $0.38) to make comparisons intuitive.
Tip 2: Add trailing zeros to make all decimals have the same number of places for easier comparison.
Tip 3: Remember that 0.5 = 0.50 = 0.500 - trailing zeros don't change the value.
Tip 4: Always compare from left to right, starting with the highest place value.
Common errors: Comparing from right to left, forgetting whole numbers, misaligning decimal points.
Memory aid: "Start big, go small - whole numbers first, then tenths, then hundredths."
Decimal comparison rules:

• Always compare from left to right (highest place value first)

• Compare whole number parts first if present

• Then compare tenths place, then hundredths place

• Equivalent decimals: 0.5 = 0.50 = 0.500

• Trailing zeros don't change the value of a decimal

Decimal Comparison Visualization
Understanding Decimal Values
Visual representation of decimal comparison:
0.35 vs 0.42
0.7 vs 0.68
1.25 vs 1.30

Analysis: The chart shows how decimal values compare visually on a number line.

  • 0.35 is less than 0.42 (35 hundredths vs 42 hundredths)
  • 0.7 is greater than 0.68 (70 hundredths vs 68 hundredths)
  • 1.25 is less than 1.30 (125 hundredths vs 130 hundredths)

Questions & Answers

Question: I'm confused about comparing 0.5 and 0.50. They look different but my teacher says they're the same. How is that possible?

Answer: Great question! 0.5 and 0.50 are indeed equal. Here's why:

  • 0.5 means 5 tenths, which is the same as 50 hundredths
  • 0.50 means 50 hundredths
  • So 5 tenths = 50 hundredths, which means 0.5 = 0.50

Think of it like money: $0.50 (50 cents) is the same as $0.5 (also 50 cents). The extra zero at the end doesn't change the value - it's called a "trailing zero" and it doesn't affect the number's worth.

When comparing decimals, you can always add or remove trailing zeros to make the comparison easier: 0.5 = 0.50 = 0.500.

Question: How do I compare 0.4 and 0.39? One has two digits and one has one digit.

Answer: To compare decimals with different numbers of digits, add zeros to make them the same length:

  • 0.4 is the same as 0.40 (4 tenths = 40 hundredths)
  • Now you can compare 0.40 and 0.39
  • 40 hundredths is greater than 39 hundredths

So 0.4 > 0.39. The key is to think of 0.4 as 0.40, which makes it easier to compare with 0.39. Both are now expressed in hundredths: 40 hundredths vs 39 hundredths.

Always remember to compare from left to right, starting with the highest place value (tenths, then hundredths).

Question: I sometimes get confused and compare from right to left. How can I remember to go left to right?

Answer: This is a common mistake! Here are some memory aids to help you remember:

  • Think of reading: We read from left to right, and decimal comparison works the same way
  • Think of importance: The leftmost digits have the most impact on the number's value
  • Think of money: $1.23 is more than $0.99 because the 1 in the ones place is more important than the 9 in the tenths place

Remember: "Start big, go small" - begin with the largest place value (ones, tenths) and work toward smaller ones (hundredths). The leftmost digits determine the number's size more than the rightmost digits.

Practice saying: "Compare from left to right, whole numbers first, then tenths, then hundredths."