Practice Subtracting Decimals to Hundredths: Exercises for Grade 4

Master subtracting decimals to hundredths: alignment, borrowing, and word problems through these focused practice exercises.

Solution: Exercises 1 to 3
1 Basic subtraction to hundredths
Exercise 1
Subtract:
\(9.87 - 3.45\)
Definition:

Subtracting to hundredths: Align decimal points and subtract each place value column up to the hundredths place

Subtraction method:
  1. Line up the decimal points
  2. Subtract hundredths column first
  3. Subtract tenths column
  4. Subtract ones column
  5. Place the decimal point in the answer
Setup
\(9.87\)
\(−3.45\)
Subtraction
\(6.42\)
Step 1: Align decimal points

\(9.87\)
\(−3.45\)
\(\overline{~~~~~~}\)

Step 2: Subtract hundredths column

\(7 - 5 = 2\)

Step 3: Subtract tenths column

\(8 - 4 = 4\)

Step 4: Subtract ones column

\(9 - 3 = 6\)

\(9.87 - 3.45 = 6.42\)
Final answer:

\(9.87 - 3.45 = 6.42\)

Applied rules:

• Alignment: Always line up decimal points before subtracting

• Place value: Subtract digits in the same place value columns

• Decimal point: Place decimal point in the answer directly below others

2 Borrowing across tenths
Exercise 2
Subtract:
\(7.03 - 2.58\)
Definition:

Borrowing across tenths: When subtracting hundredths and the top digit is smaller, borrow from tenths

Setup
\(7.03\)
\(−2.58\)
Borrowing
\(6.9[13]\)
Result
\(4.45\)
Step 1: Align decimal points

\(7.03\)
\(−2.58\)
\(\overline{~~~~~~}\)

Step 2: Need to borrow in hundredths

We can't subtract \(8\) from \(3\), so we borrow from tenths

Step 3: Borrow from tenths

Tenths has \(0\), so we borrow from ones: \(7.03 = 6.9[13]\)

Step 4: Complete subtraction

Hundredths: \(13 - 8 = 5\)
Tenths: \(9 - 5 = 4\)
Ones: \(6 - 2 = 4\)

\(7.03 - 2.58 = 4.45\)
Final answer:

\(7.03 - 2.58 = 4.45\)

Applied rules:

• Borrowing rule: When top digit is smaller, borrow from next higher place value

• Zero borrowing: If a zero needs to borrow, it becomes \(9\) and borrows from the next column

• Decimal point: Keep aligned in final answer

3 Word problem
Exercise 3
Emma had $15.75. She bought a snack for $4.89. How much money does she have left?
Definition:

Word problem: Identify key information and convert to mathematical expression

Initial amount
\$15.75
Amount spent
\$4.89
Money left
\$10.86
Step 1: Identify the operation

Money left = Initial money − Money spent

\$15.75 − \$4.89

Step 2: Set up subtraction

\(15.75\)
\(−4.89\)
\(\overline{~~~~~~}\)

Step 3: Subtract hundredths

We can't subtract \(9\) from \(5\), so we borrow: \(15.75 = 15.6[15]\)

\(15 - 9 = 6\)

Step 4: Continue subtraction

Tenths: \(6 - 8\) (borrow from ones): \(16 - 8 = 8\)
Ones: \(14 - 4 = 10\)
Tens: \(1 - 0 = 1\)

Emma has \$10.86 left
Final answer:

Emma has \$10.86 left

Applied rules:

• Problem solving: Identify operation from context ("left" indicates subtraction)

• Decimal alignment: Align decimal points when subtracting money

• Borrowing: Use when top digit is smaller than bottom digit

Subtracting Decimals to Hundredths: Rules and Methods
\(9.87 - 3.45 = 6.42\)
Basic Subtraction to Hundredths
Rule 1
Align Decimal Points
Always line up decimal points before subtracting
Rule 2
Borrow When Needed
If top digit is smaller, borrow from next column
Rule 3
Same Place Values
Subtract digits in the same place value columns
Key definitions:

Decimal to Hundredths: A decimal number that has two digits after the decimal point (e.g., 3.45, 0.72, 12.99)

Hundredths place: The second digit after the decimal point represents 1/100 of a whole

Decimal point: The dot that separates the whole number part from the fractional part

Complete methodology:
  1. Read the problem: Understand what is being asked
  2. Identify numbers: Find the decimal numbers to subtract
  3. Align decimals: Line up decimal points vertically
  4. Subtract column by column: Start from the hundredths column
  5. Place decimal point: Put it directly below the others
Tip 1: Always align decimal points first - this is the most important step!
Tip 2: Check your answer by adding the result to the number you subtracted.
Tip 3: When borrowing across zeros, turn zeros into nines and borrow from the next non-zero digit.
Tip 4: Practice with money examples since dollars and cents naturally use hundredths.
Common errors: Misaligning decimal points, forgetting to borrow, subtracting bottom from top regardless of size.
Practice tips: Start with simple decimals, practice borrowing across zeros, use money examples for real-world context.
Decimal Subtraction to Hundredths: Advanced Concepts
\(7.03 - 2.58 = 4.45\)
Borrowing Across Tenths
Place Values
Ones.Tenths.Hundredths
Position determines value of each digit
Borrowing Rule
Borrow 1 from Left
When top digit is smaller than bottom digit
Checking Answer
Add Result Back
Verify by adding difference to subtracted amount
More definitions:

Minuend: The number being subtracted from (top number)

Subtrahend: The number being subtracted (bottom number)

Difference: The result of the subtraction

Steps for borrowing across tenths:
  1. Look at the hundredths column where you need to borrow
  2. If the top digit is smaller than the bottom digit, borrow from tenths
  3. If the tenths digit is zero, borrow from the ones place
  4. Adjust the tenths digit and add 10 to the hundredths digit
  5. Complete the subtraction
Memory aid: "If you see a zero, go to the hero!" - borrow from the first non-zero digit to the left.
Real world: Think of decimal subtraction as taking away money, weight, or distance.
Important facts to remember:

• Always align decimal points before subtracting

• When borrowing, decrease the left digit by 1

• The decimal point in the answer lines up with the others

• Check your answer by adding the difference to the subtrahend

• Focus on the hundredths place when subtracting to hundredths

Questions & Answers

Question: Why do I need to align decimal points when subtracting decimals to hundredths? Can't I just subtract them like regular numbers?

Answer: Aligning decimal points is crucial because it ensures you're subtracting digits with the same place value. Look at this example:

Without lining up:
9.87
-3.4
----
6.47 ← This is wrong!

With decimal points lined up:
9.87
-3.40 ← Added zero to make hundredths column
----
6.47 ← This is correct!

When you don't align decimal points, you might subtract tenths from ones or hundredths from tenths, which gives incorrect results. The decimal point acts as a reference point that keeps place values organized.

Question: My child gets confused when subtracting decimals like 7.03 - 2.58. How can I help them understand borrowing across tenths?

Answer: Borrowing across tenths can be tricky! Here's a helpful approach:

Visual method: Think of 7.03 as 703 hundredths. Then subtract 258 hundredths from 703 hundredths, which equals 445 hundredths or 4.45.

Step-by-step:

  • Start at the hundredths column: Can't subtract 8 from 3
  • Move to tenths: It's 0, so can't borrow from it
  • Go to ones: Borrow 1 from 7, making it 6
  • This turns the 0 in tenths into 10, then borrow 1 from that, making it 9
  • The 3 in hundredths becomes 13, now you can subtract: 13-8=5

A fun memory trick: "If you see a zero, go to the hero!" - borrow from the first non-zero digit to the left.

Question: How can I check if my decimal subtraction to hundredths is correct? I want to make sure I got the right answer.

Answer: There's a great way to check your decimal subtraction answers! It's called the "addition check" method:

Example: If you calculated 9.87 - 3.45 = 6.42

Check: Add your answer (6.42) to the number you subtracted (3.45)
6.42 + 3.45 = 9.87 ✓

If your addition gives you back the original number (9.87), then your subtraction was correct!

Another quick check: Estimate the answer first. For 9.87 - 3.45, think "about 10 - 3 = 7", so your answer should be close to 7. Since 6.42 is close to 7, that's another sign your answer is reasonable.

Detailed Summary: Subtracting Decimals to Hundredths Mastery

Key Definitions

Decimal to Hundredths: A decimal number that extends to the hundredths place (two digits after the decimal point), such as 3.45, 0.72, or 12.99.

Hundredths Place: The second digit after the decimal point, representing 1/100 of a whole unit (0.01).

Decimal Point: The dot (.) that separates the whole number part from the fractional part in a decimal number.

Place Value: The value of a digit based on its position in the number (ones, tenths, hundredths, etc.).

Core Rules and Principles

Alignment Rule: Always align decimal points when subtracting decimals to hundredths. This ensures you're working with digits of the same place value.

Borrowing Rule: When subtracting and the top digit is smaller than the bottom digit in any column, borrow 1 from the next higher place value column.

Place Value Rule: Only subtract digits that are in the same place value positions (hundredths with hundredths, tenths with tenths, etc.).

Step-by-Step Methods

Subtracting Decimals to Hundredths:

  1. Write the numbers vertically with decimal points aligned
  2. Ensure both numbers have the same number of decimal places (add zeros if needed)
  3. Starting from the hundredths place, subtract each column
  4. If the top digit is smaller than the bottom digit, borrow from the next column
  5. Place the decimal point in the answer directly below the others

Borrowing Across Zero:

  1. When you need to borrow but encounter a zero, move to the next non-zero digit
  2. Decrease that digit by 1
  3. Change all zeros in between to 9s
  4. Increase the zero you were trying to borrow from to 10
  5. Continue with the subtraction

Concrete Examples

Simple Example: 0.87 - 0.32 = 0.55 (no borrowing needed)

Intermediate Example: 5.23 - 1.47 = 3.76 (requires borrowing in hundredths)

Advanced Example: 7.03 - 2.58 = 4.45 (requires borrowing across tenths)

Word Problem: $15.75 - $4.89 = $10.86 (real-world context)

Tips, Tricks, and Common Pitfalls

Tips:

  • Always align decimal points first - this prevents most errors
  • Add zeros at the end of shorter decimals to make subtraction easier
  • Check your answer by adding the result to the number you subtracted
  • Think of decimals as money ($0.87 is easier to understand than 0.87)
  • Practice with real-world examples like measuring lengths or calculating change

Common Pitfalls:

  • Misaligning decimal points leading to wrong place values
  • Forgetting to borrow when subtracting
  • Subtracting the smaller number from the larger regardless of position
  • Not placing the decimal point in the correct position in the answer

Key Notes for Memorization

"ABD": Remember the acronym "Align, Borrow, Decimal" for decimal subtraction.

Memory Aid: "If you see a zero, go to the hero!" - borrow from the first non-zero digit to the left when borrowing across zeros.

Check Your Work: Always verify by adding the result to the number you subtracted, or by estimating the answer first.

Focus on Hundredths: When subtracting to hundredths, pay special attention to the hundredths place and ensure both numbers have two decimal places.