Subtract Decimals: Finding 5.4 - 0.21 Step by Step

Decimal Subtraction with Borrowing Across Places

5.40.21-

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Place 0 in missing digits, position the decimal point:
00:06 Let's subtract from right to left
00:09 The digit is too small for subtraction, so we'll borrow from the next
00:12 The next digit will decrease by 1, and our digit will increase by 10
00:18 Now subtract from the larger number
00:21 Calculate and place accordingly
00:28 Continue to subtract, calculate and place accordingly
00:46 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

5.40.21-

2

Step-by-step solution

To solve this problem, we will subtract the decimal number 0.210.21 from 5.45.4 by following these steps:

  • Step 1: Align the decimal points in both numbers.

  • Step 2: Note that 5.45.4 can be written as 5.405.40 to facilitate subtraction.

  • Step 3: Subtract 0.210.21 from 5.405.40 by starting from the rightmost decimal place.

Now, let's work through each step:

Step 1: Align the decimals:
5.4  0.213232 \begin{aligned} 5&.4\\ - ~~0&.21\\ \hline{\phantom{3232}} \end{aligned}

Step 2: Perform the subtraction, starting from the rightmost digit:

  • Subtract the hundredths column: 010 - 1 requires borrowing.
    From 44 in the tenths column, reduce it to 33, making the hundredth column 1010, then 101=910 - 1 = 9.

  • Subtract the tenths column: 32=13 - 2 = 1.

  • Subtract the units column: 50=55 - 0 = 5.

The result of the subtraction is:
    5.19     5.19

Therefore, the solution to the problem is 5.195.19.

3

Final Answer

5.19

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Line up decimal points to ensure correct place values
  • Technique: Add zeros as placeholders: 5.4 becomes 5.40 for easier subtraction
  • Check: Verify 5.19 + 0.21 = 5.40, which equals our original 5.4 ✓

Common Mistakes

Avoid these frequent errors
  • Not aligning decimal points properly
    Don't subtract digits without aligning decimals = 5.4 - 0.21 becomes 5.2 - 0.1 = 5.1! This ignores place values completely. Always line up the decimal points first, then add zeros as needed.

Practice Quiz

Test your knowledge with interactive questions

Choose the correct writing form:

FAQ

Everything you need to know about this question

Why do I need to write 5.4 as 5.40?

+

Adding the zero makes subtraction easier! 5.40 and 5.4 are exactly the same number, but writing 5.40 gives you a digit in the hundredths place to work with.

What does 'borrowing' mean in decimal subtraction?

+

Borrowing is when you can't subtract a larger digit from a smaller one. Take 1 from the next column to the left, making it 10 in your current column. Just like with whole numbers!

How do I know when I need to borrow?

+

You need to borrow when the top digit is smaller than the bottom digit in any column. In 5.40 - 0.21, we can't do 0 - 1, so we borrow from the 4.

Can I check my answer without adding?

+

Yes! You can also count up from 0.21 to 5.4. Start with 0.21, add your answer 5.19, and see if you get 5.4. Both methods work great!

What if there are more decimal places?

+
  • Same process: Align decimal points
  • Add zeros: Make both numbers have the same decimal places
  • Subtract normally: Borrow when needed

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Decimal Fractions - Basic questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

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