GMAT Online Course: Decimals Adding & Subtracting
- Goalisb
- Jul 14
- 17 min read
GMAT Decimals: The Unshakable Rule for Adding & Subtracting (Why Alignment is Everything)
Adding and subtracting decimals might seem straightforward, but a single, critical rule governs these operations to ensure accuracy: lining up the decimal points. Neglecting this rule is a primary source of errors, especially under the pressure of the GMAT. Let's break down why this rule is paramount and how to master it.
The Golden Rule: Line Up Decimal Points!
Imagine you're adding apples and oranges. You wouldn't just lump them together without differentiating, right? Similarly, with decimals, you can only add or subtract digits that represent the same place value. This is precisely why aligning the decimal points is non-negotiable.
When you line up the decimal points, you automatically align:
Ones with ones
Tens with tens
Tenths with tenths
Hundredths with hundredths
...and so on!
This ensures that you are consistently combining or differentiating quantities of the same magnitude.
Visualizing Alignment:
Let's say you want to add 12.34 and 5.6.
Incorrect:
12.34
+ 5.6
-------
(Looks messy, hard to see what's what)
Correct:
12.34
+ 5.6
-------
(Clear alignment of decimal points, and thus, place values)
The Strategic Helper: Inserting Zeros for Alignment
Once your decimal points are aligned, you might notice that some numbers have more decimal places than others. For instance, in 12.34 + 5.6, 12.34 has two decimal places, while 5.6 only has one.
This is where inserting trailing zeros comes in. Adding zeros to the end of a decimal (after the last non-zero digit) does not change its value, but it does help visually align the columns and prevent mistakes. Think of 5.6 as 5.60 – they represent the exact same value.
12.34
+ 5.60 <-- We added a zero here!
-------
Now, every column (hundredths, tenths, ones, tens) has a digit, making the operation much clearer and less prone to errors.
Adding Decimals: Step-by-Step Mastery
Process:
Write the numbers vertically, ensuring their decimal points are perfectly aligned.
If necessary, add trailing zeros to the number(s) with fewer decimal places to match the number with the most decimal places.
Add the numbers as you would whole numbers, starting from the rightmost column.
Carry over digits to the next column to the left when a sum exceeds 9.
Place the decimal point in the answer directly below the aligned decimal points in the numbers being added.
Example 1: Simple Addition
Calculate 7.35 + 2.12
7.35
+ 2.12
-------
9.47
5 + 2 = 7 (hundredths place)
3 + 1 = 4 (tenths place)
Decimal point placed.
7 + 2 = 9 (ones place)
Example 2: Adding with Varying Decimal Places
Calculate 15.8 + 3.472
15.800 <-- Added two zeros to 15.8
+ 3.472
---------
19.272
0 + 2 = 2 (thousandths place)
0 + 7 = 7 (hundredths place)
8 + 4 = 12. Write 2, carry 1 to the ones place. (tenths place)
Decimal point placed.
1 (carried) + 5 + 3 = 9 (ones place)
1 (tens place) remains 1.
Subtracting Decimals: Step-by-Step Mastery
Process:
Write the numbers vertically, ensuring their decimal points are perfectly aligned. The larger number usually goes on top.
If necessary, add trailing zeros to the number(s) with fewer decimal places to match the number with the most decimal places.
Subtract the numbers as you would whole numbers, starting from the rightmost column.
Borrow from the next column to the left when a digit is too small to subtract from.
Place the decimal point in the answer directly below the aligned decimal points.
Example 1: Simple Subtraction
Calculate 8.76 - 3.25
8.76
- 3.25
-------
5.51
6 - 5 = 1 (hundredths place)
7 - 2 = 5 (tenths place)
Decimal point placed.
8 - 3 = 5 (ones place)
Example 2: Subtracting with Varying Decimal Places and Borrowing
Calculate 25.3 - 8.175
25.300 <-- Added two zeros to 25.3
- 8.175
---------
17.125
Thousandths: Can't do 0 - 5. Borrow from the hundredths 0. But 0 has nothing, so borrow from 3 in tenths place.
3 becomes 2. The hundredths 0 becomes 10, then gives 1 to thousandths becoming 9. Thousandths 0 becomes 10.
10 - 5 = 5.
Hundredths: Now have 9 - 7 = 2.
Tenths: Now have 2 - 1 = 1.
Decimal point placed.
Ones: Can't do 5 - 8. Borrow from 2 in tens place.
2 becomes 1. 5 becomes 15.
15 - 8 = 7.
Tens: Now have 1 (remaining from original 2).
Result: 17.125
GMAT Relevance & Key Takeaways
Accuracy is Paramount: Unlike estimation, when adding or subtracting, the GMAT expects precision. Sloppy alignment is the primary cause of errors.
Word Problems: Decimals frequently appear in word problems involving money, measurements (length, weight, volume), and statistics. The ability to add/subtract them quickly and accurately is essential.
Data Sufficiency: You might need to add or subtract decimals to determine if a statement provides sufficient information.
Don't Rush the Setup: The biggest mistake is rushing to line up numbers in your head or haphazardly on scratch paper. Take an extra second to set up the problem neatly.
Mastering decimal addition and subtraction isn't just about getting the right answer; it's about building a solid foundation for more complex decimal operations and ensuring your GMAT calculations are consistently accurate.
Version 2: Self-Paced Course - "Lesson 4.4: Adding and Subtracting Decimals – The Pillar of Place Value Operations"
Greetings and welcome to Lesson 4.4 of Module 4! In our previous illuminating lessons, we meticulously constructed a robust understanding of decimal place values, harnessed the power of scientific notation, and honed our strategic approximation skills through rounding and estimation. Now, we arrive at the very heart of decimal arithmetic: Adding and Subtracting Decimals. These are fundamental, bedrock operations that form the indispensable prerequisites for all more complex decimal manipulations. While seemingly straightforward, the simplicity of these operations belies a critical requirement for precision that, if overlooked, can lead to significant errors, particularly under the demanding time constraints of the GMAT Quantitative section.
This lesson will provide an exhaustive, systematic breakdown of the immutable rules governing decimal addition and subtraction. We will not merely state the rules; we will delve into the profound why behind them, emphasizing the pivotal role of place value. We will explore the critical technique of aligning decimal points, demonstrating its absolute necessity, and then introduce the highly practical strategy of inserting trailing zeros for foolproof alignment. Through a series of diverse, highly detailed examples for both addition and subtraction, we will navigate scenarios involving varying numbers of decimal places, the crucial processes of carrying and borrowing, and potential pitfalls. By the conclusion of this meticulously detailed session, you will possess not only the procedural knowledge but also the conceptual clarity to perform these operations with unwavering confidence, speed, and precision, directly translating into higher accuracy on your GMAT exam.
I. The Indispensable Principle: Aligning Decimal Points – The Cornerstone of Decimal Arithmetic
The cornerstone of accurate decimal addition and subtraction is a single, non-negotiable principle: the decimal points of all numbers involved MUST be perfectly aligned vertically. This is not a mere suggestion for neatness; it is a mathematical imperative.
The Conceptual Rationale (Why this rule is Sacred):
Recall from Lesson 4.1 that each digit in a decimal number occupies a specific place value. For instance, in 3.14, the 3 is in the ones place, the 1 is in the tenths place, and the 4 is in the hundredths place.
When you add or subtract numbers, you are inherently combining or differentiating quantities that represent the same unit. You add hundreds to hundreds, tens to tens, ones to ones, tenths to tenths, hundredths to hundredths, and so on.
Aligning the decimal points guarantees that digits of identical place values are positioned directly above or below one another. This systematic vertical arrangement prevents the accidental addition of a digit in the tenths place to a digit in the hundredths place, which would fundamentally violate the principles of place value and inevitably lead to an incorrect result.
Visualizing Correct vs. Incorrect Alignment:
Let's consider an attempt to add 12.345 and 6.78.
Incorrect Alignment (A Recipe for Error):
12.345 <-- Misaligned decimal points + 6.78 ----------
(In this scenario, you might mistakenly add the 5 to nothing, the 4 to the 8, the 3 to the 7, and so on, completely disregarding their true place values.)
Correct Alignment (The Foundation of Accuracy):
12.345 + 6.78 ----------
(Here, 5 (thousandths) aligns with nothing; 4 (hundredths) aligns with 8 (hundredths); 3 (tenths) aligns with 7 (tenths); 2 (ones) aligns with 6 (ones); 1 (tens) aligns with nothing. This is mathematically sound.)
II. The Strategic Aid: Inserting Trailing Zeros for Enhanced Clarity and Precision
Even after meticulously aligning decimal points, you will frequently encounter scenarios where the numbers involved possess a differing number of decimal places. For example, 12.34 has two decimal places, while 5.6 has only one.
This is precisely where the strategy of inserting trailing zeros becomes an invaluable aid.
The Mathematical Justification: Appending zeros to the rightmost end of a decimal number (after the last non-zero digit) does not alter its fundamental value. For instance, 5.6 is numerically equivalent to 5.60, 5.600, or 5.6000. Conceptually, 5.6 means 5 and 6 tenths. 5.60 means 5 and 6 tenths and 0 hundredths. The 0 hundredths adds no value.
The Practical Advantage: While mathematically unnecessary for the underlying calculation, these trailing zeros serve a crucial practical purpose: they visually complete the columns for each place value. This completion significantly enhances readability, minimizes the potential for column misalignment errors, and ensures that every column has a corresponding digit (even if it's a zero) for the arithmetic operation. This seemingly minor step can dramatically improve calculation accuracy, especially under exam conditions.
Applying the Zero Insertion Strategy:
For our example 12.34 + 5.6:
12.34 (This number has 2 decimal places)
+ 5.6 (This number has 1 decimal place)
To ensure all columns are visually complete, we extend 5.6 to match the two decimal places of 12.34:
12.34
+ 5.60 <-- We strategically added a zero here to match the hundredths place
----------
Now, the hundreds column, the tens column, the ones column, the tenths column, and the hundredths column all have clearly defined digits for both numbers, making the addition process far more intuitive and less prone to oversight.
III. The Art of Adding Decimals: A Meticulous Step-by-Step Protocol
The process of adding decimals is fundamentally identical to adding whole numbers, with the singular, critical addition of decimal point alignment.
Detailed Step-by-Step Protocol:
Vertical Arrangement and Decimal Alignment: Precisely write down the numbers one beneath the other, ensuring that their decimal points are perfectly aligned in a vertical column. This is your absolute first and most critical step.
Zero Padding (If Necessary): Inspect the number of decimal places in each value. Identify the number that possesses the greatest number of decimal places. Then, for all other numbers, strategically append trailing zeros so that they all possess the same maximum number of decimal places. This creates visually complete columns and prevents confusion.
Summation (Right to Left): Commence the addition process from the rightmost column (the smallest place value, e.g., thousandths, then hundredths, etc.), moving progressively to the left.
Carrying Over (Standard Arithmetic): If the sum of the digits in any given column exceeds 9, write down the unit digit of the sum in that column's result row and "carry over" the tens digit (e.g., if sum is 15, write down 5 and carry over 1) to the column immediately to its left. This carrying process can extend across the decimal point.
Decimal Point Placement: Upon completion of all column additions, position the decimal point in your final sum (the answer) directly in the vertical line established by the aligned decimal points of the numbers you were adding.
Illustrative Examples with Exhaustive Detail:
Example 1: Basic Addition with Consistent Decimal Places
Calculate: 23.45 + 16.23
23.45 (Decimal points aligned)
+ 16.23
---------
39.68
Hundredths Place: 5 + 3 = 8. Write down 8.
Tenths Place: 4 + 2 = 6. Write down 6.
Decimal Point: Place the decimal point directly below the others.
Ones Place: 3 + 6 = 9. Write down 9.
Tens Place: 2 + 1 = 3. Write down 3.
Final Sum: 39.68
Example 2: Addition with Varying Decimal Places and Zero Padding
Calculate: 5.7 + 12.049
05.700 <-- Added two zeros to 5.7 to match thousandths place.
+ 12.049
----------
17.749
Thousandths Place: 0 + 9 = 9. Write down 9.
Hundredths Place: 0 + 4 = 4. Write down 4.
Tenths Place: 7 + 0 = 7. Write down 7.
Decimal Point: Place the decimal point directly below.
Ones Place: 5 + 2 = 7. Write down 7.
Tens Place: 0 + 1 = 1. Write down 1. (Note: Adding a leading zero to 5.7 as 05.700 can help with alignment in the tens column visually if needed, though not strictly required for the value itself).
Final Sum: 17.749
Example 3: Addition with Significant Carrying Over (Across Decimal Point)
Calculate: 4.876 + 9.135
4.876
+ 9.135
----------
14.011
Thousandths Place: 6 + 5 = 11. Write down 1, carry over 1 to the hundredths place.
Hundredths Place: 1 (carried) + 7 + 3 = 11. Write down 1, carry over 1 to the tenths place.
Tenths Place: 1 (carried) + 8 + 1 = 10. Write down 0, carry over 1 to the ones place.
Decimal Point: Place the decimal point directly below.
Ones Place: 1 (carried) + 4 + 9 = 14. Write down 4, carry over 1 to the tens place.
Tens Place: 1 (carried) remains 1.
Final Sum: 14.011
IV. The Mechanics of Subtracting Decimals: A Rigorous Step-by-Step Protocol
Subtracting decimals also mirrors whole number subtraction, but the concept of "borrowing" takes on added importance, especially when navigating across the decimal point or dealing with trailing zeros.
Detailed Step-by-Step Protocol:
Vertical Arrangement and Decimal Alignment: As with addition, the decimal points of the numbers (minuend and subtrahend) must be perfectly aligned vertically. The number from which you are subtracting (the minuend) generally goes on top.
Zero Padding (If Necessary): Identify the number with the greatest number of decimal places. Add trailing zeros to the other number(s) to match this maximum number of decimal places. This is particularly crucial in subtraction to ensure you have digits to subtract from, preventing errors when borrowing.
Subtraction (Right to Left): Begin subtracting from the rightmost column (smallest place value), moving progressively to the left.
Borrowing (Standard Arithmetic): If a digit in the top number (minuend) is smaller than the corresponding digit in the bottom number (subtrahend), you must "borrow" 1 from the digit in the column immediately to its left. This borrowed 1 effectively adds 10 to the current column's digit (e.g., borrowing from the ones place for the tenths place means 1 one becomes 10 tenths). This borrowing process can extend across the decimal point and across multiple zeros.
Decimal Point Placement: Place the decimal point in your final difference (the answer) directly below the aligned decimal points.
Illustrative Examples with Exhaustive Detail:
Example 1: Basic Subtraction with Consistent Decimal Places
Calculate: 38.95 - 12.43
38.95
- 12.43
---------
26.52
Hundredths Place: 5 - 3 = 2. Write down 2.
Tenths Place: 9 - 4 = 5. Write down 5.
Decimal Point: Place the decimal point directly below.
Ones Place: 8 - 2 = 6. Write down 6.
Tens Place: 3 - 1 = 2. Write down 2.
Final Difference: 26.52
Example 2: Subtraction with Varying Decimal Places and Essential Zero Padding
Calculate: 15.0 - 6.78
15.00 <-- Added one zero to 15.0 to create a hundredths place
- 6.78
----------
8.22
Hundredths Place: Can't do 0 - 8. We need to borrow.
Borrow from the 0 in the tenths place. But the tenths 0 has nothing to give.
So, we must borrow from the 5 in the ones place.
The 5 (ones) becomes 4.
The 0 (tenths) becomes 10.
Now, the 10 (tenths) can lend 1 to the hundredths place. The 10 (tenths) becomes 9.
The 0 (hundredths) becomes 10.
Now, 10 - 8 = 2. Write down 2.
Tenths Place: Now we have 9 (from the borrowed 10) minus 7.
9 - 7 = 2. Write down 2.
Decimal Point: Place the decimal point directly below.
Ones Place: Now we have 4 (from the original 5) minus 6. Can't do 4 - 6. Borrow from the 1 in the tens place.
The 1 (tens) becomes 0.
The 4 (ones) becomes 14.
14 - 6 = 8. Write down 8.
Tens Place: Now we have 0 (from the original 1). This is effectively an empty column.
Final Difference: 8.22
Example 3: Subtraction with Complex Borrowing Across Multiple Zeros and Decimal Point
Calculate: 20.005 - 12.348
1 9.99(10) <-- Visualization of borrowing path
2 0.005
- 1 2.348
------------
7.657
Thousandths Place: Can't do 5 - 8. Need to borrow.
Borrow from the 0 in the hundredths. But it has nothing.
Borrow from the 0 in the tenths. But it has nothing.
Borrow from the 0 in the ones place. But it has nothing.
Finally, borrow from the 2 in the tens place.
The 2 (tens) becomes 1.
The 0 (ones) becomes 10.
The 10 (ones) lends 1 to tenths, becoming 9.
The 0 (tenths) becomes 10.
The 10 (tenths) lends 1 to hundredths, becoming 9.
The 0 (hundredths) becomes 10.
The 10 (hundredths) lends 1 to thousandths, becoming 9.
The 5 (thousandths) becomes 15.
Now, 15 - 8 = 7. Write down 7.
Hundredths Place: Now we have 9 minus 4.
9 - 4 = 5. Write down 5.
Tenths Place: Now we have 9 minus 3.
9 - 3 = 6. Write down 6.
Decimal Point: Place the decimal point directly below.
Ones Place: Now we have 9 minus 2.
9 - 2 = 7. Write down 7.
Tens Place: Now we have 1 (from the original 2) minus 1.
1 - 1 = 0. This is a leading zero, so it's not written.
Final Difference: 7.657
V. GMAT Relevance & Strategic Insights
Mastering decimal addition and subtraction is more than just a procedural exercise; it's a fundamental prerequisite for success in a wide array of GMAT quantitative problems.
Ubiquitous in Word Problems: Decimals are omnipresent in GMAT word problems involving real-world quantities:
Money: Calculating total costs, change due, profit/loss.
Measurements: Combining lengths, weights, volumes, or finding differences.
Statistics: Calculating averages, deviations, or combining data sets.
Data Sufficiency Integration: These operations are frequently necessary as an intermediate step to evaluate whether a statement provides sufficient information to answer a question. You might need to add or subtract quantities presented as decimals to test a hypothesis.
Problem Solving Foundation: While rarely tested in isolation, these operations are the bedrock upon which more complex decimal multiplications, divisions, and percentage calculations are built. A single error here can cascade through an entire multi-step problem.
Key to Accuracy, Not Speed (for these ops): Unlike estimation where speed is key, for addition and subtraction, the emphasis is on accuracy. Take the extra second to perform careful alignment and borrowing/carrying. Rushing the setup is the single biggest contributor to errors.
Scratch Paper Discipline: Cultivate disciplined use of scratch paper. Write numbers neatly, ensure perfectly vertical alignment of decimal points, and use clear, small digits for carrying/borrowing. Messy work leads to messy answers.
VI. Practice Questions: (With Exhaustive Step-by-Step Solutions)
Add 17.5, 3.08, and 0.654.
a) 21.234
b) 21.134
c) 21.334
d) 21.434
Subtract 5.912 from 12.0.
a) 6.088
b) 6.188
c) 7.088
d) 7.188
A shopper buys items costing Rs 23.75, Rs 15.50, and Rs 8.25. If they pay with a Rs 50.00 note, how much change should they receive?
a) Rs 2.50
b) Rs 3.50
c) Rs 2.75
d) Rs 3.75
A plumber cut 2.75 meters of pipe from a 5-meter length. He then joined another piece of pipe 1.85 meters long to the remaining piece. What is the final length of the pipe?
a) 4.10 meters
b) 3.10 meters
c) 4.20 meters
d) 3.20 meters
Exhaustive Step-by-Step Solutions to Practice Questions:
Add 17.5, 3.08, and 0.654.
Goal: Add three decimals with varying numbers of decimal places.
Step 1: Vertically align decimal points and pad with zeros. The number 0.654 has the most decimal places (three).
17.500 3.080 + 0.654 ---------
Step 2: Add from right to left, carrying over as needed.
Thousandths Place: 0 + 0 + 4 = 4. Write 4.
Hundredths Place: 0 + 8 + 5 = 13. Write 3, carry 1 to the tenths place.
Tenths Place: 1 (carried) + 5 + 0 + 6 = 12. Write 2, carry 1 to the ones place.
Decimal Point: Place the decimal point in the answer.
Ones Place: 1 (carried) + 7 + 3 + 0 = 11. Write 1, carry 1 to the tens place.
Tens Place: 1 (carried) + 1 = 2. Write 2.
Result: 21.234.
Final Answer: a) 21.234.
Subtract 5.912 from 12.0.
Goal: Subtract a decimal from a whole number, requiring zero padding and borrowing.
Step 1: Vertically align decimal points and pad with zeros. 12.0 is a whole number conceptually, but for decimal operations, it's 12.000 to match 5.912's three decimal places. The larger number, 12.0, goes on top.
12.000 - 5.912 ---------
Step 2: Subtract from right to left, borrowing as needed.
Thousandths Place: Can't do 0 - 2. Borrow from the 0 in hundredths (nothing to give). Borrow from 0 in tenths (nothing to give). Borrow from 2 in ones.
2 (ones) becomes 1. 0 (tenths) becomes 10.
10 (tenths) becomes 9. 0 (hundredths) becomes 10.
10 (hundredths) becomes 9. 0 (thousandths) becomes 10.
Now, 10 - 2 = 8. Write 8.
Hundredths Place: Now have 9 - 1 = 8. Write 8.
Tenths Place: Now have 9 - 9 = 0. Write 0.
Decimal Point: Place the decimal point.
Ones Place: Now have 1 - 5. Can't do. Borrow from 1 in tens.
1 (tens) becomes 0. 1 (ones) becomes 11.
11 - 5 = 6. Write 6.
Tens Place: Now have 0 (leading zero, not written).
Result: 6.088.
Final Answer: a) 6.088.
A shopper buys items costing Rs 23.75, Rs 15.50, and Rs 8.25. If they pay with a Rs 50.00 note, how much change should they receive?
Goal: Two-step problem: First, add the costs. Second, subtract the total cost from the payment.
Step 1: Calculate total cost by adding the item prices.
23.75 15.50 + 8.25 --------- 47.50
Hundredths: 5 + 0 + 5 = 10. Write 0, carry 1.
Tenths: 1 (carried) + 7 + 5 + 2 = 15. Write 5, carry 1.
Decimal point.
Ones: 1 (carried) + 3 + 5 + 8 = 17. Write 7, carry 1.
Tens: 1 (carried) + 2 + 1 = 4. Write 4.
Total Cost = Rs 47.50.
Step 2: Calculate change by subtracting total cost from payment.
50.00 - 47.50 --------- 2.50
Hundredths: 0 - 0 = 0. Write 0.
Tenths: 0 - 5. Can't do. Borrow from 0 in ones (nothing). Borrow from 5 in tens.
5 (tens) becomes 4. 0 (ones) becomes 10.
10 (ones) becomes 9. 0 (tenths) becomes 10.
Now, 10 - 5 = 5. Write 5.
Decimal point.
Ones: Now 9 - 7 = 2. Write 2.
Tens: Now 4 - 4 = 0. (leading zero, not written).
Result: Rs 2.50.
Final Answer: a) Rs 2.50.
A plumber cut 2.75 meters of pipe from a 5-meter length. He then joined another piece of pipe 1.85 meters long to the remaining piece. What is the final length of the pipe?
Goal: Two-step problem: First, subtract the cut length. Second, add the joined length.
Step 1: Calculate the remaining length after cutting.
5.00 <-- Pad 5 with zeros - 2.75 --------- 2.25
Hundredths: 0 - 5. Can't do. Borrow from 0 in tenths (nothing). Borrow from 5 in ones.
5 (ones) becomes 4. 0 (tenths) becomes 10.
10 (tenths) becomes 9. 0 (hundredths) becomes 10.
Now, 10 - 5 = 5. Write 5.
Tenths: Now 9 - 7 = 2. Write 2.
Decimal point.
Ones: Now 4 - 2 = 2. Write 2.
Remaining length = 2.25 meters.
Step 2: Add the new piece to the remaining length.
2.25 + 1.85 --------- 4.10
Hundredths: 5 + 5 = 10. Write 0, carry 1.
Tenths: 1 (carried) + 2 + 8 = 11. Write 1, carry 1.
Decimal point.
Ones: 1 (carried) + 2 + 1 = 4. Write 4.
Result: 4.10 meters.
Final Answer: a) 4.10 meters.
VII. Comprehensive Self-Assessment Checklist for Lesson 4.4 Mastery
This detailed checklist is your tool to confirm your deep understanding of Adding and Subtracting Decimals. Ensure you can confidently answer "Yes" to each question. If any are "No," dedicate additional time to revisit those specific concepts and examples.
Can you articulate why aligning decimal points is the fundamental rule for addition and subtraction of decimals?
[ ] Yes [ ] No
Do you always remember to perfectly align decimal points before performing addition or subtraction?
[ ] Yes [ ] No
Do you understand the purpose and benefit of inserting trailing zeros to align digits when numbers have different numbers of decimal places?
[ ] Yes [ ] No
Are you proficient in adding multiple decimal numbers, including those with varying decimal places and requiring carrying over digits?
[ ] Yes [ ] No
Are you proficient in subtracting decimal numbers, including those requiring extensive borrowing across multiple zeros and across the decimal point?
[ ] Yes [ ] No
Can you accurately perform addition and subtraction of decimals in typical GMAT word problem contexts (e.g., money, measurements)?
[ ] Yes [ ] No
Do you maintain neatness and precision on your scratch paper to avoid alignment errors?
[ ] Yes [ ] No
Are you aware of common pitfalls (e.g., misaligning, incorrect borrowing/carrying, forgetting decimal point in answer) and how to avoid them?
[ ] Yes [ ] No
