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A3.6 · Estimate change from a cash payment

Learn to estimate change from a cash payment through clear examples and targeted practice.

Ontario Grade 11 Mathematics

Earning and Purchasing

Use rounding and a quick check to judge whether change seems right

At a store, you may want to know roughly how much change to expect before the cashier hands it to you. You do not always need an exact answer to notice that something seems wrong. Estimating change means finding an amount close to the change due, using numbers that are easier to work with. A calculator is useful for exact subtraction, but rounding first can give you a fast mental check. In this lesson, the amount owed is already known, and the goal is only to estimate the change from the cash payment.

What you will learn

1. What an estimate tells you

Change is the money returned when a cash payment is greater than the amount owed. For example, if a bill is CAD 12 and you pay CAD 20, some of your payment comes back as change.
An estimate is a close, useful answer, not an exact answer. To estimate change, make the amount owed easier to subtract from the payment. A common choice is to round the amount owed to the nearest whole dollar. Then subtract that rounded amount from the payment.
Rounding means replacing an amount with a nearby, simpler amount. When cents are 50 or more, round up to the next dollar. When cents are less than 50, round down to the previous whole dollar. This rule gives a consistent estimate, though it may be a little high or low.
The payment amount matters too. If you pay an exact whole-dollar amount, the subtraction is often simple after rounding the amount owed. If you pay with a larger bill, such as CAD 50, round the amount owed and subtract it from CAD 50. The result is still an estimate.
estimated change≈cash payment−rounded amount owed\text{estimated change} \approx \text{cash payment} - \text{rounded amount owed}

2. A practical routine

Use this routine when you want a quick estimate at a checkout. First, identify the amount owed and the cash payment. Do not estimate from the price of just one item if a final total is already given. The amount owed is the total you must pay.
Next, round the amount owed to a nearby whole dollar. Keep the payment as written if it is already a simple amount, such as CAD 20 or CAD 50. Subtract the rounded amount owed from the payment. This gives the estimated change.
Finally, ask whether the estimate makes sense. If the payment is only a little more than the amount owed, the change should be small. If the payment is much larger, the change should be larger. This size check can catch a subtraction mistake.
A calculator or spreadsheet can help with the subtraction, but it does not decide whether the estimate is sensible. You must still enter the right payment and rounded amount owed. On a spreadsheet, you could place the payment in one cell and the rounded amount owed in another, then subtract the second value from the first. Use the result as an estimate, not as a claim about the exact change.

3. How close is close enough?

Rounding changes the amount used in the subtraction, so it also changes the estimated change. If you round the amount owed up, your estimated change will be a little smaller than the exact change. If you round it down, your estimated change will be a little larger.
For example, rounding CAD 16.72 to CAD 17 makes the estimated change smaller than it would be using CAD 16.72. The difference is only 28 cents. That can be useful for a quick check, but it is not exact. If you need to know the precise change, subtract the original amount owed from the payment using a calculator or careful written arithmetic.
Keep the purpose in mind: an estimate helps you decide whether the change seems reasonable. It is especially helpful when the answer is clearly far from what you expected. If your estimate is CAD 6 and the cashier returns only a coin, pause and check the receipt and payment. Small differences between an estimate and the actual change can be normal because of rounding.
You can also think about the change by counting up from the amount owed toward the payment. For an amount owed near CAD 14 and a payment of CAD 20, the change should be around CAD 6. Counting up can support your estimate, but the rounding-and-subtracting routine is a clear way to make the estimate.

4. Make the estimate useful

Choose a rounding amount that is easy to subtract and close enough to the amount owed. For everyday cash payments, rounding to a whole dollar is often a useful balance: it is quick, and the difference is less than 50 cents. A rougher estimate may still help, but it may be less useful for checking a small amount of change.
Before subtracting, make sure the payment is at least as much as the amount owed. If it is not, it is not a cash payment that can cover the bill, and there is no change to estimate from that payment alone.
Keep dollars and cents in mind even when you round. For example, an estimate of CAD 13 means about thirteen dollars of change, not exactly thirteen dollars. Do not report the rounded result as the exact amount returned.
A good estimate is quick, clear, and close enough to support a decision. Say it as an estimate: “I expect about CAD 6 in change.” Then compare the change received with that expectation. If there is a large gap, check the transaction rather than assuming the estimate was exact.

Worked example

A small cash payment

A café bill is CAD 18.67. A customer pays CAD 20. Estimate the change.
  1. Identify the amounts
    The customer owes CAD 18.67 and pays CAD 20. The payment is greater than the amount owed, so change is due.
  2. Round the amount owed
    Round CAD 18.67 up to CAD 19 because the cents are at least 50. This makes the subtraction easier and changes the amount by only 33 cents.
    CAD 18.67≈CAD 19\text{CAD }18.67 \approx \text{CAD }19
  3. Subtract to estimate
    Subtract the rounded amount owed from the payment. The estimate is about CAD 1 in change.
    20−19=120 - 19 = 1
  4. Check the estimate
    The payment is only a little more than the bill, so a small amount of change makes sense. The exact change is CAD 1.33, which is close to the estimate.
    20−18.67=1.3320 - 18.67 = 1.33
Answer: The estimated change is about CAD 1.
Check: The exact change is CAD 1.33. The estimate is 33 cents lower because the amount owed was rounded up.

Worked example

A larger cash payment

A customer’s total at a market is CAD 36.82. The customer pays CAD 50. Estimate the change.
  1. Identify the amounts
    The total owed is CAD 36.82 and the cash payment is CAD 50. Since the payment is larger, the customer will receive change.
  2. Round the amount owed
    Round CAD 36.82 up to CAD 37. The rounded amount is only 18 cents above the total, so it is a close whole-dollar amount for estimating.
    CAD 36.82≈CAD 37\text{CAD }36.82 \approx \text{CAD }37
  3. Subtract from the payment
    Subtract CAD 37 from CAD 50. This gives an estimated change of CAD 13.
    50−37=1350 - 37 = 13
  4. Check the result
    A bill near CAD 37 paid with CAD 50 should lead to change near CAD 13. The exact change is CAD 13.18, so the estimate is close.
    50−36.82=13.1850 - 36.82 = 13.18
Answer: The estimated change is about CAD 13.
Check: The exact change is CAD 13.18. The estimate is 18 cents lower because the amount owed was rounded up.

Common mistakes and how to avoid them

Calling the rounded estimate the exact change.
Correction: Use words such as “about CAD 13.” For exact change, subtract the original amount owed, including cents.
Subtracting the payment from the amount owed.
Correction: Change is the part of the payment left over after the amount owed is covered, so subtract the amount owed from the payment.
Rounding the amount owed in the wrong direction or ignoring the cents.
Correction: For the nearest whole dollar, cents below 50 round down and cents of 50 or more round up.
Using an estimate that does not fit the size of the payment.
Correction: Pause and compare the amount owed with the payment. A payment only slightly higher than the bill should not produce a very large estimate of change.

Lesson summary

Check your understanding

Question 1

A customer owes CAD 24.38 and pays CAD 30. Using the nearest whole dollar, what is the estimated change?
  1. About CAD 5
  2. About CAD 6
  3. About CAD 24
  4. About CAD 30
Show answer and explanation
About CAD 6
Round CAD 24.38 down to CAD 24, then subtract from CAD 30. The estimate is CAD 6. The exact change is CAD 5.62, so the estimate is close.

Question 2

A customer owes CAD 11.76 and pays CAD 20. What is the nearest-whole-dollar estimate of the change?
  1. About CAD 8
  2. About CAD 9
  3. About CAD 11
  4. About CAD 20
Show answer and explanation
About CAD 8
Round CAD 11.76 up to CAD 12. Then CAD 20 minus CAD 12 is CAD 8. The exact change is CAD 8.24, so the estimate is close.

Key terms

Amount owed
The total that must be paid for a purchase.
Cash payment
Cash given to pay all or part of an amount owed.
Change
Money returned when a cash payment is more than the amount owed.
Estimate
An answer close to the exact amount, used when a quick check is enough.
Round
Replace an amount with a nearby, simpler amount, such as a whole dollar.

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About this lesson

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Mathematics (MEL3E), expectation A3.6. It is a study resource, not an official curriculum publication.

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