Approximation & estimation · Ages 12–13
Estimating when shopping
Enough money? Round up. Reached a total? Round down.
How to do it
Method
Enough money? Round up. Reached a total? Round down
13 + 24 + 10 = 47 ≤ 50, so $50 is surely enough
Another way
Work it out exactly
12.8 + 23.5 + 9.9 = 46.2 ≤ 50
In full
First decide whether you need the estimate too big or too small. "Is the money enough?": round every price up, so the estimate is too big; if even that is within the budget, the money is surely enough. Say $12.8, $23.5 and $9.9, rounded up to the dollar: 13 + 24 + 10 = 47, so $50 is surely enough. "Does it reach $200 for the free gift?": round the prices down; if the too-small total already reaches $200, the real one surely does. Rounding off is sometimes over and sometimes under, so it promises nothing. The most items you can buy is rounded down (an item you can't afford doesn't count); the fewest notes you need is rounded up. When an estimate can't decide, work it out exactly.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Buying $16.3, $5.9 and $12.6, paying $100. Rounded up, the total is $, so the change is at least $.
Fill in each blank
Show the answer and working
Answer: 36, 64
Rounded up, 36 is too big, so no more than that is spent: the change is at least 100 − 36 = 64 dollars.
Example 2
$41.5, $78.2, $65.6: with each price rounded down to the dollar, the estimated total is $.
Show the answer and working
Answer: 184
41 + 78 + 65 = 184. Rounding down: the cents all go.
Example 3
Buying $29.1, $19.4 and $19.3 with $63. Which conclusion and reason are both right?
- A. Enough: rounded down, $67 is within $63
- B. Not enough: rounded down, $67 is already over $63
- C. Enough: rounded up, $70 is within $63
- D. Not enough: rounded up, $70 is over $63
Choose the right answer
Show the answer and working
Answer: B. Not enough: rounded down, $67 is already over $63
To be sure it is enough, use the estimate that is too big (rounded up, 70); to be sure it isn't, the one that is too small (rounded down, 67).
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.You have $40 and want three things: $6.1, $5.2 and $11.7. To be sure, by estimating, that the money is enough, what should you do to each price?
- A. Round it off to the dollar
- B. Round it down to the dollar
- C. Count only the dearest
- D. Round it up to the dollar
Choose the right answer
Answer:
2.Buying $27.4, $7.7 and $28.7 with $66. Which conclusion and reason are both right?
- A. Not enough: rounded up, $65 is over $66
- B. Enough: rounded down, $62 is within $66
- C. Not enough: rounded down, $62 is already over $66
- D. Enough: rounded up, $65 is within $66
Choose the right answer
Answer:
3.Notebooks cost $2.7 each. At most how many can $100 buy?
Answer:
4.8 tickets at $69 each. What is the fewest $100 notes to take?
Answer:
5.$75.6, $15.5, $88.8: rounding the prices down to the dollar shows for sure that the total reaches $179.
True or false?
Answer:
All the answers
- 1. D. Round it up to the dollar
- 2. D. Enough: rounded up, $65 is within $66
- 3. 37 notebooks
- 4. 6 notes
- 5. False
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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