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Estimate the Result of an Arithmetic Operation
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When we’re in a hurry or don’t have a pen and paper, rounding can help us estimate harder arithmetic problems. This skill will help when quickly trying to see if we can afford everything on our grocery list or what this month’s budget adds up to. This is done by rounding to the highest place value we see (356 → 400 and 22.4 → 20). Then, addition and subtraction can be done on these rounded values much more easily. The answer we get won’t be exact, but it will be a good estimate.

### Practice Problems

1. What is the result when front-end rounding is applied to the number $$35,073.290$$?
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Solution
Solution: $$40,000$$
Details:
Round to the highest place value, when using front-end rounding. The number 3 has the highest place value.
$${\color{red}3}5,073.290$$

To determine if 3 is to be rounded up or left unchanged, we look to the right of 3 at the number 5.
$${\color{red}3}{\color{green}5},073.290$$

Consider the position of the number 5 in the number line. The number 5 is in the middle of 0 and 10.

Numbers 5 and greater indicate you should round up.

The number 3 will increase to 4. All the numbers to the right, become zeros.
$${\color{red}4}{\color{green}0},000.000$$

The rounded answer is $$\textbf{40,000}$$. (It is mathematically acceptable to drop all zeros after the decimal.)
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Use rounding to estimate the solution to the problem:
2. $$26.37 + 61.72 = ?$$ (
Solution
Solution: 90
Details:
• The number $$26.37$$ rounds to 30.
• The number $$61.72$$ rounds to 60.
• So, $$26.37 + 61.72$$ is about equal to: $$30 + 60 = 90$$
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3. $$739.6 + 479.6 = ?$$ (
Video Solution
Solution: 1200
Details:

(Video Source | Transcript)
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4. $$6.6 − 2.5 = ?$$ (
Solution
Solution: 4
Details:
• The number $$6.6$$ rounds to 7.
• The number $$2.5$$ rounds to 3.
• So, $$7 − 3 = 4$$
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5. $$39.225 − 13.581 = ?$$ (
Solution
Solution: 30
Details:
• The number $$39.225$$ rounds to 40.
• The number $$13.581$$ rounds to 10.
• So, $$40 − 10 = 30$$
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6. $$3299.06 − 5323.11 = ?$$ (
Video Solution
Solution: $$-2000$$
Details:

(Video Source | Transcript)
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