Estimating and Checking Reasonableness

Learn rounding and place value, checking magnitude.

Lesson 3 of 32 parts Practice Flashcards

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Rounding and Place Value

Objective: Explain rounding and place value, apply the stated method, and check its conditions.

Rounding replaces a number by a nearby value at a selected place. Examine the next lower place to choose the nearer endpoint; with the usual classroom half-up rule, a 5 rounds upward. Rounding creates an approximation, not equality. An estimate should be marked or described as approximate.

Formulas

Nearest hundred: choose the nearer multiple of 100

Worked examples

Try itRound 767 to the nearest hundred.Show answer

Step 1: Look at the tens digit to decide whether to round up. Step 2: If it is at least 5, use the next hundred; otherwise use the lower hundred. Step 3: The rounded value is 800.

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Rounding and Place Value

Objective: Explain rounding and place value, apply the stated method, and check its conditions.

Formulas

Nearest hundred: choose the nearer multiple of 100

Worked examples

Try itRound 767 to the nearest hundred.Show answer

Step 1: Look at the tens digit to decide whether to round up. Step 2: If it is at least 5, use the next hundred; otherwise use the lower hundred. Step 3: The rounded value is 800.

Checking Magnitude

Objective: Explain checking magnitude, apply the stated method, and check its conditions.

A reasonableness check compares an answer with the scale implied by the problem. Rounded inputs or compatible numbers provide a quick benchmark. Estimates do not replace an exact calculation when the question requires precision or a boundary decision. Keep the units and size of the quantities in the check.

Formulas

Total cost = price per item × item count

Worked examples

Try itA bag costs $6. Estimate the cost of 70 bags using the exact whole-dollar price.Show answer

Step 1: Use price times number of bags: 6·70. Step 2: First calculate 6·7=42. Step 3: Multiply by 10 to get $420.

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