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Estimation and Error Checks

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Prerequisites

Arithmetic

Arithmetic | 14 of 17

Prerequisites: Addition, Multiplication. Enables: None.

Estimation, rounding, and error checks

Estimation gives a quick approximate answer before or after exact calculation.

Rounding

To round to a place value:

  1. Locate the target place.

  2. Check the digit to its right.

  3. If the digit is $5$ or greater, round up.

  4. If the digit is less than $5$, keep the target digit unchanged.

Example:

Round $48.376$ to the nearest hundredth.

The hundredths digit is $7$.

The next digit is $6$, so round up:

$$ 48.376 \approx 48.38 $$

Compatible numbers

Compatible numbers are numbers chosen to make mental arithmetic easier.

Example:

$$ 198 + 403 \approx 200 + 400 = 600 $$

Estimating products

Round factors before multiplying.

Example:

$$ 49 \cdot 21 \approx 50 \cdot 20 = 1000 $$

Exact value:

$$ 49 \cdot 21 = 1029 $$

The estimate is reasonable.

Estimating quotients

Choose nearby values that divide easily.

Example:

$$ 302 \div 6 \approx 300 \div 6 = 50 $$

Error checks

Use inverse operations:

OperationInverse check
AdditionSubtraction
SubtractionAddition
MultiplicationDivision
DivisionMultiplication

Examples:

If

$$ 248 + 376 = 624 $$

then check:

$$ 624 - 376 = 248 $$

If

$$ 84 \div 7 = 12 $$

then check:

$$ 12 \cdot 7 = 84 $$

Previous: Powers, Roots, and Scientific Notation | Arithmetic course map | Next: Problem-Solving Workflow

Practice Arithmetic