Number and Place Value - Rounding to the nearest 10, 100, 1000, 10,000

Grade 4IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Rounding makes a number simpler while keeping its value close to the original.

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The Target Digit is the digit in the place value you are rounding to (e.g., the Tens place).

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The Deciding Digit is the digit immediately to the right of the target digit.

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The '5 or More' Rule: If the deciding digit is 5, 6, 7, 8, or 9, increase the target digit by 1.

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The '4 or Less' Rule: If the deciding digit is 0, 1, 2, 3, or 4, the target digit stays the same.

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Placeholders: All digits to the right of the rounded place must be changed to zeros.

📐Formulae

\text{If } d_{right} \ge 5 \rightarrow \text{Round Up (Target Digit + 1)}

\text{If } d_{right} < 5 \rightarrow \text{Round Down (Keep Target Digit)}

\text{Place Value Positions: } [10,000][1,000][100][10][1]

💡Examples

Problem 1:

Round 86 to the nearest 10.

Solution:

90

Explanation:

The target digit is 8 (tens). The digit to the right is 6. Since 6 is '5 or more', we round the 8 up to 9 and change the units to 0.

Problem 2:

Round 432 to the nearest 100.

Solution:

400

Explanation:

The target digit is 4 (hundreds). The digit to the right is 3. Since 3 is '4 or less', the 4 stays the same. Change all digits to the right to 0.

Problem 3:

Round 7,500 to the nearest 1,000.

Solution:

8,000

Explanation:

The target digit is 7 (thousands). The digit to the right is 5. According to the rule, 5 means we round up. 7 becomes 8, and the rest become zeros.

Problem 4:

Round 24,999 to the nearest 10,000.

Solution:

20,000

Explanation:

The target digit is 2 (ten-thousands). The digit to the right is 4. Since 4 is '4 or less', the 2 stays the same. All digits to the right (4, 9, 9, 9) become 0.