The process of rounding in the decimal system follows these general steps:
1. Identify the Place Value:
- Determine the place value to which you want to round the number. This could be the nearest tenth, hundredth, thousandth, and so on.
2. Look at the Digit to the Right:
- Examine the digit immediately to the right of the place value you identified in Step 1.
3. Rounding Rules:
- If the digit to the right is 4 or less (0, 1, 2, 3, or 4), leave the digit you are rounding unchanged.
- If the digit to the right is 5 or more (5, 6, 7, 8, or 9), add 1 to the digit you are rounding.
4. Drop or Change Subsequent Digits:
- After applying the rounding rule in Step 3, you may need to drop all subsequent digits to the right. Alternatively, you may need to change them all to zeros.
Here are a few examples of how rounding works in the decimal system:
- Round 3.141592 to the nearest hundredth:
- Place value: Hundredth (second digit after the decimal point)
- Digit to the right: 5
- Rounding rule: Add 1 to the hundredth place (4 becomes 5)
- Result: 3.14
- Round 27.8324 to the nearest tenth:
- Place value: Tenth (first digit after the decimal point)
- Digit to the right: 3
- Rounding rule: Leave the tenth place unchanged (8 remains 8)
- Result: 27.8
- Round 1234.5678 to the nearest thousandth:
- Place value: Thousandth (third digit after the decimal point)
- Digit to the right: 7
- Rounding rule: Add 1 to the thousandth place (6 becomes 7)
- Result: 1234.568
By applying these rounding rules, you can simplify numbers while preserving their essential value and accuracy for specific purposes or calculations.