Using Input/Output Tables to Round Numbers

An input-output table can round numbers by applying the same rounding rule to every input. Working through the table shows the rule is consistent, and it makes the deciding digit easy to spot.

How an input-output table works

An input-output table has two columns. Each number in the input column is put through the same rule, and the result goes in the output column. The rule is stated at the top, so the table is really a list of worked examples of one instruction.

For rounding, the rule names the place you are rounding to: to the nearest ten, hundred, thousand, and so on. Every row uses that same place, which is what makes the pattern visible.

The rounding rule

1. Find the digit in the place you are rounding to. Underline it.
2. Look at the digit immediately to its right. That is the deciding digit, and it is the only one that matters.
3. If the deciding digit is 5 or more, add one to the underlined digit. If it is 4 or less, leave the underlined digit alone.
4. Replace every digit to the right of the underlined one with zeros.

Worked example: rounding to the nearest hundred

Rule: round each input to the nearest hundred.

• Input 1,462. The hundreds digit is 4, and the digit to its right is 6. Six is 5 or more, so 4 becomes 5. Output: 1,500.
• Input 2,830. The hundreds digit is 8, and the digit to its right is 3. Three is 4 or less, so 8 stays. Output: 2,800.
• Input 5,950. The hundreds digit is 9, and the digit to its right is 5, so 9 must go up. Nine rounds to ten, which carries into the thousands: 5,9 becomes 6,0. Output: 6,000.
• Input 743. The hundreds digit is 7, and the digit to its right is 4, so 7 stays. Output: 700.

Read down the output column and the rule is obvious: every answer ends in two zeros, because rounding to the nearest hundred always does.

Common mistakes

• Looking at the wrong digit. Only the digit immediately to the right decides. When rounding 1,462 to the nearest hundred, the 2 is irrelevant.
• Rounding twice. Rounding 1,449 to the nearest ten first gives 1,450, which then rounds up to 1,500 — but the correct answer to the nearest hundred is 1,400. Round once, from the original number.
• Forgetting the carry. When the underlined digit is 9 and it must go up, it becomes 0 and one is added to the place on its left.
• Leaving the digits on the right unchanged. They all become zeros.

Practice questions on rounding with input-output tables

Rule: round each input to the nearest thousand.

1. Input 4,382
2. Input 7,500
3. Input 12,049
4. Input 9,624
5. Input 99,700

Answers

1. 4,000. The thousands digit is 4 and the deciding digit is 3.
2. 8,000. The deciding digit is exactly 5, so the 7 goes up.
3. 12,000. The thousands digit is 2 and the deciding digit is 0.
4. 10,000. The thousands digit is 9 and the deciding digit is 6, so the 9 carries.
5. 100,000. The thousands digit is 9 and the deciding digit is 7, carrying all the way through.

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