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

Grade 4IB

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

🔑Concepts

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Identify the Target Place: To round a number, first locate the digit in the place value you are rounding to. For example, if rounding to the nearest 100100, the target is the hundreds column. Imagine a place value chart where the number 4,5624,562 has the digit 55 in the hundreds spot.

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The Decider Digit: Look at the digit immediately to the right of your target place. This is the 'decider' that tells you whether to round up or stay the same. If rounding to the nearest 1010, the ones digit is your decider. If rounding to the nearest 10001000, the hundreds digit is your decider.

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The Rounding Up Rule: If the decider digit is 5,6,7,8,5, 6, 7, 8, or 99, you increase the target digit by 11. Visualize a number line where 1515 is exactly in the middle of 1010 and 2020; because it hits the 55 mark, it rounds up to the next ten, which is 2020.

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The Rounding Down (Staying the Same) Rule: If the decider digit is 0,1,2,3,0, 1, 2, 3, or 44, the target digit stays exactly as it is. You can visualize a hill where numbers 1,2,3,1, 2, 3, and 44 do not have enough momentum to get over the top, so they slide back down to the previous multiple.

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Replacing with Zeros: After determining the value of the target digit, every digit to its right must be changed to 00. This ensures the final number is a clean multiple of 10,100,10, 100, or 10001000. For instance, rounding 732732 to the nearest hundred results in 700700.

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The Midway Point Concept: The number 55 is the critical tipping point. On a number line between 300300 and 400400, the number 350350 is right in the center. In rounding, we always round 'up' to 400400 when the decider digit is exactly 55.

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Multiple Rounding: Sometimes rounding to different place values changes the result significantly. For example, 1,4991,499 rounded to the nearest 10001000 is 1,0001,000, but rounded to the nearest 1010 it is 1,5001,500.

📐Formulae

If Decider Digit ≥5→TargetDigit+1\ge 5 \rightarrow Target Digit + 1

If Decider Digit < 5 \rightarrow Target Digit + 0$

Nearest 10: Look at 10010^0 (Ones Place)

Nearest 100: Look at 10110^1 (Tens Place)

Nearest 1000: Look at 10210^2 (Hundreds Place)

💡Examples

Problem 1:

Round 4,3674,367 to the nearest 100100.

Solution:

  1. Identify the target digit in the hundreds place: 33.
  2. Identify the decider digit to the right (tens place): 66.
  3. Apply the rule: Since 6≥56 \ge 5, we round the target digit up.
  4. Target digit 33 becomes 44.
  5. Change all digits to the right to zero: 4,4004,400.

Explanation:

We look at the tens digit to decide the hundred. Since 6060 is closer to the next hundred than the previous one, the number 4,3674,367 rounds up to 4,4004,400.

Problem 2:

Round 8,5428,542 to the nearest 10001000.

Solution:

  1. Identify the target digit in the thousands place: 88.
  2. Identify the decider digit to the right (hundreds place): 55.
  3. Apply the rule: Since the decider is 55, the rule is to round up.
  4. Target digit 88 becomes 99.
  5. Change all digits to the right (hundreds, tens, and ones) to zeros: 9,0009,000.

Explanation:

The number 8,5428,542 is between 8,0008,000 and 9,0009,000. Because the hundreds digit is 55, it meets the threshold to round up to the higher thousand.