Answered

Round each number to the nearest ten and to the nearest hundred.



Rounded to the Nearest TenRounded to the Nearest Hundred

694

749

397

Verified Answer :

  • Round numbers to the nearest ten by examining the units digit: keep the tens place if the units digit is \(0-4\), or increment the tens place if the units digit is \(5-9\).
  • Round numbers to the nearest hundred by examining the tens digit: keep the hundreds place if the tens digit is \(0-4\), or increment the hundreds place if the tens digit is \(5-9\).
  • The final results for the numbers 694, 749, and 397 are:
  • 694 rounds to \(\boxed{690}\) (ten) and \(\boxed{700}\) (hundred).
  • 749 rounds to \(\boxed{750}\) (ten) and \(\boxed{700}\) (hundred).
  • 397 rounds to \(\boxed{400}\) (ten) and \(\boxed{400}\) (hundred).

Explanation

  1. Rounding Rules Explained

To round an integer to the nearest ten, we look at the digit in the units (ones) place. If the unit digit is 0, 1, 2, 3, or 4, we round down by keeping the tens digit as it is and changing the units digit to 0. If the unit digit is 5, 6, 7, 8, or 9, we round up by increasing the tens digit by 1 and changing the units digit to 0.
To round an integer to the nearest hundred, we look at the digit in the tens place. If the tens digit is 0, 1, 2, 3, or 4, we round down by keeping the hundreds digit as it is and changing both the tens and units digits to 0. If the tens digit is 5, 6, 7, 8, or 9, we round up by increasing the hundreds digit by 1 and changing both the tens and units digits to 0.

  1. Step-by-Step Rounding Calculation
  • For 694:
  • Nearest ten: The unit digit is 4. Since 4 is less than 5, we round down, resulting in 690.
  • Nearest hundred: The tens digit is 9. Since 9 is 5 or greater, we round up, resulting in 700.
  • For 749:
  • Nearest ten: The unit digit is 9. Since 9 is 5 or greater, we round up, resulting in 750.
  • Nearest hundred: The tens digit is 4. Since 4 is less than 5, we round down, resulting in 700.
  • For 397:
  • Nearest ten: The unit digit is 7. Since 7 is 5 or greater, we round up, resulting in 400.
  • Nearest hundred: The tens digit is 9. Since 9 is 5 or greater, we round up, resulting in 400.
  1. Final Results Table

The results of the rounding operations are presented in the following table:

Nearest TenNearest Hundred \) 694690700 \) 749750700 \) 397400400 \)

Examples

Rounding is a vital skill used in daily life for quick estimations. For instance, if you are shopping and see a shirt costing \$397, you might round it to \$400 to estimate your budget quickly. Similarly, if you are planning a trip and need to account for 749 miles, saying it's about 750 miles is much easier to work with. These approximations help you make fast, practical decisions without needing exact precision at every step.

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