Verified Answer :

  • Round \(252\) to \(300\) and \(147\) to \(100\), yielding an estimated difference of \(300 - 100 = 200 \text{ cm}\).
  • Round \(418\) to \(400\) and \(566\) to \(600\), yielding an estimated sum of \(400 + 600 = 1000 \text{ L}\).
  • Final answers: \(\boxed{200 \text{ cm}, 1000 \text{ L}}\).

Explanation

  1. Rounding and Estimating the Expressions

To estimate the results, we first round each measurement to the nearest hundred. The rule for rounding to the nearest hundred is to look at the tens digit:

  • If the tens digit is 5 or greater, round up to the next hundred.
  • If the tens digit is less than 5, round down to the current hundred.

For the first expression, \(252 \text{ cm} - 147 \text{ cm}\):

  • The number 252 has a tens digit of 5, so we round up to 300.
  • The number 147 has a tens digit of 4, so we round down to 100.

The estimated difference is \(300 - 100 = 200\). Thus, \(252 \text{ cm} - 147 \text{ cm} \approx 200 \text{ cm}\).

For the second expression, \(418 \text{ L} + 566 \text{ L}\):

  • The number 418 has a tens digit of 1, so we round down to 400.
  • The number 566 has a tens digit of 6, so we round up to 600.

The estimated sum is \(400 + 600 = 1000\). Thus, \(418 \text{ L} + 566 \text{ L} \approx 1000 \text{ L}\).

Examples

Estimating values is a vital skill in daily life, especially when you need a quick answer without doing exact arithmetic. For example, if you are shopping and see items costing \$252 and \$147, you can quickly estimate that the difference in price is about \$100 by rounding both numbers to \$300 and \$100. Similarly, if you are measuring water for two large tanks, knowing that about 400 L plus 600 L equals 1000 L helps you quickly gauge the total capacity needed. These techniques allow you to make fast, informed decisions when precise calculations are not strictly necessary.

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