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Chapter 1: Problem 82

Round the number to the given place value. \(1638 ;\) hundreds

Short Answer

Expert verified
Therefore, when \(1638\) is rounded to the nearest hundred, we get \(1600\).

Step by step solution

01

Identify the digit in the hundreds place

In this number, the digit 6 is in the hundreds place.
02

Look at the digit to the right

The digit immediately to the right of the hundreds place is in the tens place, which is 3. If this digit is 5 or more, we round up, if it's less than 5, we round down.
03

Apply the rule for rounding

Since the digit in the tens place in this number is 3 (which is less than 5), we don't alter the digit in the hundreds place, and replace all the digits to the right of it with zeros.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Place Value
Understanding place value is crucial when working with numbers, especially during rounding. Place value refers to the position of a digit in a number, which determines its value. In our number system, this typically includes positions such as units, tens, hundreds, and so on. Each position represents a power of ten.
For example, in the number 1638:
  • The digit 8 is in the units place, representing 8.
  • The digit 3 is in the tens place, representing 30.
  • The digit 6 is in the hundreds place, representing 600.
  • The digit 1 is in the thousands place, representing 1000.
When rounding numbers, identifying the right place value is the first step. Knowing the place value allows us to decide whether to keep the digit as it is or adjust it, based on the rounding rules. It helps in maintaining the overall value of the number correctly when simplifying it.
Hundreds Place
The hundreds place is a key concept in rounding, especially when dealing with larger numbers. It refers to the third digit from the right in a whole number. Knowing which digit is in the hundreds place is critical, as rounding often depends on it.

In the number 1638, the digit in the hundreds place is 6. This represents 600 in terms of place value. When rounding to the nearest hundred, we look closely at this digit and the one right after it.

Whenever you round to the nearest hundred:
  • Check the digit in the tens place (one position to the right of the hundreds).
  • If the digit in the tens place is 5 or greater, increase the hundreds digit by 1.
  • If it is less than 5, leave the hundreds digit as is.
In practice, this means 1638 rounded to the hundreds would remain 1600, since the tens digit is 3, which does not meet the requirement to round up.
Tens Place
The tens place is immediately to the right of the hundreds place in a whole number. It plays an essential role in rounding numbers. When rounding to the hundreds place, we look at the tens place to determine whether the hundreds digit should stay the same or increase by one.

For 1638, the tens place contains the digit 3. This digit is significant when deciding how to round to the nearest hundred. With our rules for rounding:
  • A tens digit of 5 or higher prompts rounding up in the hundreds place.
  • A tens digit less than 5 means you round down, leaving the hundreds digit unchanged.
Therefore, since the tens digit 3 is less than 5, 1638 remains rounded down to 1600. This step ensures accurate simplification of numbers while preserving the intent of their values.

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