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Chapter 1: Problem 22

Round each number to the given place value. \(3511 ;\) thousands

Short Answer

Expert verified
4000

Step by step solution

01

Identify the digit in the thousands place

The number is 3511. Find the digit in the thousands place. In this case, it is '3'.
02

Look at the digit in the next smaller place value

Now, look at the digit to the right of the thousands place. This is the hundreds place digit, which is '5'.
03

Determine whether to round up or down

If the digit in the hundreds place is 5 or greater, round up. Otherwise, round down. Since the digit is '5', round up.
04

Round the number

Round the thousands place digit up by adding 1 to '3', making it '4'. All digits to the right of the thousands place become zero. Thus, 3511 rounded to the nearest thousands is 4000.

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Key Concepts

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

Place Value
Place value is a fundamental concept in mathematics where the position of a digit in a number determines its value. In a multi-digit number, each digit is placed in a specific position such as units, tens, hundreds, and thousands. For example, in the number 3511, the digits are as follows:
  • 3 is in the thousands place
  • 5 is in the hundreds place
  • 1 is in the tens place
  • 1 is in the units place

Understanding place value is essential for operations like addition and subtraction, as it helps to align digits properly. It also plays a crucial role in rounding numbers, where identifying the place value to round to is the first step.
Rounding Rules
Rounding numbers involves increasing or decreasing a number to the nearest desired place value. There are specific rules to follow:
  • Identify the place value to which you want to round.
  • Check the digit immediately to the right of this place value.
  • If the digit is 5 or greater, round up by adding one to the place value digit.
  • If the digit is less than 5, round down by leaving the place value digit unchanged.

This process simplifies complex numbers, making them easier to use in estimates and calculations. So, applying these rules to our initial example, 3511 is rounded up to 4000 because the hundreds place digit is 5.
Nearest Thousand
Rounding to the nearest thousand means modifying a number so that it is closest to an exact thousand. Let's walk through this with our example, 3511:
  • First, identify the thousands place digit, which is 3 in 3511.
  • Next, look at the hundreds place digit, which is 5.
  • Since the hundreds place digit is 5 or more, we round up the thousands place digit from 3 to 4.
  • Finally, replace all digits to the right of the thousands place with zeroes, resulting in 4000.

Rounding to the nearest thousand helps simplify large numbers, making them easier to understand and work with in everyday scenarios like budgeting or estimating distances.

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