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Chapter 3: Problem 55

Round each number to the given place value. 2986 to the nearest thousand

Short Answer

Expert verified
2986 rounded to the nearest thousand is 3000.

Step by step solution

01

Identify the Place Value

Determine which digit represents the thousand's place in the number 2986. Here, the thousand's place is represented by 2.
02

Look at the Next Smaller Place Value

Check the digit immediately to the right of the thousand's place to decide whether to round up or down. In 2986, this digit is 9 (in the hundred's place).
03

Decide to Round Up or Down

Since the digit in the hundred's place (9) is 5 or greater, we round the thousand's place digit up from 2 to 3.
04

Adjust the Number

After rounding up the thousand's digit, change all digits to the right of the thousand's place to zeros. Thus, 2986 becomes 3000.

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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 a fundamental concept in mathematics. Place value refers to the value of each digit in a number based on its position. For example, in the number 2986:
  • The digit "2" is in the thousand's place, meaning it represents 2000.
  • The digit "9" is in the hundred's place, meaning it represents 900.
  • The digit "8" is in the ten's place, meaning it represents 80.
  • The digit "6" is in the unit's place, meaning it represents 6.
Knowing the place value helps us correctly round numbers. By identifying each digit's position, we determine how large or small its impact is on the overall number. This is crucial when you are working with tasks like rounding, where identifying the correct place value dictates how you should adjust the number.
Nearest Thousand
When rounding to the nearest thousand, our main focus is on the thousand's place. This means that you begin by identifying this specific place and then decide whether or not to modify its value. In the example exercise with the number 2986:
  • The digit in the thousand's place is "2".
Next, we determine which thousand 2986 is closest to: 2000 or 3000. This is evaluated by looking at the next smaller place value, which in this case, is the hundred's place.
We use this smaller place value to determine if the number should be rounded up to the next thousand or remain the same. This gives a clear understanding of how rounding affects the number in question, switching its nearest thousand by considering the next digit.
Rounding Rules
Rounding numbers follows specific rules. These rules help to ensure consistency and accuracy in mathematical computation. Here are the basic rounding rules:
  • If the digit to the right of your target place is less than 5, you round down.
  • If it is 5 or greater, you round up.
In the exercise with the number 2986, we look at the digit "9" in the hundred's place. Since 9 is greater than 5, we follow the rule to round up. This means increasing the thousand's place digit "2" to "3".
After rounding up, all digits to the right of the thousand's place become zeros, simplifying 2986 to 3000. These rules are simple but highly effective in ensuring precision when approximating numbers to a desired place value.

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