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Chapter 1: Problem 18

Round each of the numbers to the nearest hundred. $$954$$

Short Answer

Expert verified
954 rounded to the nearest hundred is 1000.

Step by step solution

01

Identify the Hundreds and Tens Digits

In the number 954, we first find the digit in the hundreds place and the digit in the tens place. The hundreds digit is 9, and the tens digit is 5.
02

Determine Rounding Rule

The rounding rule states that if the tens digit is 5 or greater, we round up. If it's less than 5, we round down. Here, the tens digit is 5, which means we will round up.
03

Perform the Rounding

Since we are rounding up, we add 1 to the hundreds digit, changing the 9 to a 10. This makes the number 1000, and all digits following the hundreds place become zero.

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Key Concepts

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

Understanding Place Value
Place value is a fundamental concept in mathematics that helps us understand the value of each digit in a number based on its position. In the number 954, each digit has a different value based on its position in the number. For example:
  • The digit 9 is in the hundreds place. It represents 900 (or 9 groups of one hundred).
  • The digit 5 is in the tens place, representing 50 (or 5 groups of ten).
  • The digit 4 is in the ones place, representing just 4.
Understanding place value is crucial when rounding because it helps us determine which digits to focus on when making decisions about rounding. In this exercise, knowing that the hundreds digit is 9 and the tens digit is 5 is key to applying the appropriate rounding rule.
Applying Rounding Rules
Rounding rules simplify numbers for easier use and understanding. The basic rules help decide whether a number should be rounded up or down. Here are the simple steps for rounding to the nearest hundred, as in this exercise:
  • Identify the tens digit: It helps determine whether you should round up or down.
  • If the tens digit is 5 or larger, increase the hundreds digit by 1, which is called rounding up.
  • If the tens digit is less than 5, keep the hundreds digit the same, effectively rounding down.
  • After adjusting the hundreds digit, change all trailing digits (in this case, tens and ones) to zero.
In our exercise with the number 954, the tens digit is 5, so we round up, increasing the hundreds digit from 9 to 10. The final rounded number is 1000.
Building Number Sense
Number sense involves having a good intuition for numbers and their relationships. It's an important skill that helps with everyday math problems, including rounding. Developing number sense can improve both your understanding and your ability to work with numbers flexibly and efficiently.
  • Recognize the size of numbers: This helps in estimating and rounding.
  • Understand that rounding is about finding a simpler, nearby number that can make calculations easier.
  • See that rounding can also help in checking if answers are reasonable during problem-solving.
  • Develop the habit of estimating results before performing operations to ensure results make sense.
By practicing with exercises like rounding 954 to 1000, you build a stronger number sense. This will benefit you not just with rounding but with many other aspects of math.

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