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Chapter 1: Problem 36

Round each of the numbers to the nearest thousand. $$688,909$$

Short Answer

Expert verified
688,909 rounded to the nearest thousand is 689,000.

Step by step solution

01

Identify the Thousands Place

Look at the number 688,909. The digit in the thousands place is '8'.
02

Look at the Hundreds Digit

The digit right after the thousands place, which is the hundreds digit, is also '9' in this case.
03

Apply Rounding Rule

When rounding to the nearest thousand, if the hundreds digit is 5 or more, round up the thousands digit. Since the hundreds digit is '9', we round '8' in the thousands place up to '9'.
04

Construct the Rounded Number

Change the thousands digit from '8' to '9', and change all digits to its right to zeros. The rounded number becomes 689,000.

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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 an essential concept in mathematics that helps us understand the position of each digit in a number. This position determines the value of that particular digit. For example, in the number 688,909, the place values from right to left are:
  • Units
  • Tens
  • Hundreds
  • Thousands
  • Ten thousands
  • Hundred thousands
In this exercise, we focus on the thousands place. Here, the digit '8' is located in the thousands place, which means it represents 8,000. Knowing place value is crucial because it allows you to determine which digit is significant when rounding numbers.
Mastering Rounding Rules
Rounding numbers makes calculations easier by altering numbers to simpler forms, closer to any desired place value. To round a number like 688,909 to the nearest thousand, follow these simple rules:
  • First, identify which place you need to round to. In this case, it's the thousands place.
  • Next, check the digit immediately to the right (the hundreds place) to determine if it will influence the rounding. Here, the relevant digit is '9'.
  • If this digit is 5 or more, increase the rounding digit by one. If it is 4 or less, the rounding digit stays the same.
In our example, the hundreds digit '9' is greater than 5, so you round '8' in the thousands place up to '9', turning the number into 689,000. Rounding rules are straightforward but remembering to check just the right-side digit builds confidence in doing so correctly.
Basic Math Operations and Practice
Basic math operations such as addition, subtraction, multiplication, and division may seem simple, but they often require precision. Rounding numbers is a fundamental skill in mathematics operations to ensure calculations are manageable and results are comprehensible.

Here's how rounding supports these operations:
  • **Addition and subtraction:** Rounding can help estimate sums and differences to quickly verify if computed answers are reasonable.
  • **Multiplication and division:** These operations can become more straightforward with rounded numbers, leading to easier mental calculations.
While rounding is typically done to make math simpler, the practice is also about improving accuracy and efficiency. Integrating rounding into your calculations means adopting a strategic approach to mathematical problem-solving, which is invaluable at any level of mathematics.

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Most popular questions from this chapter

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