Problem 5 - Fundamentals of Mathematics

Question

Use the method of rounding whole numbers to solve each problem. Round 59,600 to the nearest thousand.

Step-by-Step Solution

Answer

59,600 rounded to the nearest thousand is 60,000.

Step 1: Identify the place to round to

We need to round 59,600 to the nearest thousand. The digit in the thousands place is 9.

Step 2: Review the digit to the right

The digit immediately to the right of the thousands place is in the hundreds place, which is 6.

Step 3: Determine whether to round up or down

Since the hundreds digit is 6, which is greater than 5, we round the thousands place up from 9 to 10.

Step 4: Adjust the number

Rounding up 9 to the next thousand requires carrying over to the next highest thousands, transitioning 59 to 60. The thousands place becomes 0 and the ten-thousands place increases by 1.

Step 5: Finalize the rounded number

Hence, 59,600 rounded to the nearest thousand becomes 60,000.

Key Concepts

Nearest Thousand

Rounding a number to the nearest thousand means adjusting the number so that it is closest to a multiple of 1,000. When we do this for the number 59,600, we are asking which multiple of 1,000 is nearest to it. The multiples of 1,000 close to 59,600 are 59,000 and 60,000. By rounding 59,600, we find out which of these two numbers the original number is closest to.
To decide this, we look at the hundreds place, which is one place to the right of the thousands place. This digit helps us determine if 59,600 should go up to 60,000 or stay at 59,000.

Rounding Up

Rounding up is a crucial part of the rounding process. It means increasing the number in the place value you are rounding to.
Here's how it worked in our example of 59,600:

• First, we reviewed the hundreds place, which was filled by the digit 6.
• Since 6 is greater than 5, we follow the rounding rule that tells us to "round up."
• This means increasing the digit in the thousands place (which is 9) by 1.

In the thousands place, 9 becoming 10 means we transition from 59,000 to 60,000. The initial thousands digit transforms into 0, carrying the addition over to the ten-thousands place, making it 60,000.

Place Value Identification

Place value identification is the foundation of rounding numbers. It involves recognizing where each digit falls in the number, such as units, tens, hundreds, and so forth.
In the number 59,600, the places are as follows:

• The 'thousands' place is filled by the digit 9.
• The 'hundreds' place, one spot to the right, holds the digit 6.
• To the left and right, you also find the 'ten-thousands', 'tens', and 'units' places.

Identifying these places is essential because they dictate how we approach rounding. We focused on the thousands and hundreds places to determine how to round 59,600. Understanding place values allows for accurate rounding and helps you easily handle larger numbers.