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Chapter 3: Problem 53

Round each number to the given place value. 1026 to the nearest hundred

Short Answer

Expert verified
1026 rounded to the nearest hundred is 1000.

Step by step solution

01

Identify the Place to Round

In the number 1026, the digit in the hundreds place is '0'. This is the digit that you will focus on modifying during the rounding process.
02

Determine the Next Digit

Look at the digit to the right of the hundreds place, which is '2' in this case. This digit will help you determine whether to round up or down.
03

Apply Rounding Rules

According to rounding rules, if the digit to the right is 5 or greater, round the target digit up. Here, since '2' is less than 5, you round down, which means the hundreds digit remains '0'.
04

Set Remaining Digits

Once you know that the hundreds digit stays the same, set the digits to the right (the tens and the ones places) to zero. Thus, rounding 1026 gives you 1000.

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Key Concepts

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

Place Value
Understanding the concept of place value is essential when rounding numbers. Place value refers to the position of a digit within a number, which determines its numerical value. Each position represents a power of ten, increasing as you move from right to left.

For example, in the number 1026:
  • The digit '6' is in the ones place.
  • The digit '2' is in the tens place.
  • The digit '0' is in the hundreds place.
  • The digit '1' is in the thousands place.
Identifying the correct place value is the first step in any rounding problem. In the exercise, we focused on the hundreds place, where the digit was '0'. Recognizing these positions helps you know which digits to alter and which to leave unchanged during rounding.
Rounding Rules
Rounding rules provide a systematic way to make numbers simpler and more manageable. The two main rules you need to remember are:
  • If the digit to the right of your desired place (in our example, the hundreds place) is 5 or greater, round the target digit up by adding one.
  • If the digit is less than 5, keep the target digit the same and zero all digits to the right.
In the number 1026, we examined the digit '2', which is immediately right of the hundreds place. Since '2' is less than 5, we applied the rule to "round down," leaving the hundreds digit as '0'. Knowing and applying these rounding rules make handling other numbers much more straightforward.
Nearest Hundred
Rounding a number to the nearest hundred means adjusting it so that it's close to a whole hundred. This simplification makes numbers easier to work with in estimations and mental calculations.

When asked to round to the nearest hundred:
  • Identify the hundreds digit you are rounding to.
  • Look at the digit right next to it, in the tens place.
In our example with 1026, the digit in the hundreds position was '0'. The digit to the right was '2', meaning we needed to round down. Thus, 1026 rounded to the nearest hundred is 1000.

Mastering the concept of rounding to the nearest hundred can multiply your efficiency in quick calculations further down the road.

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Most popular questions from this chapter

Simplify each expression. First use the distributive property to multiply and remove parentheses. $$ 2(3 x+1)+5(x-2) $$

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