Question

Round \(2,867\) to the nearest ten. A. \(2,900\) B. \(2,960\) C. \(3,000\) D. \(2,870\)

Short answer

The number 2,867 rounded to the nearest ten is 2,870. (Option D)

Step-by-step solution

Identify the Place to Round

To round the number 2,867 to the nearest ten, find the digit in the tens place. In 2,867, the tens digit is 6.

Find the Next Lower and Higher Ten

The number line segment between which we'll round lies between 2,860 and 2,870 because these are the tens we are rounding between.

Check the Neighboring Digit

Look at the digit to the right of the tens place, which is the ones place in the number 2,867. The digit is 7.

Apply Rounding Rule

According to rounding rules, if the ones digit is 5 or greater, the number in the tens place should be rounded up. Since 7 is greater than 5, we round up.

Calculate the Result

Round 2,867 up to the nearest ten. The tens place becomes 7, resulting in the rounded number 2,870.

Key concepts

Place Value

Understanding place value is essential when it comes to rounding numbers. Place value refers to the value of each digit in a number, determined by its position. For example, in the number 2,867, each digit has a different place value:

• The digit 2 is in the thousands place, representing 2,000.
• The digit 8 is in the hundreds place, representing 800.
• The digit 6 is in the tens place, representing 60.
• The digit 7 is in the ones place, representing 7.

Recognizing these positions helps you decide how to round numbers accurately. When asked to round to the nearest ten, you focus on the tens and ones digits. Understanding which digit's value will impact the rounding decision is key, and it all starts with recognizing the place value of each digit. Remember, place value gives each digit its meaning and determines its contribution to the overall number.

Number Line

A number line is a visual tool that can make rounding numbers much clearer. It helps you see where a number falls between two endpoints.
When rounding 2,867 to the nearest ten, visualize a number line that includes values from 2,860 to 2,870. 2,867 is placed almost at the end of this segment. By seeing the number's position on this line, it'll become evident whether it's closer to 2,860 or 2,870.
This proximity helps determine how the number should be rounded. Visualizing using a number line can simplify the rounding process, making abstract concepts more tangible.

Rounding Rules

Rounding rules guide us in rounding numbers. Here is how these rules work in a simple way:
1. Identify the place you need to round to, such as tens, hundreds, etc.
2. Observe the digit immediately to the right of this place.
3. Apply the following rules:

• If the digit is 4 or less, keep the digit you're rounding to the same.
• If the digit is 5 or more, increase the digit in the place you're rounding to by one.

These simple rules help to decide whether to round a number up or down based on its additional value. For example, since 7 is greater than 5, the number 6 in the tens place of 2,867 is increased by one, rounding it up to 870. Rounding is all about approximating a number so it is easier to work with, while staying as close to the original value as possible.

Tens Place

The tens place is crucial when rounding numbers to the nearest ten. This place value represents the part of the number that's ten times a single unit.
For 2,867, the digit in the tens place is 6. This means there are six groups of ten, or 60. When rounding to the nearest ten, you are determining whether the tens digit stays the same or increases.
The decision is based on the value of the ones digit, which nudges the tens place up or leaves it as is.
Understanding the role of the tens place is vital in rounding exercises since it dictates the final rounded number.