Learn on PengiThe Art of Problem Solving: Prealgebra (AMC 8)Chapter 6: Decimals

Lesson 2: Rounding

In this Grade 4 lesson from The Art of Problem Solving: Prealgebra, students learn how to round integers and decimals to specified place values, including the nearest tenth, hundredth, and thousandth. The lesson covers the halfway-point rule — always rounding up to the larger value — and applies rounding to both positive and negative numbers. Students practice these skills through problems drawn from AMC 8 competition math contexts.

Section 1

Rounding Whole Numbers Using Place Value Rules

Property

How to round a whole number to a specific place value:

  1. Locate the given place value.
  2. Underline the digit to the right of the given place value.
  3. Determine if this digit is greater than or equal to 5.
    • Yes: add 1 to the digit in the given place value. Handle any regrouping (like 9 becoming 10).
    • No: do not change the digit in the given place value.
  4. Replace all digits to the right of the given place value with zeros.

Examples

  • To round 4,8624,862 to the nearest hundred, look at the tens digit (6). Since 6≥56 \ge 5, round up the hundreds digit. The result is 4,9004,900.
  • Rounding 12,34512,345 to the nearest thousand means looking at the hundreds digit (3). Since 3<53 < 5, the thousands digit stays the same. The result is 12,00012,000.
  • Rounding 49,85049,850 to the nearest thousand involves looking at the hundreds digit (8). Since 8≥58 \ge 5, we add 1 to the 9, which requires regrouping. The result is 50,00050,000.

Explanation

Rounding simplifies a number. Look at the digit just to the right of the place you're rounding to. If that digit is 5 or more, you round up. If it's 4 or less, you keep the digit the same.

Section 2

Round Decimals to Nearest Integer

Property

To round a decimal to the nearest integer, find the closest whole number. Since 1=1001 = 10^0, rounding to the nearest integer means rounding to the nearest multiple of 1.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Rounding Whole Numbers Using Place Value Rules

Property

How to round a whole number to a specific place value:

  1. Locate the given place value.
  2. Underline the digit to the right of the given place value.
  3. Determine if this digit is greater than or equal to 5.
    • Yes: add 1 to the digit in the given place value. Handle any regrouping (like 9 becoming 10).
    • No: do not change the digit in the given place value.
  4. Replace all digits to the right of the given place value with zeros.

Examples

  • To round 4,8624,862 to the nearest hundred, look at the tens digit (6). Since 6≥56 \ge 5, round up the hundreds digit. The result is 4,9004,900.
  • Rounding 12,34512,345 to the nearest thousand means looking at the hundreds digit (3). Since 3<53 < 5, the thousands digit stays the same. The result is 12,00012,000.
  • Rounding 49,85049,850 to the nearest thousand involves looking at the hundreds digit (8). Since 8≥58 \ge 5, we add 1 to the 9, which requires regrouping. The result is 50,00050,000.

Explanation

Rounding simplifies a number. Look at the digit just to the right of the place you're rounding to. If that digit is 5 or more, you round up. If it's 4 or less, you keep the digit the same.

Section 2

Round Decimals to Nearest Integer

Property

To round a decimal to the nearest integer, find the closest whole number. Since 1=1001 = 10^0, rounding to the nearest integer means rounding to the nearest multiple of 1.

Examples