# 40 Round Decimals Lesson 3.4

## Introduction

Welcome to Lesson 3.4 of our math series! In this lesson, we will be exploring the concept of rounding decimals. Rounding decimals is an essential skill to have in your math toolbox, as it allows you to estimate and work with numbers in a more manageable way. Whether you're a student looking to improve your math skills or an adult looking for a refresher, this lesson will provide you with a comprehensive understanding of rounding decimals.

## What are decimals?

Before we dive into rounding decimals, let's quickly review what decimals are. Decimals are a way of representing numbers that fall between whole numbers. They consist of two main components: a whole number part and a fractional part. The fractional part is separated from the whole number part by a decimal point. For example, in the number 3.14, 3 is the whole number part and 14 is the fractional part.

### Understanding place value

In order to round decimals, it's important to have a solid understanding of place value. Place value refers to the value assigned to each digit in a number based on its position. In a decimal number, the digits to the left of the decimal point represent whole numbers, while the digits to the right represent fractions.

### Identifying the rounding digit

When rounding decimals, we focus on a specific digit called the rounding digit. This digit tells us which digit to look at when deciding how to round the number. For example, if we want to round the number 3.14 to the nearest whole number, the rounding digit would be 4, as it is the first digit to the right of the decimal point.

## Rounding decimals to the nearest whole number

One of the most common ways to round decimals is to round them to the nearest whole number. To do this, we follow a simple set of rules:

### Rule 1: Look at the rounding digit

To round a decimal to the nearest whole number, we start by looking at the rounding digit. In our example of 3.14, the rounding digit is 4.

### Rule 2: Check the digit to the right of the rounding digit

The next step is to look at the digit to the right of the rounding digit. If this digit is 5 or greater, we round the rounding digit up by 1. If the digit is less than 5, we leave the rounding digit unchanged. In our example, the digit to the right of 4 is 1, which is less than 5. Therefore, we leave the rounding digit unchanged.

### Rule 3: Drop all digits to the right of the rounding digit

Finally, we drop all digits to the right of the rounding digit. In our example, since we didn't round up 4, we drop the digits 14, leaving us with 3 as the rounded whole number.

## Rounding decimals to a specific decimal place

In addition to rounding decimals to the nearest whole number, we can also round them to a specific decimal place. This is useful when we want to work with numbers that are easier to manage. To round decimals to a specific decimal place, we follow a similar set of rules as when rounding to the nearest whole number:

### Rule 1: Look at the rounding digit

Just like before, we start by looking at the rounding digit. For example, if we want to round the number 3.14159 to two decimal places, the rounding digit would be 1.

### Rule 2: Check the digit to the right of the rounding digit

Next, we look at the digit to the right of the rounding digit. If this digit is 5 or greater, we round the rounding digit up by 1. If the digit is less than 5, we leave the rounding digit unchanged. In our example, the digit to the right of 1 is 4, which is less than 5. Therefore, we leave the rounding digit unchanged.

### Rule 3: Drop all digits to the right of the desired decimal place

Finally, we drop all digits to the right of the desired decimal place. In our example, since we are rounding to two decimal places, we drop all digits to the right of the 1, leaving us with 3.14 as the rounded number.

## Rounding decimals to a specific significant figure

In some cases, we may want to round decimals to a specific significant figure. Significant figures are the digits that carry meaning in a number. To round decimals to a specific significant figure, we use a similar set of rules:

### Rule 1: Look at the rounding digit

As always, we start by looking at the rounding digit. For example, if we want to round the number 0.00621 to two significant figures, the rounding digit would be 6.

### Rule 2: Check the digit to the right of the rounding digit

Next, we look at the digit to the right of the rounding digit. If this digit is 5 or greater, we round the rounding digit up by 1. If the digit is less than 5, we leave the rounding digit unchanged. In our example, the digit to the right of 6 is 2, which is less than 5. Therefore, we leave the rounding digit unchanged.

### Rule 3: Drop all digits to the right of the desired significant figure

Finally, we drop all digits to the right of the desired significant figure. In our example, since we are rounding to two significant figures, we drop all digits to the right of the 6, leaving us with 0.0062 as the rounded number.

## Conclusion

Rounding decimals is a valuable skill that enables us to work with numbers in a more practical manner. By understanding the rules and techniques for rounding decimals to the nearest whole number, specific decimal places, and significant figures, we can confidently estimate and manipulate numbers in various mathematical contexts. Whether you're calculating measurements, solving equations, or simply trying to get a ballpark estimate, rounding decimals is a fundamental skill that will serve you well in your mathematical journey.