LESSON: Rounding Decimals

INTRODUCTION

READ: Rounding Decimals Using a Number Line

Rounding Decimals Using a Number Line

Let’s think back for a minute to rounding whole numbers. When we were rounding whole numbers, we could round a number to any place value that we wanted to. We could round to tens, hundreds, thousands, etc.

To do this, we followed a few simple rules.

1. Look at the digit to the right of the place value you are rounding.
2. If the digit to the right is a five or greater, you round up.
3. If the digit to the right is less than 5, you round down.

Example

Round to the nearest ten, 46

The four is in the tens place, that is the place we are rounding. The six is in the ones place that is the digit we look at. Since 6 is a five or greater, we round up.

46 becomes 50. Our answer is 50.

There are a couple of different ways that we can round decimals.

First, let’s look at rounding them using a number line.

Here we have a number line. You can see that it start with zero and ends with one. This number line has been divided up into quarters.

It goes from 0 to .25 to .50 to .75 to 1.0.

Example

.33

Here we have .33. The first thing that we want to do is to graph it on a number line.

We want to round to the nearest quarter. This number line gives us a terrific visual to do this.

Which quarter is .33 closest to? It is closest to .25.

Our answer is .25.

We can also round decimals to the nearest whole using a number line.

Example

Round 4.2 to the nearest whole.

Here we can use our number line to show us which whole number 4.2 is closest too.

Is 4.2 closer to 4.0 or 5.0 on the number line? It is closer to 4.0.

Our answer is 4.0.

READ: Rounding Decimals A Given Place Value

Rounding Decimals A Given Place Value

We can also use place value to help us in rounding numbers. Once again, we are going to follow the same rules that we did when rounding whole numbers except this time we will be rounding to the nearest whole or tenths, hundredths, thousandths, etc.

Example

Round .345 to the nearest tenth

To help us with this, let’s put the number in our place value chart.

Now we are rounding to the nearest tenth.

3 is in the tenths place.

4 is the digit to the right of the place we are rounding.

It is less than 5, so we leave the 3 alone.

Our answer is .3.

Notice that we don’t include the other digits because we are rounding to tenths. We could have put zeros in there, but it isn’t necessary.

Example

Round .567 to the nearest hundredth

To help us with this, let’s use our place value chart again.

Now we are rounding to the nearest hundredth.

The 6 is in the hundredths place.

The 7 is the digit to the right of the hundredths place.

Since a 7 is a 5 or greater, we round up to the next digit.

6 becomes 7.

Our answer is .57.

Notice in this case that the five is included. Because it is to the left of the place we are rounding, it remains part of the number.

READ: Round Very Small Decimals

Round Very Small Decimal Fractions to the Leading Digit

We know that a decimal is a part of a whole. We also know that some decimals are smaller than others. If we have a decimal that is 5 tenths of a whole, this is a larger decimal than 5 hundredths of a whole. Let’s look at those two decimals.

Example

.5 ______ .05

If we were going to compare these two decimals, we would add a zero to the first decimal so that it has the same number of digits as the second.

.50 > .05

We can see that the five tenths is greater than five hundredths. This example can help us to determine very small decimals.

A decimal is a very small decimal depending on the number of places represented after the decimal point. The more decimal places, the smaller the decimal is.

Here is an example of a very small decimal:

.000056787

Because this decimal has so many digits, we can say that it is a very tiny decimal. We can round tiny decimals like this one too. We use something called the leading digit to round a very small decimal. The leading digit is the first digit of the decimal that is represented by a number not by a zero.

In this example, the leading digit is a five:

.000056787

To round this decimal, we use the leading decimal and add in the rounding rules that we have already learned. The digit to the right of the five is a six. Six is greater than 5, so we round up.

Our answer is .00006.

Notice that we include the zeros to the left of the leading digit, but we don’t need to include any of the digits after the leading digit. That is because we rounded that digit so we only need to include the rounded part of the number.

READ: Rounding Very Large Numbers

Rounding Very Large Numbers to Decimal Representations of Thousands, Millions, etc.

We just finished rounding some very tiny numbers, but what about really large numbers? Can we use rounding to help us to examine some really large numbers?

Here are the sales totals for the three top movies according to movie sales.

1. Star Wars IV - $460,998,007
2. Avatar - $558,179,737
3. Titanic - $600,788,188

Those are some big numbers! Here is where rounding can be very helpful. We can round each of these numbers to the nearest hundred million.

First, let’s find the hundred millions place.

1. Star Wars IV - $460,998,007
2. Avatar - $558,179,737
3. Titanic - $600,788,188

The place that is highlighted is the hundred millions place. Now we want to round to the nearest hundred million. We do this by looking at the number to the right of the place that we are rounding.

Let’s look at each movie individually.

1. Star Wars IV - The number after the 4 is a 6, so we round up to a 5. The rest of the numbers are zeros.

500,000,000

2. Avatar - The number after the 5 is a 5, so we round up to 6. The rest of the numbers are zeros.

600,000,000

3. Titanic - The number after the 6 is a zero. So the 6 stays the same and the rest of the numbers are zeros.

600,000,000

If we want to compare these numbers now we can see that Avatar and Titanic had the highest sales and Star Wars IV had the least highest sales. Sometimes we can get confused reading numbers with so many digits in them. Rounding the numbers helps us to keep it all straight.

EXAMPLE 1

Rounding Decimals

EXAMPLE 2

EXAMPLE 3

CHECK Yourself! Rounding Decimals