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# Decimal Rounding on a Number Line

## Rounding according to proximity on number line

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Decimal Rounding on a Number Line

Have you ever made a new sign? Have you ever had to round measurements? Well, Jose is going to need to do both of those things.

Mr. Harris has given Jose the task of creating a new sign for “Add It Up Ice Cream”. The paint on the old sign is chipped and peeling, so Mr. Harris is hoping for a beautiful new sign to attract business. Jose loves to paint and design things so he is the right person for the job. Jose is excited. He takes down the old sign and begins thinking about how he is going to design it. Here is some of the information that Jose has to work with.

• The original sign is 4.25’ $\times$ 2.5’
• The letters on the original sign are 1.67' high

While Jose is working on his drawing, Mr. Harris walks up behind him. “Jose, I think we should work with a new sign board too. Please round the length of the sign to the nearest half foot and the width to the nearest whole foot. Also, please make the letters a bit larger than the original. Maybe round up to the nearest foot on those too,” Mr. Harris says to Jose with a twinkle in his eye.

Jose smiles at Mr. Harris and then shrugs when Mr. Harris walks away.

Jose will need to remember how to round decimals for this plan to work.

In this Concept, you will need to learn how to round decimals to help Jose.

### Guidance

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.

Round the number 46 to the nearest ten

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 starts 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.

.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.

Round 4.2 to the nearest whole number.

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

Wow! It is great to be able to see this so clearly.

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.

Now let's practice. Round each decimal.

#### Example A

Round $.47$ to the nearest tenth.

Solution: This decimal rounds to .5.

#### Example B

Round $3.01$ to the nearest whole value.

Solution: This decimal rounds to 3.

#### Example C

Round $.89$ to the nearest whole value.

Solution: This decimal rounds to 1.

Now that you have had a chance to learn about rounding decimals, you are ready to help Jose with his dilemma. Let’s look at the problem once again.

Mr. Harris has given Jose the task of creating a new sign for “Add It Up Ice Cream”. The paint on the old sign is chipped and peeling, so Mr. Harris is hoping for a beautiful new sign to attract business. Jose loves to paint and design things so he is the right person for the job. Jose is excited. He takes down the old sign and begins thinking about how he is going to design it.

Here is some of the information that Jose has to work with.

• The original sign is 4.25’ $\times$ 2.5’
• The letters on the original sign are 1.67' high

While Jose is working on his drawing, Mr. Harris walks up behind him. “Jose, I think we should work with a new sign board too. Please round the length of the sign to the nearest half foot and the width to the nearest whole foot. Also, please make the letters a bit larger than the original. Maybe round up to the nearest foot on those too,” Mr. Harris says to Jose with a twinkle in his eye. Jose smiles and Mr. Harris and then shrugs when Mr. Harris walks away.

There are two parts to Jose’s sign dilemma.

The first part is to round the length to the nearest half foot and the width of the original sign to the nearest foot. Let’s look at the dimensions of the original sign: 4.25’ $\times$ 2.5’.

We want to round the length to the nearest half foot: 4.25 rounds to 4.5. Because the nearest half foot to .25 is .50. The new length of the sign is 4.5’.

Next, we look at the width of the sign. We want to round the width to the nearest foot, so we round 2.5’ to 3 feet. The new width of the sign is 3 feet.

Jose has been having a trickier time with the sizing of the letters. The current size of the letters is 1.67’. He needs to round it to the nearest foot.

Let’s look at the decimal part of the measurement.

The decimal .67 is closer to one whole than to .50, so we round up.

This is actually quite simple. The question is whether 1.67 is closer to 1 or to 2. If we use the trick we have been practicing and look at the decimal along as if it were a whole number, then the question becomes: Is 67 closer to 0 or to 100? Since 67 is obviously closer to 100, .67 is closer to 1. Since we have already 1 whole, we add 1 more whole, and as a result, 1.67 feet rounds to 2 feet.

You can use the rules for rounding whenever you are rounding any decimal.

### Vocabulary

Round
to use place value to change a number whether it is less than or greater than the digit in the number
Decimal
a part of a whole written to the right of a decimal point. The place value of decimals is marked by THS (such as tenTHS, hundredTHS, etc).

### Guided Practice

Here is one for you to try on your own. Draw a number line to help you.

If you were going to round 4.67 to the nearest whole number, would you round up to 5 or down to 4?

To answer this question, you have to look at the decimal part of the number. The decimal .67 is greater than .50, so we have to round up. Therefore we would round up to 5.

This is our answer.

### Practice

Directions: Use the number line and round to the nearest decimal on the number line.

1. 2.54

2. 2.12

3. 2.78

4. 2.89

5. 2.33

6. 2.42

7. 2.97

8. 2.01

9. 2.11

10. 2.27

11. 2.15

12. 1.98

13. 1.87

14. 2.76

15. 2.9

### Vocabulary Language: English

Decimal

Decimal

In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).
Round

Round

To round is to reduce the number of non-zero digits in a number while keeping the overall value of the number similar.