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# 3.14: Large Decimal Rounding

Difficulty Level: At Grade Created by: CK-12
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Practice Large Decimal Rounding to Decimal Representations

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Kyle learns that the sun is 92,960,000 miles away from the Earth. He wants to round the distance to the nearest ten million so that he can easily compare the distance to other distances. Unfortunately, he does not know how to round to the nearest ten million. How can Kyle round 92,960,00 to the nearest ten million?

In this concept, you will learn how to round very large numbers and decimal representations.

### Rounding Large Whole Numbers

Rounding can be very helpful with large numbers. A real world example is a movie box office gross. Every time a new movie comes out a company keeps track of the total of the movie sales, often in the tens or hundreds of millions.

Let's look at an example. Here are a few sales totals for three movies.

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

This is where rounding can be very helpful. You can round each of these numbers to the nearest hundred million. You do this by looking at the number to the right of the place that you are rounding.

Let’s look at each movie separately.

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

500,000,000

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

600,000,000

You can compare these numbers and see that Avatar and Titanic had the highest sales and Star Wars IV had the lowest sales out of the three movies.

### Examples

#### Example 1

Earlier, you were given a problem about Kyle who has just learned the distance from the sun to the Earth.

How can he round 92,960,000 to the nearest ten million?

First, locate the digit that is in the ten millions place.

9

Next, determine if the number to the right of the ten millions place is 5 or greater.

No

Then, leave the number in the ten millions place the same.

90,000,000

#### Example 2

Round 9,346,788 to the nearest million.

First, locate the digit that is in the millions place.

9

Next, determine if the number to the right of the millions place is 5 or greater.

No

Then, leave the number in the millions place the same.

9,000,000

#### Example 3

Round 5,689,432 to the nearest million.

First, locate the digit that is in the millions place.

5

Next, determine if the number to the right of the millions place is 5 or greater.

Yes

Then, round the number up to the next million.

6,000,000

#### Example 4

Round 156,789,345 to the nearest hundred million.

First, locate the digit that is in the hundred millions place.

1

Next, determine if the number to the right of the hundred millions place is 5 or greater.

Yes

Then, round the number up to the next hundred millions.

200,000,000

#### Example 5

Round 3,456,234,123 to the nearest billion.

First, locate the digit that is in the billions place.

3

Next, determine if the number to the right of the billions place is 5 or greater.

No

Then, leave the number in the billions place the same.

3,000,000,000

### Review

Round each number to the specified place value.

1. 5,689,123 to the nearest million
2. 456,234 to the nearest ten thousand
3. 678,123 to the nearest thousand
4. 432,234 to the nearest hundred thousand
5. 567,900 to the nearest thousand
6. 1,234,600 to the nearest million
7. 1,980,000 to the nearest million
8. 23,800,990 to the nearest ten - million
9. 18,900,000 to the nearest ten - million
10. 12,890,000 to the nearest million
11. 1,234,567,800 to the nearest billion
12. 3,450,230,000 to the nearest billion
13. 4,590,000,000 to the nearest billion
14. 3,870,000,100 to the nearest billion
15. 13,567,122,320 to the nearest billion

To see the Review answers, open this PDF file and look for section 3.14.

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