3.14: Large Decimal Rounding to Decimal Representations
Have you ever been to Disneyland? Well, millions of people go to Disneyland every year. Take a look.
Kyle is doing a project on Disneyland. Using the internet, he has discovered that last year 14,870,000 people attended Disneyland.
If Kyle was going to round this number to the nearest million, how would he do it? Could he use a decimal representation to help him?
This Concept is all about rounding very large numbers and decimal representations. By the end of it, you will know how to help Kyle.
Guidance
In the last Concept, you learned how to round some very tiny numbers, but what about really large numbers? Can we use rounding to help us to examine some really large numbers?
Let’s think about this.
Every time a new movie comes out a company keeps track of the total of the movie sales. If you go to www.the-numbers.com/movies/records you can see some of these numbers.
Here are the sales totals for the three top movies according to movie sales.
- Star Wars IV - $460,998,007
- Avatar - $558,179,737
- Titanic - $600,788,188
Wow! 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.
- Star Wars IV - $460,998,007
- Avatar - $558,179,737
- Titanic - $600,788,188
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 sales.
Sometimes we can get confused reading numbers with so many digits in them. Rounding the numbers helps us to keep it all straight.
Here are a few for you to try. Round each to the correct decimal place.
Example A
Round the nearest million, 5,689,432.
Solution: 6,000,000
Example B
Round to the nearest hundred million, 156,789,345
Solution: 200,000,000
Example C
Round to the nearest billion, 3,456,234,123
Solution: 3,000,000,000
Now back to Disneyland. Here is the original problem once again.
Kyle is doing a project on Disneyland. Using the internet, he has discovered that last year 14,870,000 people attended Disneyland.
If Kyle was going to round this number to the nearest million, how would he do it? Could he use a decimal representation to help him?
To round this number to the nearest million, we can look at the number after the 4. It is an 8. That means that we can round up.
14,870,000 becomes 15,000,000.
This is our answer.
Vocabulary
Here are the vocabulary words in this Concept.
- 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).
- Leading Digit
- the first digit of a tiny decimal that is not a zero
Guided Practice
Here is one for you to try on your own.
After researching Disneyland, Kyle moved on to Six Flags. He discovered that 25,300,000 people attended Six Flags in 2011. Can you round that to the nearest million?
Answer
To do this, we need to look at the place value of the number after the 5. The five is in the millions place, so we look to the right of that number. It is a 3, so we don't round up.
Our answer is 25,000,000.
Video Review
Here are a few videos for review.
James Sousa, Rounding Decimals
Khan Academy Rounding Decimals
Practice
Directions: 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
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).Leading Digit
The leading digit of a decimal number less than one is the first digit to the right of the decimal point that is not a zero.Round
To round is to reduce the number of non-zero digits in a number while keeping the overall value of the number similar.Image Attributions
Description
Learning Objectives
Here you'll round very large numbers to decimal representations.