1. Today we will estimate very large and very small numbers.
estimate – a very close guess; an educated guess; to make an approximate calculation of something
very large numbers – numbers in the millions or higher; have 7 or more digits
very small numbers - numbers in the thousandths or smaller; thousandths are fractional parts of 1000
Concept

2. Guess how many gumballs in machine 1
Guess how many gumballs in machine 1? How many do you think are in machine 2?
Why?
Did you count them?
This is estimating!
APK 2

3. estimate
A very close guess; an educated guess; to make an approximate calculation of something; the term rounding is also used to request an estimate.
is approximately 70
Eight days is approximately 1 week.
TPS
APK

4. very large numbers
Numbers greater than 1 million
1,000,000
457,923,493
10,000,000,000,000
TPS
APK

5. very small numbers
numbers less than 1. They are represented by numbers to the RIGHT of the decimal point. They are also called decimals. .5
5 tenths
.075
75 thousandths
TPS
APK

6. decimal
a number less than 1. It is represented by numbers to the RIGHT of the decimal point. .5
5 tenths
.75
75 hundredths
APK

7. Remember! Quotient=division Product= multiplication Sum=addition
Difference=subtraction

8. decimal 1
0.5
1.50
APK

9. decimal 1
0.75
1.750
APK

10. Place Value
Billions
Millions
Thousands
Hundreds
367,671,690,492

11. When To Estimate When the question asks: “Estimate how many…”
“About how many…”
Can you think of anymore? CD

12. Why is it important that we can estimate very large and very small numbers?
Not all math problems require specific answers so being able to estimate saves time.
Estimating is a great way to eliminate wrong answer choices
What are other reasons why it is important to know how to estimate very large and very small numbers?
IMP

13. Estimating Very Large Numbers
Step 1: Find the place value you will be rounding to and
underline it.
Step 2: Look at the number to the right. If the number is greater than 5, add
1 to the number you are rounding. If the number is less than 5, the number you
are rounding stays the same.
Step 3: All the numbers to the right of the number that you are rounding
will become zero.
Round 123,456,789 to the nearest hundred.
123,456,789
Underline the number in the hundreds place.
8 is greater than 5 so you add one to the hundreds place.
You made need to include a mini lesson on dividing decimals at this point. Scholars may have forgotten how to add a decimal point and zeros to the dividend
123,456,880
Replace all the numbers to the right of the thousands place with zero.
123,456,800 CD

14. Estimate!
1,893, =
Look at the number that you are going to estimate.
Round the number to the largest place value that you can.
In this case, it would be to the millions and would make the number 2,000,000.
2,000, = 10,000,000

15. Estimate!
1,893, =
Look at the number that you are going to estimate.
Round the number to the largest place value that you can.
In this case, it would be to the millions and would make the number 2,000,000.
2,000, = 10,000,000
Discussion
When rounding, always look at what the problem is asking you to do. In this case, it is asking you multiply by 5.
Multiplying by 5 and then rounding the large number to 2,000,000 would make it easier to estimate and give you a closer estimate to the actual answer that would be 9,466,350 which is closer to 10,000,000.
If you would have rounded down to 1,000,000, your answer would have been 5,000,000, and that is NOT closer to the actual answer of 9,466,350.

16. Estimate!
3,450, =
Look at the number that you are going to estimate.
Round the number to the largest place value that you can.
In this case, you would round to 3,500,000.
3,500, =700,000

17. Estimate!
3,450, =
Look at the number that you are going to estimate.
Round the number to the largest place value that you can.
In this case, you would round to 3,500,000.
3,500, =700,000
Discussion
In this case, again, you would look at what the problem is asking you to do. It is asking you to divide by 5.
Here instead of rounding down to 3,000,000 you would instead round to 3,500,000. Here is the reason why.
If you round to 3,000,000, your answer would be 600,000. The actual answer is 690,000.
Instead, you would round to 350,000 and then divide and you answer would be 700,000, which is close to 690,000.

18. Guided Practice

19. Estimating Very Large Numbers
Step 1: Find the place value you will be rounding to and
underline it.
Step 2: Look at the number to the right. If the number is greater than 5, add
1 to the number you are rounding. If the number is less than 5, the number you
are rounding stays the same.
Step 3: All the numbers to the right of the number that you are rounding
will become zero.
Round 736,987,383 to the nearest thousand.
736,987,383
Underline the number in the thousands place.
3 is less than 5 so you so the number in the thousands place stays the same.
You made need to include a mini lesson on dividing decimals at this point. Scholars may have forgotten how to add a decimal point and zeros to the dividend
736,987,383
Replace all the numbers to the right of the thousands place with zero.
736,987,000 CD

20. Estimating Very Small Numbers
Step 1: Find the place value you will be rounding to and
underline it.
Step 2: Look at the number to the right. If the number is greater than 5, add
1 to the number you are rounding. If the number is less than 5, the number you
are rounding stays the same.
Step 3: All the numbers to the right of the number that you are rounding
will become zero.
Round to the nearest tenth.
Underline the number in the thousands place.
3 is less than 5 so you so the number in the thousands place stays the same.
You made need to include a mini lesson on dividing decimals at this point. Scholars may have forgotten how to add a decimal point and zeros to the dividend
Replace all the numbers to the right of the thousands place with zero. You can drop all the extra zero’s at the end.
0.8 CD

21. Estimate!
857,393, =
Look at the number that you are going to estimate.
Round the number to the largest place value that you can.
In this case, it would be to the hundred millions and would make the number 900,000,000.
900,000, = 3,600,000,000
3,429,572,228 is the closest answer!

22. Estimate! 0.8736 5= Look at the number that you are going to estimate.=
Look at the number that you are going to estimate.
Round the number to the largest place value that you can.
In this case, it would be to the tenths place and would make the number
= 5
4.5 is the answer closest to 5!

23. Estimating Very Large Numbers
Step 1: Find the place value you will be rounding to and
underline it.
Step 2: Look at the number to the right. If the number is greater than 5, add
1 to the number you are rounding. If the number is less than 5, the number you
are rounding stays the same.
Step 3: All the numbers to the right of the number that you are rounding
will become zero.
Round 849,847,999,987 to the nearest hundred million.
849,847,999,987
Underline the number in the hundred millions place.
4 is less than 5 so number you are rounding remains the same.
You made need to include a mini lesson on dividing decimals at this point. Scholars may have forgotten how to add a decimal point and zeros to the dividend
849,847,999,987
Replace all the numbers to the right of the hundred millions place with zero.
849,800,000,000 CD

24. Let’s review! Closure What does estimate mean? A close guess!
What are very large numbers?
Numbers in the millions or billions. Numbers like 2,304,000 and 2,455,098,098
What are very small numbers?
Numbers smaller than one.
Numbers like and 0.4
Closure
Closure