Today we will estimate very large and very small numbers.

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? How many do you think are in machine 2? Why? Did you count them? This is estimating! APK

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. 37 + 32 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 0 1.50 APK

9. decimal 1 0 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. 123,456,880 Replace all the numbers to the right of the thousands place with zero. 123,456,800 CD

14. Estimate! 1,893,270 5= • 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. • 2,000,000 5= 10,000,000

15. Estimate! 1,893,270 5= • 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. • 2,000,000 5= 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! 3,450,000 5= • 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. • 3,500,000 5=700,000

17. Estimate! 3,450,000 5= • 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. • 3,500,000 5=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. 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 0.83746 to the nearest tenth. 0.83746 Underline the number in the thousands place. 3 is less than 5 so you so the number in the thousands place stays the same. 0.83746 Replace all the numbers to the right of the thousands place with zero. You can drop all the extra zero’s at the end. 0.80000 0.8 CD

21. Estimate! 857,393,057 4= • 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. • 900,000,000 4= 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. • 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 1.0000. • 1.000 5= 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. 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 0.456 and 0.4