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

APK

Guess how many gumballs in machine 1? How many do you think are in machine 2?

Why?

This is estimating!

Did you count them?

estimate

APK

37 + 32 is approximately 70

Eight days is approximately 1 week.

A very close guess; an educated guess; to make an approximate calculation of something; the term rounding is also used to request an estimate.

TPS

very large numbersNumbers greater than 1 million

457,923,493

10,000,000,000,000

1,000,000

APKTPS

very small numbers

.5

5 tenths

numbers less than 1. They are represented by numbers to the

RIGHT of the decimal point. They are also called decimals.

.075

75 thousandthsAPK

TPS

decimal

.5

5 tenths

a number less than 1. It is represented by numbers to the

RIGHT of the decimal point.

.75

75 hundredthsAPK

Remember!

Quotient=divisionProduct= multiplication

Sum=additionDifference=subtraction

1 00.5

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decimal

1.50

1 00.75

APK

decimal

1.750

Place Value

367,671,690,492

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When To EstimateWhen the question asks:

– “Estimate how many…”– “About how many…”– Can you think of anymore?

CD

Why is it important that we can estimate very large and very small

numbers?

IMP

What are other reasons why it is important to know how to estimate very large and very small numbers?

Estimating is a great way to eliminate wrong answer choices

Not all math problems require specific answers so being able to estimate saves time.

Estimating Very Large NumbersStep 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.

CD

Round 123,456,789 to the nearest hundred.

123,456,789Underline the number in the hundreds place.8 is greater than 5 so you add one to the hundreds place. 123,456,880Replace all the numbers to the right of the thousands place with zero.

123,456,800

Estimate!

1,893,270 5=1. Look at the number that you are going to

estimate.2. Round the number to the largest place value

that you can.3. In this case, it would be to the millions and

would make the number 2,000,000.4. 2,000,000 5= 10,000,000

Estimate!

1,893,270 5=1. Look at the number that you are going to estimate.2. Round the number to the largest place value that you can.3. In this case, it would be to the millions and would make the

number 2,000,000.4. 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.

Estimate!

3,450,000 5=1. Look at the number that you are going to

estimate.2. Round the number to the largest place value

that you can.3. In this case, you would round to 3,500,000.4. 3,500,000 5=700,000

Estimate!

3,450,000 5=1. Look at the number that you are going to estimate.2. Round the number to the largest place value that you can.3. In this case, you would round to 3,500,000.4. 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.

Guided Practice

Estimating Very Large NumbersStep 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.

CD

Round 736,987,383 to the nearest thousand.

736,987,383Underline the number in the thousands place.3 is less than 5 so you so the number in the thousands place stays the same. 736,987,383Replace all the numbers to the right of the thousands place with zero.

736,987,000

Estimating Very Small NumbersStep 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.

CD

Round 0.83746 to the nearest tenth.

0.83746Underline the number in the thousands place.3 is less than 5 so you so the number in the thousands place stays the same. 0.83746Replace all the numbers to the right of the thousands place with zero. You can drop all the extra zero’s at the end.

0.800000.8

Estimate!857,393,057 4=

1. Look at the number that you are going to estimate.

2. Round the number to the largest place value that you can.

3. In this case, it would be to the hundred millions and would make the number 900,000,000.

4. 900,000,000 4= 3,600,000,0005. 3,429,572,228 is the closest answer!

Estimate!

0.8736 5=1. Look at the number that you are going to

estimate.2. Round the number to the largest place value

that you can.3. In this case, it would be to the tenths place

and would make the number 1.0000.4. 1.000 5= 55. 4.5 is the answer closest to 5!

Estimating Very Large NumbersStep 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.

CD

Round 849,847,999,987 to the nearest hundred million.

849,847,999,987Underline the number in the hundred millions place.4 is less than 5 so number you are rounding remains the same. 849,847,999,987Replace all the numbers to the right of the hundred millions place with zero.

849,800,000,000

Let’s review!

• 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

Closure