Transcript Document

6.1.2.2
Judge the reasonableness of
the results of rational number
estimates and/or
computations.
Let’s review
rounding!
Simple Steps to Estimating whole
numbers
• 1. Find whatever place value you are
looking to estimate to
2. look at the digit to the right.
If the digit to the right is "5 or higher"
the place value INCREASES by 1.
4. If the digit to the right IS NOT "5 or
higher"
the place value STAYS as it is.
5. All the rest of the numbers to the right of
the place value become ZEROS.
Example 1: Estimate 1,754 to the
nearest thousand.
1,754 >>> 1 is in the thousands place.
Look to the right of the 1
and notice that there is a 7.
7 is "5 or higher",
so the 1 increases by 1
and becomes a 2.
All the other numbers to the right
of the 2 now become Zeros.
Meaning: 1,754 rounds UP to 2,000
Example 2: Estimate 32,795
to the nearest ten-thousand
32,795 >>> 3 is in the ten-thousands place.
Look to the right of the 3
and notice that there is a 2.
2 is NOT "5 or higher",
so the 3 STAYS as it is.
All the other numbers to the right
of the 3 now become Zeros.
Meaning: 32,795 rounds DOWN to 30,000
Remember!
~ If the number to the right
of the place value you're looking to
estimate
is "5 or higher",
increase the place value number by 1.
~ If the number to the right
of the place value you're looking to
estimate
is NOT "5 or higher",
the place value number STAYS
as it is.
Rounding is one way to
estimate products. Now
that we have determined
that rounding can be used
to estimate results we can
also justify the
reasonableness of rounding
products as well.
For instance, let's take a look at
the cost of a six pack of
soda. We know that a six pack of
soda cost about $2.99.
So, if we round $2.99 to the nearest
dollar, it would be $3.00.
Saying a six pack of soda costs $3.00
would be reasonable.
Saying a six pack of soda costs $10.00
would not be reasonable.
Let's take a look at how to round
numbers to multiply…
Round to the greatest place value to
estimate products.
Estimate 2 x 258 = ?
You need to round 258 to the greatest
place value.
Step 1 Compare. The 2 in 258 means 2
hundreds. So 258 is between 200 and
300.
Step 2 Round to the closer hundred.
The halfway point between 200 and
300 is 250.
258 is closer to 300 than 200.
Step 3 Use the rounded number to
estimate.
2 x 258 rounds to about
2 x 300 = 600
2 x 258 is about 600.
Estimate to the nearest ten.
16
x2
?
20
x2
40
Use the rounded number to estimate.
16 rounds to about 20
2 x 16 is about 2 x 20 = 40.
40 is a reasonable answer.
Estimate to the nearest hundred.
157
x 2
?
200
x2
400
Use the rounded number to estimate.
157 rounds to about 200
2 x 157 is about 2 x 200 = 400.
400 is a reasonable answer.
Estimate to the nearest thousand.
6400
x 2
?
6000
x 2
12,000
Use the rounded number to estimate.
6400 rounds to about 6000
2 x 6400 is about 2 x 6000 = 12,000.
12,000 is a reasonable answer.
Use compatible numbers
to estimate the quotient
44
6
Round 44 to the closest product of 6.
6 x 7 = 42 and 6 x 8 = 48
42 is closest to 44, so the answer
would be 7.
Estimate the quotient:
85 ⌯ 7
Since 7 x 12 is 84, that is
the closest product of 7.
So the estimate of
85 ⌯ 7 = 12
Round to the greatest place value
to estimate products.
Round to compatible numbers to
estimate quotients.
Use the rounded number to justify
the reasonableness of estimating.
Justify Reasonableness
Answer the following
questions dealing with
estimation. Make sure
your answers are
reasonable.
Alyssa wants to fill her swimming
pool.
It holds no more than 23 gallons of
water.
If her bucket holds 2 gallons, how
many will she need to fill without
overflowing the pool?
22
If there is complete sunshine
for a total of 470 minutes,
‘About’ how many hours of complete
sunshine was there?
8
Dan is doing yard work for his dad.
He is working for about 50 minutes a day.
If he works for 3 days,
'about' how many hours will he work
altogether?
3
Mike has math homework.
He has to do 4 rows of problems.
There are 9 problems in each row.
If he can do 10 problems every 15
minutes,
'about' how long will it take Mike to
finish his homework?
1 hour
There are 9 groups at the beach.
The groups have an average of 18 people each.
If the beach is supposed to have 2 lifeguards for
every 150 people, how many lifeguards should
be on duty?
2
Courtney is painting a sunset.
She uses five colors, and 2 tubes of each color.
If each tube of paint costs $4.50,
about how much will she spend on the paint?
About $50
Now, let’s do some practicing!