Transcript Using Rounded Numbers

Using Rounded Numbers
Lesson 1.4.2
1
Lesson
1.4.2
Using Rounded Numbers
California Standards:
What it means for you:
Mathematical Reasoning 2.1
Use estimation to verify the
reasonableness of calculated
results.
Mathematical Reasoning 2.6
Indicate the relative advantages
of exact and approximate solutions
to problems and give answers to a
specified degree of accuracy.
You’ll learn when it’s a good idea to
use rounding, and how to check your
answers using rounded numbers.
Key words:
•
•
•
•
•
•
rounding
place value
accuracy
check
reasonable
estimate
2
Lesson
1.4.2
Using Rounded Numbers
This Lesson will tell you more about
using rounded numbers.
“It’s about…
…126.5 cm”
…127 cm”
…130 cm”
“about 200 miles”
“50,000 people”
You’ll think about how much certain
numbers should be rounded.
You’ll also see how rounded numbers
are useful for checking your work.
24.6 × 3.97 = 97.662
25 × 4 = 100
3
Lesson
1.4.2
Using Rounded Numbers
Sometimes You Need to Choose How Much to Round
People round numbers to different place values depending
on what the numbers are being used for.
“Add 6.25 lb of chemical X”
“I weigh 100 lb.”
“Use 0.5 lb flour.”
4
Lesson
1.4.2
Example
Using Rounded Numbers
1
Below are three situations connected with the distance
between Town A and Town B. Match each situation to
the most suitable level of rounding.
Situation
A road sign in Town A shows the distance to Town B.
Jada lives in Town B. She tells a friend from another state
how far away she lives from Town A.
A mapping company is making an accurate map of the area.
Distances
203.56 miles
204 miles
200 miles
Solution
A road
The
friend
mapping
sign
would
wouldn’t
company
only give
want
needs
distances
a rough
to know
idea
to the
exact
ofnearest
how
distances
farhundredth
away to
Town
draw
A is.
of aaccurate
Jada
an
mile.
couldThe
tell
map.
road
her friend
They
sign would
would
that she
give
use
lives
the200
figure
distance
miles
of 203.56
as
from
204Town
miles.
miles.
A.
This exact
The
is accurate
distance
enough,
doesn’t
andmatter
can betoread
someone
easily who
by a lives
passing
far away.
driver.
5
Solution follows…
Lesson
1.4.2
Using Rounded Numbers
Guided Practice
Exercises 1–2 give three figures: one exact and two
rounded numbers.
Choose which you think is most suitable, and explain your choice.
(In each case, the first figure given is the exact answer.)
1. Ana Lucia writes in a history essay:
Thomas Jefferson lived to the age of 83 / 80 / 100.
83 years. Either of the rounded figures would be misleading.
2. On a form, Gavin gives his height as:
160.67 cm / 161 cm / 200 cm.
161 cm. Nobody would need to know his height to the nearest 0.01 cm.
To round up to 200 cm would suggest Gavin is much taller than he really is.
6
Solution follows…
Lesson
1.4.2
Using Rounded Numbers
Guided Practice
Exercises 3–4 give three figures: one exact and two rounded
numbers.
Choose which you think is most suitable, and explain your choice.
(In each case, the first figure given is the exact answer.)
3. A school records how many students are in school each day.
Today there are 3914 / 3900 / 4000 students attending.
3914 students. The school will want an accurate record of student numbers,
for example in case there is a fire, so only the exact number will do.
4. Mr. Anderson returns from a vacation in England with £10 left over
from his extra cash. £1 is worth $1.85965. He changes the money
at the bank and receives $18.5965 / $18.60 / $19.
$18.60. The bank can’t give him 0.65 cents, and wouldn’t
round to the nearest dollar.
7
Solution follows…
Lesson
1.4.2
Using Rounded Numbers
The Amount of Rounding Affects the Accuracy
If you use rounding to estimate a sum,
be careful how much you round.
1552 + 2676 = 4228
1550 + 2680 = 4230
Rounding to higher place values
usually gives an estimate farther from
the actual answer than rounding to
lower place values.
1600 + 2700 = 4300
2000 + 3000 = 5000
8
Lesson
1.4.2
Example
Using Rounded Numbers
2
Lucas wants to add 3439 and 5482. He doesn’t
need an exact answer, so he decides to use
rounding. Lucas's work is shown on the right.
3000
+ 5000
8000
How could he have found a more accurate answer?
Solution
Lucas rounded to the nearest thousand, so he got an
estimate of 8000. If he had rounded to the nearest
hundred, he would have gotten 3400 + 5500 = 8900,
which is much closer to the actual answer of 8921.
9
Solution follows…
Lesson
1.4.2
Using Rounded Numbers
Guided Practice
5. Estimate 962 – 246 by rounding to the nearest hundred.
1000 – 200 = 800
6. Estimate 962 – 246 by rounding to the nearest ten.
960 – 250 = 710
7. Calculate 962 – 246 exactly.
Which of your two estimates was closer to the actual result?
962 – 246 = 716
Ex.6 gave a much closer estimate than Ex.5.
10
Solution follows…
Lesson
1.4.2
Using Rounded Numbers
Rounded Numbers Can Be Used to Check Work
Many times you’ll want to check your work without doing
the calculation all over again.
Rounding is a way to see if your answer is reasonable.
11
Lesson
1.4.2
Example
Using Rounded Numbers
3
Calculate 2343 + 5077.
Then check your work by rounding to the nearest hundred.
Solution
Actual sum:
2343
+ 5077
7420
Rounded sum:
These are rounded
to the nearest
hundred
2300
+ 5100
7400
The answer to the rounded sum is close to the answer to the
actual sum, so the answer to the actual sum is reasonable.
12
Solution follows…
Lesson
1.4.2
Example
Using Rounded Numbers
4
Martin is trying to solve 29.6 × 9.8. He gets the answer 192.08.
Check Martin’s answer by rounding to the nearest ten.
Solution
Rounded sum: 30 × 10 = 300
Martin’s answer is a long way from the rounded answer,
so it looks like his answer of 192.08 might be wrong.
In fact 29.6 × 9.8 = 290.08
This is much closer to the rounded estimate.
13
Solution follows…
Lesson
1.4.2
Using Rounded Numbers
Guided Practice
In Exercises 8–11, check the answers given by rounding
to the place value shown in parentheses.
Say whether the answers are reasonable.
8. 1818 + 700 = 3918 (hundred)
1800 + 700 = 2500, this isn’t close to the answer, so 3918 is unreasonable
9. 22 × 79 = 738 (ten)
20 × 80 = 1600, this isn’t close to the answer, so 738 is unreasonable
10. 490 + 770 = 1260 (hundred)
500 + 800 = 1300, this is close to the answer, so 1260 is reasonable
11. 642 – 369 = 273 (ten)
640 – 370 = 270, this is close to the answer, so 273 is reasonable
14
Solution follows…
Lesson
1.4.2
Using Rounded Numbers
Guided Practice
In Exercises 12–15, check the answers given by rounding
to the place value shown in parentheses.
Say whether the answers are reasonable.
12. 2.85 × 52.1 = 96.385 (one)
3 × 52 = 156, this isn’t close to the answer, so 96.385 is unreasonable
13. 68 × 47 = 5032 (ten)
70 × 50 = 3500, this isn’t close to the answer, so 5032 is unreasonable
14. 32.815 + 84.565 = 117.38 (ten)
30 + 80 = 110, this is close to the answer, so 117.38 is reasonable
15. 10.48 × 67.02 = 902.3696 (one)
10 × 67 = 670, this isn’t close to the answer, so 902.3696 is unreasonable
15
Solution follows…
Lesson
1.4.2
Using Rounded Numbers
Independent Practice
In Exercises 1–6, use rounding to check the answers given,
and say whether or not you think they are reasonable:
1. 6898 + 517 = 7415
Reasonable
3. 547 × 695 = 527,855
Unreasonable
5. 96 × 7973 = 526,218
Unreasonable
2. 97 × 411 = 13,677
Unreasonable
4. 74,861 – 2940 = 65,621
Unreasonable
6. 4362 – 1855 = 2507
Reasonable
16
Solution follows…
Lesson
1.4.2
Using Rounded Numbers
Independent Practice
7. Darnell is trying to work out the answer to 52 + 871.
Darnell thinks the answer is 923.
He asks Zoe and Enrique if his answer looks about right.
Zoe thinks the answer should be near to 1000.
Enrique thinks the answer should be about 920.
Why might Zoe and Enrique have gotten different answers?
Zoe rounded to the nearest hundred, Enrique rounded to the nearest ten.
17
Solution follows…
Lesson
1.4.2
Using Rounded Numbers
Independent Practice
8. In the Olympic 100 meters final, the first three athletes
finish the race in times of 9.89 seconds, 9.94 seconds,
and 9.99 seconds, to the nearest hundredth of a second.
Why would it not be a good idea to round these any further?
To the nearest tenth, the first two athletes both ran 9.9 seconds.
To the nearest second, the first three athletes all ran 10 seconds.
Both of these are misleading as they make it sound like the race
was a dead heat.
18
Solution follows…
Lesson
1.4.2
Using Rounded Numbers
Independent Practice
9. Town C is putting up a new sign showing its population.
The population is 45,691 people, but this figure is changing
all the time so the town decides to use a rounded figure.
What figure do you think they should use:
45,690, 45,700, 46,000, or 50,000?
Explain your answer.
The figure 45,690 could be out of date almost as soon as the exact
number, as the population could quickly rise or fall by 10. 50,000 is not
very close to the real population so that would not be a sensible choice.
Rounding to either the nearest hundred or the nearest thousand would
be sensible choices.
19
Solution follows…
Lesson
1.4.2
Using Rounded Numbers
Round Up
Remember that a rounded number is usually not the
same as the real figure. It only gives you a guide to
how big the real number is.
20