Transcript Rounding Numbers

Rounding Numbers
Lesson 1.4.1
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Lesson
1.4.1
Rounding Numbers
California Standard:
What it means for you:
Mathematical Reasoning 2.1
Use estimation to verify the
reasonableness of calculated
results.
You’ll learn about rounding exact
figures to make them easier to
work with.
Key words:
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•
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•
rounding
place value
digit
decimal
tenth
hundredth
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Lesson
1.4.1
Rounding Numbers
Rounding involves replacing one number with another
number that’s easier to work with.
9.9 × 22 = 217.8
10 × 22 = 220
“(9.9 × 22) is about 220”
You’ll use rounded numbers in the next couple of
Lessons to check and to estimate answers.
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Lesson
1.4.1
Rounding Numbers
Rounded Numbers Can Be Easier To Use
Suppose you wanted to find 18 × 43, but had lost your
calculator. You could find an answer close to 18 × 43
by rounding to the nearest ten.
“Rounding to the nearest ten” means replacing a
number with the nearest multiple of 10.
Replacing a number with a higher number is called
rounding up.
Replacing a number with a lower number is called
rounding down.
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Lesson
1.4.1
Example
Rounding Numbers
1
Round 18 and 43 to the nearest ten.
Solution
You need to decide whether to round up or down.
Look at the digit in the ones place:
• If the ones digit is 5 or more, round up.
• If the ones digit is 4 or less, round down.
Start with 18:
The digit in the ones place is 8.
8 is more than 5, so round up.
18 rounded up to the nearest ten is 20.
Next, 43:
The digit in the ones place is 3.
3 is less than 4, so round down.
43 rounded down to the nearest ten is 40.
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Solution follows…
Lesson
1.4.1
Rounding Numbers
By rounding, you can replace 18 × 43 with 20 × 40.
This is much easier to solve:
20 × 40 = 800
800 is fairly close to the real answer:
18 × 43 = 774
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Lesson
1.4.1
Rounding Numbers
Guided Practice
In Exercises 1–8, round the numbers to the nearest ten.
1. 36
40
2. 84
80
3. 199
200
4. 4006
4010
5. 267
270
6. 7161
7160
7. 2994
2990
8. 2995
3000
9. During a science experiment, a group of students observed
that there were 415 ants in a colony.
Round this amount to the nearest ten. 420
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Solution follows…
Lesson
1.4.1
Rounding Numbers
You Can Round to Different Place Values
You can round numbers to place values other than tens.
Write the number.
Underline the digit in the position
you want to round to.
• If the digit to the right of the underlined
digit is 5 or more, round up.
• If the digit to the right of the underlined
digit is 4 or less, round down.
35,926
21,337
35,926
21,337
35,926
21,337
36,000
21,300
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Lesson
1.4.1
Example
Rounding Numbers
2
Round 25,281 to the nearest hundred.
Solution
Write the number and underline the hundreds digit:
25,281
You’re rounding to the nearest hundred,
so that’s going to be either 25,200 or 25,300.
The digit to the right of the underline is 8.
That’s greater than 5, so round up.
25,300
So 25,281 rounds up to 25,300, to the nearest hundred.
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Solution follows…
Lesson
1.4.1
Rounding Numbers
Guided Practice
In Exercises 10–13, round the numbers to the
nearest hundred.
10. 38,383
38,400
11. 5756
5800
12. 8128
8100
13. 40,079
40,100
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Solution follows…
Lesson
1.4.1
Rounding Numbers
Guided Practice
In Exercises 14–17, round the numbers to the
nearest thousand.
14. 11,905
12,000
15. 8117
8000
16. 2,599,582
2,600,000
17. 464,333
464,000
18. Clara lives in a city that has a population of 82,458 people.
Write this population rounded to the nearest thousand.
82,000
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Solution follows…
Lesson
1.4.1
Rounding Numbers
You Can Round Decimals Just Like Whole Numbers
You round decimals in the same way as whole numbers.
Instead of rounding to the nearest ten,
hundred, and so on, you round to the nearest
one, tenth, hundredth, or any other number of
decimal places.
0.746
0.746
0.75
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Lesson
1.4.1
Example
Rounding Numbers
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Round 0.0815 to the nearest thousandth.
Solution
Write the number and underline the thousandths digit: 0.0815
The nearest thousandth will be either
0.081 or 0.082.
Look to the right of the underline.
The digit to the right is 5, so round up.
0.082
So 0.0815 rounds up to 0.082, to the nearest thousandth.
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Solution follows…
Lesson
1.4.1
Rounding Numbers
Guided Practice
In Exercises 19–22, round the numbers
to the nearest tenth.
19. 28.0634
28.1
20. 2.247
2.2
21. 5.78
5.8
22. 6.892
6.9
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Solution follows…
Lesson
1.4.1
Rounding Numbers
Guided Practice
In Exercises 23–26, round the numbers
to the nearest hundredth.
23. 0.1066
0.11
24. 15.596
15.60
25. 409.4902
409.49
26. 7.734
7.73
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Solution follows…
Lesson
1.4.1
Rounding Numbers
Guided Practice
In Exercises 27–30, round the numbers
to the nearest thousandth.
27. 9.46071
9.461
28. 1.7254
1.725
29. 5.226822
5.227
30. 3.1007
3.101
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Solution follows…
Lesson
1.4.1
Rounding Numbers
Guided Practice
31. A distance of 1 mile is equal to 1.609344 km.
Write this to the nearest hundredth of a kilometer.
1.61 km
Exercises 32–34 are about Malik, who has $12.57
in his pocket.
32. How much money does Malik have to the nearest dollar?
$13.00
33. How much money does Malik have to the nearest dime?
$12.60
34. How much money does Malik have to the nearest quarter?
$12.50
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Solution follows…
Lesson
1.4.1
Rounding Numbers
Independent Practice
In Exercises 1–5, round the number 94,521.8375:
1. to the nearest hundred
94,500
2. to the nearest hundredth
94,521.84
3. to the nearest thousandth
94,521.838
4. to the nearest thousand
95,000
5. to the nearest one
94,522
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Solution follows…
Lesson
1.4.1
Rounding Numbers
Independent Practice
6. The number 3478 was rounded to 3480.
To what place value was the number rounded?
Tens
7. Raul’s thermometer shows that the temperature is 91.5 °F.
What is the temperature to the nearest degree? 92 °F
8. Mount Whitney is 14,505 feet high.
Write this figure to the nearest hundred feet.
14,500 feet
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Solution follows…
Lesson
1.4.1
Rounding Numbers
Independent Practice
9.
The average distance from the Earth to the Moon
is 238,857 miles.
What is this distance to the nearest thousand miles?
239,000 miles
10. The speed of light is 299,792,458 meters per second.
What is this to the nearest million m/s? 300,000,000 m/s
11. Jessica has $17.33.
What is this amount to the nearest quarter?
$17.25
12. A square inch is equal to 6.4516 cm². Convert 6 in² to cm²,
then round your answer to the nearest hundredth. 38.71 cm2
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Solution follows…
Lesson
1.4.1
Rounding Numbers
Round Up
Rounding numbers makes them easier
to deal with. You can use rounded numbers
to quickly find an approximate answer
when you don’t need an exact one.
They can also help you to check your work,
by letting you get an idea of how big your
answer should be.
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