lesson 1.4.1
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Rounding Numbers. Lesson 1.4.1. Lesson 1.4.1. Rounding Numbers. California Standard: Mathematical Reasoning 2.1 Use estimation to verify the reasonableness of calculated results. What it means for you: You’ll learn about rounding exact figures to make them easier to work with. Key words: - PowerPoint PPT PresentationTRANSCRIPT
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Lesson 1.4.1Lesson 1.4.1
Rounding NumbersRounding Numbers
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Lesson
1.4.1Rounding NumbersRounding Numbers
California Standard:Mathematical Reasoning 2.1Use estimation to verify the reasonableness of calculated results.
What it means for you:You’ll learn about rounding exact figures to make them easier to work with.
Key words:• rounding• place value• digit• decimal• tenth• hundredth
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Lesson
1.4.1Rounding NumbersRounding Numbers
Rounding involves replacing one number with another number that’s easier to work with.
You’ll use rounded numbers in the next couple of Lessons to check and to estimate answers.
9.9 × 22 = 217.8
10 × 22 = 220
“(9.9 × 22) is about 220”
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Rounded Numbers Can Be Easier To Use
Lesson
1.4.1Rounding NumbersRounding Numbers
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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Example 1
Solution follows…
Lesson
1.4.1Rounding NumbersRounding Numbers
Round 18 and 43 to the nearest ten.
Look at the digit in the ones place:
SolutionYou need to decide whether to round up or down.
• If the ones digit is 5 or more, round up.• If the ones digit is 4 or less, round down.
Start with 18:8 is more than 5, so round up. 18 rounded up to the nearest ten is 20.
The digit in the ones place is 8.
Next, 43:3 is less than 4, so round down. 43 rounded down to the nearest ten is 40.
The digit in the ones place is 3.
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Lesson
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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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Guided Practice
Solution follows…
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1.4.1Rounding NumbersRounding Numbers
1. 36
3. 199
5. 267
7. 2994
In Exercises 1–8, round the numbers to the nearest ten.
40
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.
2. 84
4. 4006
6. 7161
8. 2995
200
2990
270
80
4010
3000
7160
420
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You Can Round to Different Place Values
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1.4.1Rounding NumbersRounding Numbers
You can round numbers to place values other than tens.
Write the number.
• 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.
Underline the digit in the position you want to round to.
35,926
35,926
35,926
36,000
21,337
21,337
21,337
21,300
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The digit to the right of the underline is 8.That’s greater than 5, so round up.
Example 2
Solution follows…
Lesson
1.4.1Rounding NumbersRounding Numbers
Round 25,281 to the nearest hundred.
Write the number and underline the hundreds digit:
Solution
You’re rounding to the nearest hundred, so that’s going to be either 25,200 or 25,300.
So 25,281 rounds up to 25,300, to the nearest hundred.
25,281
25,300
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Guided Practice
Solution follows…
Lesson
1.4.1Rounding NumbersRounding Numbers
10. 38,383
11. 5756
12. 8128
13. 40,079
In Exercises 10–13, round the numbers to the nearest hundred.
38,400
5800
8100
40,100
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Guided Practice
Solution follows…
Lesson
1.4.1Rounding NumbersRounding Numbers
14. 11,905
15. 8117
16. 2,599,582
17. 464,333
In Exercises 14–17, round the numbers to the nearest thousand.
12,000
8000
2,600,000
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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You Can Round Decimals Just Like Whole Numbers
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1.4.1Rounding NumbersRounding 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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Look to the right of the underline. The digit to the right is 5, so round up.
Example 3
Solution follows…
Lesson
1.4.1Rounding NumbersRounding Numbers
Round 0.0815 to the nearest thousandth.
Write the number and underline the thousandths digit:
Solution
The nearest thousandth will be either 0.081 or 0.082.
So 0.0815 rounds up to 0.082, to the nearest thousandth.
0.0815
0.082
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Guided Practice
Solution follows…
Lesson
1.4.1Rounding NumbersRounding Numbers
19. 28.0634
20. 2.247
21. 5.78
22. 6.892
In Exercises 19–22, round the numbers to the nearest tenth.
28.1
2.2
5.8
6.9
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Guided Practice
Solution follows…
Lesson
1.4.1Rounding NumbersRounding Numbers
23. 0.1066
24. 15.596
25. 409.4902
26. 7.734
In Exercises 23–26, round the numbers to the nearest hundredth.
0.11
15.60
409.49
7.73
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Guided Practice
Solution follows…
Lesson
1.4.1Rounding NumbersRounding Numbers
27. 9.46071
28. 1.7254
29. 5.226822
30. 3.1007
In Exercises 27–30, round the numbers to the nearest thousandth.
9.461
1.725
5.227
3.101
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Guided Practice
Solution follows…
Lesson
1.4.1Rounding NumbersRounding Numbers
32. How much money does Malik have to the nearest dollar?
33. How much money does Malik have to the nearest dime?
34. How much money does Malik have to the nearest quarter?
Exercises 32–34 are about Malik, who has $12.57 in his pocket.
1.61 km
$13.00
$12.60
$12.50
31. A distance of 1 mile is equal to 1.609344 km. Write this to the nearest hundredth of a kilometer.
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Independent Practice
Solution follows…
Lesson
1.4.1Rounding NumbersRounding Numbers
In Exercises 1–5, round the number 94,521.8375:
94,5001. to the nearest hundred
2. to the nearest hundredth
3. to the nearest thousandth
4. to the nearest thousand
5. to the nearest one
94,521.84
94,521.838
95,000
94,522
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Independent Practice
Solution follows…
Lesson
1.4.1Rounding NumbersRounding Numbers
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?
8. Mount Whitney is 14,505 feet high. Write this figure to the nearest hundred feet.
92 °F
14,500 feet
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Independent Practice
Solution follows…
Lesson
1.4.1Rounding NumbersRounding Numbers
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?
11. Jessica has $17.33. What is this amount to the nearest quarter?
12. A square inch is equal to 6.4516 cm². Convert 6 in² to cm², then round your answer to the nearest hundredth.
300,000,000 m/s
$17.25
38.71 cm2
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Lesson
1.4.1Rounding NumbersRounding Numbers
Round UpRound 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.