1 Lesson 1.4.1 Rounding Numbers. 2 Lesson 1.4.1 Rounding Numbers California Standard: Mathematical...

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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


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


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


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


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…

Lesson


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

Lesson


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


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


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


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

Lesson


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


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


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


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


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


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


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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Solution follows…

Lesson


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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Solution follows…

Lesson


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


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.

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