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Lesson 1.4.1

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:

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Lesson 1.4.1

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  1. Rounding Numbers Lesson 1.4.1

  2. 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: • rounding • place value • digit • decimal • tenth • hundredth

  3. 9.9 × 22 = 217.8 10 × 22 = 220 “(9.9 × 22) is about 220” Lesson 1.4.1 Rounding 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.

  4. 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.

  5. Lesson 1.4.1 Rounding Numbers Example 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. The digit in the ones place is 3. Next, 43: 3 is less than 4, so round down. 43 rounded down to the nearest ten is 40. Solution follows…

  6. 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

  7. Lesson 1.4.1 Rounding Numbers Guided Practice In Exercises 1–8, round the numbers to the nearest ten. 1. 36 3. 199 5. 267 7. 2994 2. 84 4. 4006 6. 7161 8. 2995 40 80 4010 200 7160 270 2990 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 Solution follows…

  8. 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. 35,926 21,337 Underline the digit in the position you want to round to. 35,926 21,337 • If the digit to the right of the underlined digit is 5 or more, round up. 35,926 21,337 36,000 21,300 • If the digit to the right of the underlined digit is 4 or less, round down.

  9. Lesson 1.4.1 Rounding Numbers Example 2 Round 25,281 to the nearest hundred. Solution 25,281 Write the number and underline the hundreds digit: 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. 25,300 That’s greater than 5, so round up. So 25,281 rounds up to 25,300, to the nearest hundred. Solution follows…

  10. Lesson 1.4.1 Rounding Numbers Guided Practice In Exercises 10–13, round the numbers to the nearest hundred. 10. 38,383 11. 5756 12. 8128 13. 40,079 38,400 5800 8100 40,100 Solution follows…

  11. Lesson 1.4.1 Rounding Numbers Guided Practice In Exercises 14–17, round the numbers to the nearest thousand. 14. 11,905 15. 8117 16. 2,599,582 17. 464,333 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 Solution follows…

  12. 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

  13. Lesson 1.4.1 Rounding Numbers Example 3 Round 0.0815 to the nearest thousandth. Solution 0.0815 Write the number and underline the thousandths digit: The nearest thousandth will be either 0.081 or 0.082. Look to the right of the underline. 0.082 The digit to the right is 5, so round up. So 0.0815 rounds up to 0.082, to the nearest thousandth. Solution follows…

  14. Lesson 1.4.1 Rounding Numbers Guided Practice In Exercises 19–22, round the numbers to the nearest tenth. 19. 28.0634 20. 2.247 21. 5.78 22. 6.892 28.1 2.2 5.8 6.9 Solution follows…

  15. Lesson 1.4.1 Rounding Numbers Guided Practice In Exercises 23–26, round the numbers to the nearest hundredth. 23. 0.1066 24. 15.596 25. 409.4902 26. 7.734 0.11 15.60 409.49 7.73 Solution follows…

  16. Lesson 1.4.1 Rounding Numbers Guided Practice In Exercises 27–30, round the numbers to the nearest thousandth. 27. 9.46071 28. 1.7254 29. 5.226822 30. 3.1007 9.461 1.725 5.227 3.101 Solution follows…

  17. 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? 33. How much money does Malik have to the nearest dime? 34. How much money does Malik have to the nearest quarter? $13.00 $12.60 $12.50 Solution follows…

  18. Lesson 1.4.1 Rounding Numbers Independent Practice In Exercises 1–5, round the number 94,521.8375: 1. to the nearest hundred 2. to the nearest hundredth 3. to the nearest thousandth 4. to the nearest thousand 5. to the nearest one 94,500 94,521.84 94,521.838 95,000 94,522 Solution follows…

  19. 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 Solution follows…

  20. 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 Solution follows…

  21. 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 answerwhen 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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