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Mastering Whole Numbers and Integers: Reading, Writing, and Rounding Techniques

Learn to read, write, and round whole numbers and integers with precision using place value concepts. Understand the significance of periods and commas in numbering systems.

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Mastering Whole Numbers and Integers: Reading, Writing, and Rounding Techniques

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  1. CHAPTER 1 Review of Whole Numbers and Integers

  2. Learning Outcomes 1-1 • Read whole numbers. • Write whole numbers. • Round whole numbers. • Read and round integers.

  3. Read whole numbers Section 1-1 Place Value and Our Number System • Our system of numbers, the decimal number system uses 10 symbols called digits: • 0,1, 2, 3, 4, 5, 6, 7, 8, and 9. • Place-value system: a number system that determines the value of a digit by its positionin a number.

  4. Read whole numbers HOW TO: Section 1-1 Place Value and Our Number System • Beginning with the ones place on the right, the digits are grouped with three digits in each group. • For example: 286,418,917 • Each group is called a period.

  5. Understanding place value HOW TO: Section 1-1 Place Value and Our Number System • Each period has a name • Every period has a ones place, a tens place, and a hundreds place. • In a number, the first period from the left mayhave fewer than three digits. • In many cultures, the periods are separated by commas.

  6. Understanding place value HOW TO: Section 1-1 Place Value and Our Number System • Identify the period name of the leftmost group. • Read the three digit number from left to right. • Name the period. • 4,693,107 would read four million six hundred ninety-three thousand one hundred seven

  7. Exceptions… Section 1-1 Place Value and Our Number System • Do not read or name a period that is all zeros. • 34,000,892 would read thirty-four million, eight hundred ninety-two. • Do not name the units period (892). 34, 000, 892

  8. When reading whole numbers, remember… HOW TO: Section 1-1 Place Value and Our Number System • The period name will be read at each comma. • Period names are read in the singular: • (“thousand” not “thousands”). • Hundreds is not a period name. • Do not say the word “and” when readingwhole numbers. • Calculator displays ordinarily do not show commas; insert them when writing the number.

  9. Write whole numbers 1-1-2 Section 1-1 Place Value and Our Number System • Begin recording digits from left to right. • Insert a comma at each period name. • Every period after the first period must havethree digits. • Insert zeros as necessary.

  10. 8, million 903, thousand422 (units) An Example… Section 1-1 Place Value and Our Number System Eight million, nine hundred three thousand, four hundred twenty-two… …is written 8,903,422.

  11. Round whole numbers 1-1-3 Section 1-1 Place Value and Our Number System • Rounding to a specificplace: • Identify the place. • “nearest hundred”, for example. • Look at the digit immediately to the right. • Is it 5 or higher? Round up. • Is it 4 or lower? Specified digit stays the same. • All digits to the right of the specified placebecome zeros.

  12. Examples… Section 1-1 Place Value and Our Number System Round to the nearest hundred: 4,856 10,527 234,567 8,648,078 4,900 10,500 234,600 8,648,100

  13. Read and round integers 1-1-4 Section 1-1 Place Value and Our Number System • In the business world we sometimes want to express numbers that are smaller than 0. • These are referred to as negative numbers. • When the set of whole numbers is expanded to include negative numbers, this set is called theset of integers.

  14. Read and round integers HOW TO: Section 1-1 Place Value and Our Number System • When reading integers: • The rules are the same as for reading whole numbers. • State the word negative or minus to read a number less than zero. • When rounding integers: • The rules are the same as for roundingwhole numbers.

  15. An Example… Section 1-1 Place Value and Our Number System Read the number for the U.S. national debt: –$18,936,042,802,503 Negative eighteen trillion, nine hundred thirty-six billion, forty-two million, eight hundred two thousand, five hundred three dollars.

  16. –$18,936,042,802,503 The trillions digit is 8. –$18,936,042,802,503 The digit to the right is 9. An Example… Section 1-1 Place Value and Our Number System Round the previous exampleto the nearest trillion: 9 is more than 5, so increase the 8, by 1, to get 9.Replace all digits to the right of 2 with zeros. –$19,000,000,000,000 The answer is –$19 trillion.

  17. Learning Outcomes 1-2 • Add and subtract wholenumbers. • Add and subtract integers. • Multiply integers. • Divide integers. • Apply the standard order of operations to a series of operations.

  18. Key Terms… Section 1-2 Place Value and Our Number System • Addends • The numbers being added. • Sum or total • The answer or result of addition.

  19. Add and subtract whole numbers 1-2-1 Section 1-2 Operations With Whole Numbers and Integers • To add whole numbers, write the numbers in a vertical column, aligning digits according to their place values. • Beginning with the ones column, add the place digits. • Add, if necessary, to the tens column. • Repeat the operation, adding to the hundreds column, if necessary, until you have reached the farthest column of digits to the left.

  20. An Example… Section 1-2 Operations with Whole Numbers and Integers Add 1 1 2 2 • Add the ones column. • Place 8 at the bottom ofthe ones column. • Carry the 2 to the tens column. • Place the 4 in the tens column. • Carry the 2. • Finish the operation. 6 4 9 4 8 Answer: 64,948

  21. Estimating HOW TO: Section 1-2 Operations with Whole Numbers and Integers • Estimate: to find a reasonable approximateanswer for a calculation. • Use estimating as a quick tool when an exactnumber is not required. • Round whole numbers to the place desiredfor an estimate.

  22. Sales for last week’sconcession stand. Monday: $219 Tuesday: $877 Wednesday: $455 Thursday: $614 Friday: $980 An Example… Section 1-2 Operations with Whole Numbers and Integers What was the week’s total to the nearest hundred? =$3,200 $200 + $900 + $500 + $600 + $1000

  23. Subtract whole numbers HOW TO: Section 1-2 Operations with Whole Numbers and Integers • When subtracting whole numbers, the order ofthe numbers is important. • Therefore, subtraction is not commutative. 9 – 4 ≠ 4 – 9 • Grouping in subtraction is important. • Subtraction is not associative. (8 – 3) – 1 = 5 – 1 = 4 but 8 – (3 – 1) = 8 – 2 = 6 4 ≠ 6

  24. Key Terms… Section 1-2 Operations with Whole Numbers and Integers • Minuend • The beginning amount or number thata second number is being subtracted from. • Subtrahend • The number being subtracted. • Difference • The answer or result of subtracting. • Borrow • Regroup digits in the minuend by borrowing 1from the digit to the left of the specified place,and adding 10 to the specified place.

  25. 1 2 9 3 An Example… Section 1-2 Operations with Whole Numbers and Integers • Borrow 1 from the ten column, add 10 to the ones column. • Subtract 8 from 13. • Borrow 1 from the hundreds column,add 10 to the tens column. • Subtract 9 from 18. • Borrow 1 from the thousands column. • Subtract 5 from 11. Subtract 11 1 1 18 8 18 6 9 5 Answer: 695

  26. Using rounding in subtraction HOW TO: Section 1-2 Operations with Whole Numbers and Integers • Subtract 128 from 1,345 by rounding each number to the nearest hundred to estimatethe difference. • 128 would become 100. • 1,345 would become 1,300. • The estimated difference would be 1,200.

  27. Add and subtract integers 1-2-2 Section 1-2 Operations with Whole Numbers and Integers • To add two negative integers, add the numbers without regard to the signs. • Assign a negative to the sum. Last year Murphy’s Used Car Co. lost $23,000. This year they lost another $16,000. What is the total loss? –$23,000 + (–$16,000) = –$39,000 The two-year loss is –$39,000.

  28. Add and subtract integers HOW TO: Section 1-2 Operations with Whole Numbers and Integers • To add a positive and a negative integer, subtract the numbers without regard to the signs. • Look at the numbers without the signs. • Choose the larger of these numbers; • Assign the sum the sign of the larger number.

  29. An Example… Section 1-2 Operations with Whole Numbers and Integers Jeremy has a bank balance of $47,then writes a check for $89. What is the new balance,including a $30 overdraft fee? $47 + (–$89) = –$42 –$42 + (–$30) = –$72 The final balance is –$72.

  30. Multiply integers HOW TO: Section 1-2 Operations with Whole Numbers and Integers • Numbers can be multiplied in any order without affecting the result • Commutative property of multiplication. 8 × 12 = 12 × 8 96 = 96

  31. Key Terms… Section 1-2 Operations with Whole Numbers and Integers • Multiplicand • The number being multiplied. • Multiplier • The number multiplied by. • Factor • Each number involved in multiplication.

  32. Key Terms… Section 1-2 Operations with Whole Numbers and Integers • Product • The answer or result of multiplication. • Partial product • The product of one digit of the multiplier andthe entire multiplicand.

  33. Multiply Multiplicand 7 9 Multiplier x 2 3 Partial product 2 3 7 Partial product 1 5 8 _ PRODUCT 1 8 1 7 An Example… Section 1-2 Operations with Whole Numbers and Integers 1

  34. Examples to try without a calculator… Section 1-2 Operations with Whole Numbers and Integers 418 × 107 = ? Answer: 44,726 88 × 120 = ? Answer: 10,560 348 × 27 = ? Answer: 9,396

  35. Multiply integers 1-2-3 Section 1-2 Operations with Whole Numbers and Integers • To multiply a negative and a positive integer, multiply the two integers without regard tothe signs. • Assign a negative sign to the product. What is the total loss generated fromselling 87 frames each for $2 below cost? 87 × (−$2) = −$174 The total loss is −$174.

  36. Multiply integers HOW TO: Section 1-2 Operations with Whole Numbers and Integers • To multiply two negative or two positive integers, multiply the two integers without regard to the signs. • The product is positive. What is the product of (−16)(−3)? 16 × 3 = 48 The product is positive and is 48.

  37. Divide integers 1-2-4 Section 1-2 Operations with Whole Numbers and Integers • Division is used to find the number of equal parts into which a whole quantity can be separated. A $40 tip is shared equally among 5 servers. How much does each server receive? $40 ÷ 5 servers = $8 each.

  38. Key Terms… Section 1-2 Operations with Whole Numbers and Integers • Dividend • The number being divided or the total quantity. • Divisor • The number to divide by. • Quotient • The answer or result of the operation. • Whole-number part of the quotient • The quotient without regard to its remainder.

  39. Key Terms… Section 1-2 Operations with Whole Numbers and Integers • Remainder of quotient • A number that is smaller than the divisor thatremains after division is complete. • Partial dividend • The part of the dividend that is being consideredat a given step of the process. • Partial quotient • The quotient of the partial dividend and the divisor.

  40. Remainders HOW TO: Section 1-2 Operations with Whole Numbers and Integers • There will be a remainder if an amount is toosmall to be further divided by the divisor. • For example: 152 ÷ 3 = 50 R 2 • That amount may be expressed as… • A remainder (R 2). • A fraction. • A decimal.

  41. MORE Divide integers HOW TO: Section 1-2 Operations with Whole Numbers and Integers STEP 1 Beginning with its leftmost digit, identifythe first group of digits of the dividendthat is larger than or equal to the divisor. 1235 ÷ 5 = ? • Is it 1?No. • Is it 12?Yes. • 5 goes into 12 two times.Place the 2 above the 2 in the dividend.

  42. MORE Divide integers HOW TO: Section 1-2 Operations with Whole Numbers and Integers STEP 2 Multiply 2 by the divisor. Place 10 underthe 12 and subtract. The result is 2. 1235 ÷ 5 = ? STEP 3 Bring down the following digit whichis 3, and divide 5 into 23. STEP 4 The result is 4. Place the 4 directlyabove the 3 in the dividend.

  43. Divide integers HOW TO: Section 1-2 Operations with Whole Numbers and Integers STEP 5 Multiply 4 by the divisor. Place 20 underthe 23 and subtract. The result is 3. 1235 ÷ 5 = ? STEP 6 Bring down the last digit, which is 5,and divide 5 into 35. The result is 7. STEP 7 Place 7 directly above the 5. Youhave finished and the answer is 247.

  44. Examples to try without a calculator… Section 1-2 Operations with Whole Numbers and Integers Adams-Duke Realty Company estimates thatits losses for the year will be $36,000,000. What is the average loss per month? Answer: −$3,000,000 Divide the following: 63,500,000 ÷ 1,000 (mentally eliminate the ending zeros from both numbers) Answer: 63,500

  45. Apply the standard orderof operations to a series of operations 1-2-5 Section 1-2 Operations with Whole Numbers and Integers STEP 1 Perform all operations that are inside grouping symbols, such as parentheses. STEP 2 Perform all multiplications and divisions as they appear from left to right. STEP 3 Perform all additions and subtractions as theyappear from left to right.

  46. Examples to try… Section 1-2 Operations with Whole Numbers and Integers 15 – (4 + 7) = ? Answer: 4 (75 + 50 + 35 + 90) ÷ 5 = ? Answer: 50 45 − 4 × 9 = ? Answer: 9

  47. Exercise Set

  48. EXERCISE SET 2. An automobile manufacturer claims to create more than twenty thousand direct jobs. Use digits to write this number. 20,000

  49. EXERCISE SET 4. By its own claim, HFS, Inc., is the world’s largest hotel franchising organization. It claims to have five thousand, four hundred hotels with four hundred ninety-five thousand rooms in over seventy countries, and more than twenty percent of the franchises are minority-owned. Use digits to write each of the numbers. 5,400 hotels 495,000 rooms 70 countries 20 percent minority- owned

  50. EXERCISE SET Write the word name for the number. 6. LVMH had a gain of $30,860,000,000 in a recent year. Show how you would read this number. Thirty billion, eight hundred sixty million dollars 8. Delta Airlines had an annual loss of −$8,922,000,000 in a recent year. Show how you would read this number. Negative eight billion, nine hundred twenty-two million dollars

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