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Whole Numbers and Decimals: Understanding Place Value and Rounding

Learn how to use place value to understand whole numbers and decimals up to the hundred-thousandths place, and practice rounding both whole numbers and decimals.

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Whole Numbers and Decimals: Understanding Place Value and Rounding

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  1. Chapter 1 Whole Numbers and Decimals

  2. Whole Numbers and Decimals IWBAT use place value to understand whole numbers to the billions and decimals to the hundred-thousandths

  3. Place Value Chart

  4. Number Forms • Standard Form 6,035,479,518 36.00025 • Short Word Form 6 billion, 35 million, 479 thousand, 518 36 and 25 hundred-thousandths • Expanded Form 6,000,000,000+30,000,000+5,000,000+400,000+70,000+9,000+500+10+8 30+6+0.0002+0.00005

  5. Example • Write in 370,069,029 short word form and expanded form. 370 million, 69 thousand, 29 300,000,000+70,000,000+60,000+9,000+20+9 2. Write 41 hundredths standard form and expanded form. 0.41 0.4+0.01

  6. Find the Value of the Underlined Digit in Short Word Form • Look at place value section • Read the number and add section name 341,984,654 4 ten millions Ten Millions section

  7. Examples 12,144,754,984 2 billion 6 ten-thousandths 2) 144.0086 3) 23.00103 3 hundred-thousandths

  8. Practice Write the value of the underlined digit in short word form. 1) 5,040,123 2) 91,014,477 3) 0.062 4) 2.0002 Write each number in standard form. 1) 7 ten-thousandths 2) 9 billion, 9 million, 9 thousand, 9 Write in expanded form. 1) 20,065,289 2) 0.025

  9. Comparing and Ordering Decimals IWBAT compare and order decimals

  10. Comparing Decimals 8.499 ____ 8.5 Write vertically (Line up the decimal points). Add zeros if needed. 8.499 8.500 8 is the same on both sides 2) Compare whole numbers 3) Compare tenths place, then the hundredths, etc. 4 is less than 5 4) Use <, >, or = to compare 8.499 < 8.500

  11. Examples 1) 9.760 ____ 9.76 2) 6.35 ____ 6.357 9.760 9.760 6.350 6.357 9.760 = 9.76 6.35 < 6.357

  12. Ordering Decimals Follow the same steps as when comparing decimals Order 0.04, 0.93, 0.99, and 0.75 from least to greatest 0.04 0.93 0.99 0.75 Write vertically (Line up decimal points). Add zeros if needed 2) Compare place values 0.04, 0.75, 0.93, 0.99 3) Write in order from least to greatest using original numbers

  13. Examples Write in order from least to greatest. 1) 0.56; 0.021; 0.003; 0.9 2) 2; 0.15; 1.5; 2.7; 0.05; 17 0.560 0.021 0.003 0.900 2.00 0.15 1.50 2.70 0.05 17.00 0.003; 0.021; 0.56; 0.9 0.05; 0.15; 1.5; 2; 2.7; 17

  14. Practice Compare. Use <, >, or =. 1) 0.34____3.4 2) 1.5674____1.59 3) 0.7____0.71 4) 1____0.99 Write the numbers from least to greatest. 1) 2.05; 2.106; 4.5; 2.999 2) 57; 56.098; 50.897; 50.9; 57.47

  15. Problem Solving Skill: Exact or Estimated Data IWBAT determine whether data in a problem is exact or estimated

  16. Exact or Estimation Estimation Exact Uses very specific numbers • “about” • “near” • “close to” • “between” • “a little less/more than” • “around”

  17. Examples Students at Holy Angels took part in a project that reduced home energy usage. About half of the 305 students reported they had some success. Of these successful students, 95 use oil to heat their homes and the rest use electricity, gas or solar energy. 學生在聖潔的天使在一個項目，減少家庭能源的使用參加。大約有一半的305學生報告說，他們取得了一些成功。這些成功的學生中，有95利用石油來取暖，其餘用電，天然氣或太陽能。 How many students were involved in the project? 參與該項目的有多少學生？ 305 students (exact) 305名學生（具體） 2) How many homes that reduced energy used oil? 有多少家庭在減少能源使用的油？ 95 homes (exact) 95家（具體） 3) About what fraction of the students reported success? 什麼分數的學生報成功？ About half of the students (estimation) 大約有一半的學生（估計）

  18. Practice Richard’s family bought a new car for $17,659.99. The old car got less than 20 miles per gallon. They drove the old car more than 14,000 miles each year. They will drive the new car more than 15,000 miles each year. The new car gets over 30 miles per gallon. 理查德的家人買了一輛新車為$ 17,659.99 。老車之後不到20英里每加侖。他們開著一輛舊車，每年超過14000英里。他們將駕駛新車，每年超過15000英里。新車獲得超過30英里每加侖。 1) Which number is the exact number? 這數字是確切的數字？ 2) About how many gallons did they buy for the old car each year? 有多少加侖，每年他們是否買了一輛舊車？

  19. Addition Properties IWBAT use addition properties and mental math strategies.

  20. Addition Properties Identity Property + 0= Commutative Property = + + + +

  21. Associative Property ) ( + + = ( ) + +

  22. Distributive Property ( ) + = ( ) ) ( +

  23. Computing Mentally Choose a strategy and compute mentally 1) 28+74+32 Associative 28+32 + 74 60+74 134 2) 325+225 300+25+200+25 Break-Apart Strategy (Distributive) (300+200)+ (25+25) Associative and Commutative 500+50 550

  24. Examples 1) 88+64 Break-Apart 80+8+60+4 (80+60) +(8+4) 140+12 152 2) 27+81+13 Commutative 27+13+81 40+81 121

  25. Rounding Whole Numbers and Decimals IWBAT estimate and round whole numbers and decimals

  26. The Rounding Hill 4 or less, let it rest! (Stays the same) 5 or more, raise the score! (Round up)

  27. Examples Round 1,639 to the nearest hundred 1) Underline the #in the hundreds place 1,639 2) Highlight the # to the right 1,639 3) Round 1,600

  28. More Examples Round each number to the place underlined 2) 14.77 3) 123.06 4) 32.79 1) 65.45 65.45 14.77 123.06 32.79 60 33 14.8 120 Round 2,593.6781 to the place named 2) Nearest thousandth 1) Nearest hundred 2,593.6781 2,593.6781 2,600 2,593.678

  29. Practice Round each number to the place underlined. 1) 499.95 2) 17.3 3) 0.09 4) 123.106 5) 27.003 6) 1.146 Round 8,930.4692 to the place named. 1) Nearest one 2) Nearest hundredth

  30. Adding and Subtracting Whole Numbers and Decimals IWBAT add and subtract whole numbers and decimals

  31. Adding Always, ALWAYS, ALWAYS line up the decimals! Find 1.8+250.03+16.196 1) Line up decimals 1.8 250.03 16.196 + ________ 2) Place zeros in as placeholders 1.800 250.030 16.196 + ________ 268.026 3) Add

  32. Subtracting Line up the decimals and write in zeros as placeholders, if needed. Find 9.38 – 8.795 1. Line up decimals 9.38 8.795 - _____ 2. Write in zeros 9.380 8.795 - _____ 3. Subtract, regroup if needed 0.585 *Write in the leading zero

  33. Examples 1) 12 + 6.345 2) 78,839 – 51,860 3) 7.84 – 6.56 12.000 78,839 7.84 51,860 6.56 6.345 - ______ + ______ - _____ 26,979 1.28 18.345

  34. Estimating When estimating whole numbers, round to the nearest place next to a comma. When estimating decimals, round to the nearest tenth or whole number. 1) 12,600 + 2,835 2) 9.38 – 8.795 13,000 + 3,000 9.4 – 8.8 16,000

  35. Practice Estimate first. Then find the exact answer. • 12,375 + 450 + 1,055 • 158,200 – 119,678 • 15.70 + 186.59 + 3.00 • $55.99 – $9.45 • $9,576.00 + $3.89 + $339.50 • 100,000 – 49,696 • 129 – 5.063

  36. Find a Pattern IWBAT solve a problem by looking for a pattern.

  37. Guiding Principal #1 All mathematics are based on patterns. Greeting cards are arranged with 1 card in the first row, 3 in the second row, 6 in the third row, and 10 in the fourth row. If the pattern continues, how many cards are in the fifth row? 1) Write out important information or draw a picture 1 3 6 10 2) Use operations to find a pattern +2, +3, +4 3) Use the pattern to solve the problem +5; 15 cards

  38. Using the same information from the previous problem, find out how many cards are in the sixth and tenth row. Sixth Row +2, +3, +4, +5, +6 15 + 6 21 cards Tenth Row +2, +3, +4, +5, +6, +7, +8, +9, +10 21 + 7 + 8 + 9 + 10 55 cards

  39. Examples Clare designed a card with the following pattern below. Which letter will be in the 54th place? GOODLUCKGOODLUCKGOODLUCKGOODLUCK 1) Find the pattern 8 letters in each phrase 2) Use the information given and the pattern to solve 54 is not divisible by 8 but 48 is Count the remainder: 7 Answer: the letter U

  40. Practice • Sales at Jessica’s Gift Shop were about $10,000 in 1997, $11,000 in 1998, $13,000 in 1999, and $16,000 in 2000. If this pattern continues, approximately what will sales be in 2005? • Find the pattern and solve for the next number in the pattern: 1,1, 2, 3, 5, 8, 13, 21, 34, 55, _____

  41. Order of Operations IWBAT solve problems using operations in the correct order.

  42. Order of Operations *Multiplication/Division and Addition/Subtraction solved from LEFT to RIGHT

  43. Examples 1) 3 + 4 Parentheses? No Exponents? No 3 + 20 or ? Yes 23 + or - ? Yes 2) 17 – (3 +1) 2 Parentheses? Yes 17 – 4 2 Exponents? No 17 - 2 or ? Yes + or - ? Yes 15

  44. More Examples 3) 8 – 5 + 9 Parentheses? No Exponents? No or ? No + or - ? Yes 3 + 9 *Remember to work from left to right 12 Parentheses? No Exponents? No or ? Yes 4) 14 – 3 2 + 7 14 – 6 + 7 + or - ? Yes 8 + 7 *Remember to work from left to right 15

  45. Practice • 7 + 3 6 • (2 + 3) 9 • 15 – 96 12 • 12 2 – 12 • 16 (4 2) • 6 – 3 2 + 4 • 3 + (4 6) - 7

  46. Variables and Expressions IWBAT evaluate expressions with as many as three variables

  47. Vocabulary • Variable – a symbol that represents a number 1) Variables can represent ANY # 2) Variables are LOWERCASE letters • Expression – A number sentence WITHOUT an equal sign

  48. Evaluating Variable Expressions Evaluate for and 1) When there is a number in front of a variable, that means multiplication means 3 times 2) Substitute the given numbers for the specific variable (Always rewrite the problem!) 3) Use order of operations to solve 15 + 6 21

  49. Examples 1) for and 2(15) + (5 16 – 4 0) 30 + (80 – 0) 30 + 80 110

  50. Examples 2) for and 2(10) + 3(7) 20 + 21 41 3) When Lisa is years old, her sister is years old. If Lisa is 11, how old is her sister? 11 + 4 *Always label answers of word problems 15 years old

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