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Hello Natasha

Hello Natasha. This is Mrs. Bisanz , I am your teacher today. Our Lesson : Review of Decimals. Warm Up. Solve the following 5.81 + 6.32 = 12.13 3.91 + 0.1 = 4.01 Solve the following 9.11 – 3.9 = 5.21 921.8 – 865.329 = 56.471. Represent these in standard form

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Hello Natasha

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  1. Hello Natasha This is Mrs. Bisanz , I am your teacher today Our Lesson : Review of Decimals Confidential

  2. Warm Up Solve the following 5.81 + 6.32 = 12.13 3.91 + 0.1 = 4.01 Solve the following 9.11 – 3.9 = 5.21 921.8 – 865.329 = 56.471 Represent these in standard form 5.342 x 10 -4 = 0.0005342 2.812 x 106 = 2,812,000 Solve the following 3.61 ÷ 0.03 = 120.3334 15.012 ÷ 2.33 = 6.4429 Confidential

  3. Let us review what we have learnt in the last chapter Comparing and ordering Decimals Decimals are numbers, with a decimal point in it, like these: 1.5, 0.6, 3.14 their opposites, and zero Lets take an example 673,67.3, 6.73, 0.673 These three numbers above have the same three digits, in thesame order, yet they are all different Confidential

  4. 673,67.3, 6.73, 0.673 673 is a whole number, and would be read as Six hundred and seventy three The second number 67.3 contains a decimal point, marking the end of the whole number, and would be read as sixty seven point three. The third also contains a decimal point, and would be read as Six point seven three The last decimal 0.673 contains no whole number, and it begins with a zero before the decimal point. It would be read as zero point six seven three. Confidential

  5. -5.0 -4.0 -3.0 -2.0 3.0 4.0 5.0 0 1.0 2.0 -1.0 DECIMALS can be shown as points on a number line decimal on the left of zero are NEGATIVE. decimal on the right of zero are POSITIVE. Zero is the Origin. It is neither positive nor negative! Confidential

  6. -5.0 -4.0 -3.0 -2.0 3.0 4.0 5.0 0 1.0 2.0 -1.0 When we say words like more, less or equal to we compare the two numbers We can compare and order DECIMALS using the number line. smaller numbers bigger numbers Therefore... -3.2 < 1.1 Confidential

  7. We can also compare two Decimals by comparing the digits in each place value position Lets take an example : Compare 3.47 and 3.82 Align the numbers by their decimal points T O . T H Th 6 . 4 7 8 6 . 8 2 Start at the left and compare the digits in each place- value position . In the ones place , the digits are the same . In the tenths place , 4 < 8 , So, 6.478 < 6.82 Confidential

  8. Rounding and Estimation Rounding of Decimal numbers is done to get to the nearest approximate whole number. It is a kind of Estimation that we make. We use Rounding to estimate time, money, distances etc. Confidential

  9. We can round decimals to any place value. Find the place value you want (the "rounding digit") and look at the digit just to the right of it. If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it. If that digit is greater than or equal to five, add one to the rounding digit and drop all digits to the right of it. Confidential

  10. Let's take an example and understand Find the place value you want and look at the digit just to the right of it. Round 5,834 to the nearest thousandth 5,834 If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it. 8 is greater than 5 If that digit is greater than or equal to five, add one to the rounding digit and drop all digits to the right of it so we round this number as 6000 Confidential

  11. We can round the decimals to their nearest Fractions Lets round 83. 461 to the nearest tenth place 83.4 6 1 The place value number is 4 and number to its right is 6. 6 is greater than 5 so We round the number to 83.5 Confidential

  12. Now you try some questions 1.) 325.34 To the nearest Hundred 300 2.) 48,722 To the nearest Ten thousand 50,000 3.) 43.386 To the nearest Hundredth 43.39 4.) 60.584 To the nearest Tenth 60.6 Confidential

  13. Adding and Subtracting Decimals To add Decimals all we need to do is to align all decimal points in one line We start from the right end and the carry goes across the decimal point 62 . 72 +1 8 . 51 8 1 . 23 Confidential

  14. To subtract Decimals align all decimals so that the decimal points are in a vertical line. Add zeros to the right side of the decimal with fewer decimal places so that each decimal has the same number of decimal places. 89 . 30 - 45 . 11 44 . 19 We need to add one zero here to the right of decimal to make the decimal places equal Confidential

  15. Now you try some questions 1.) 438 + 13.16 = 451.16 2.) 621.581 + 4.212 = 625.793 3.) 179.8 - 120.852 = 300.652 4.) 5.8 - 5.5 = 0.3 Confidential

  16. Lets take a BREAK !! Confidential

  17. GameTime Click here to play a game Confidential

  18. Multiplying Decimals To multiply decimal numbers we first ignore the decimals and multiply as we multiply whole numbers Confidential

  19. Multiplying Decimals Starting on the right, multiply each digit in the top number by each digit in the bottom number just as you do with whole numbers Now add the products. Now place the decimal point in the answer by starting at the right and moving the number of places equal to the sum of the decimal places in both numbers multiplied. Confidential

  20. Multiplying Decimals Solving the same example 1.5 1 x 6.2 ___________ 3 0 2 9 0 6 x __________ 9 3 6 2 Just count the numbers / places from right to left in both the numbers to be multiplied ,and then add them and Insert the decimal after those many places. \ \ 1 2 \ 3 . Confidential

  21. Remember When we multiply two numbers with Same sign we get + And with Different sign we get - Confidential

  22. Lets take another example Multiply 3.77 x (- 2.8) 3 .7 7 x 2.8 __________ 3 0 1 6 7 5 4 _________ -10 .5 5 6 ____________ Remember Always count from right side to put the decimal Note the negative sign. Confidential

  23. Division with Decimals Steps for dividing by whole numbers 1) If the division problem is written across, copy the problem so that the first number is inside the division sign. If the problem is 35.2 ÷ 5 then write it as 5) 35.2 2) Place decimal point in the quotient directly above the decimal point in the dividend. 3) Now use the long division method as if there were no decimal points involved. Confidential

  24. Steps for dividing by decimal numbers • Write the first number inside the division sign • Change the divisor to a whole number by moving the decimal point to the right • Move the decimal point of the inside number ( dividend) • the same number of places to the right as you did of • the divisor. • Put the decimal point for your answer directly above the one in your inside number. • Divide the same way as you do with whole numbers Confidential

  25. Lets take an Example Change the divisor to a whole number by moving the decimal point to the right 3.33 ) 2 2.1 7 7 8 Move the decimal point of the inside number (dividend) the same number of places to the right as you did of the divisor. So we get… 333 ) 2 2 1 7. 7 8 Confidential

  26. Place a decimal point on top of the decimal point of the inside number and divide normally . 6 6 6 = Answer 333 ) 2 2 1 7. 7 8 1 9 9 8 2 1 9 7 1 9 9 8 1 9 9 8 1 9 9 8 0 Confidential

  27. You can also check your answer by multiplying the quotient with the divisor . If it is same as the dividend then your answer is correct . 0.452 ÷ 0.5 = 0.904 and 0.5 x 0.904 = 0.452 Confidential

  28. Lets try another Example with negative numbers -31.48 ÷ -4 7 . 87 -4 ) -3 1 .48 - 28 3 4 3 2 2 8 2 8 0 When we divide two numbers With the same sign we get + and with different signs we get – Confidential

  29. Now you try some questions • 8.41 ÷ 0.20 = 42.05 • 0.56 ÷ 0.12 = 4.6667 • 0.28 x 0.004 = 0.00112 • 34.01 x 1.01 = 34.3501 Confidential

  30. Scientific Notation • Scientific Notation is a way to express very large or • very small numbers. • It is most often used in “scientific” calculations • where the analysis must be very precise • Scientific notation has two parts • A non zero number between 1 and 10 • A power of 10 Confidential

  31. Scientific notation A number in scientific notation is written as the product of a number between 1 and 10 (integer or decimal ) and an integer power of 10 A number written in scientific notation has the form NX 10r where, N is between 1 and 10 r is an integer Confidential

  32. To Change from Standard form to Scientific notation Place the decimal point so that there is one non zero digit to the left of the decimal point Count the number of decimal places the decimal point has “ moved ” from the original number. This will be the exponent (power) of 10 Confidential

  33. Standard form to Scientific notation Lets take some Examples 10,000 = 1 x 104 65,000,000 = 6.5 x 107 The power of ten indicates how many places the decimal point has moved from the original number Confidential

  34. If the original number is less than 1, then the exponent is negative . If the original number is greater than 1, then the exponent is positive 579,300,000 = 5.793 x 108(Positive exponent) 0.000246 = 2.46 x 10-4 (Negative exponent) Confidential

  35. Now you try some • Write these in standard form or the scientific notation as required • 72,500 = 7.2x104 • 27,100,000 = 2.7x 107 • 5.56 x 109 = 5,560,000,000 • 1.976 x 10-4 = 0.0001976 Confidential

  36. Ben borrowed money from his three friends to buy • a camera. He promised to return the money every week. • If Ben paid $32.50 to each of his friends for five weeks • and still had $12.50 left. Find out how much money he • borrowed initially and how much money is left to be • returned to each. Total money borrowed $500 He has still to pay $4.1667 to each Confidential

  37. 2.) Cooper family went for their weekly shopping at the super market. They bought five coke cans for $1.30 each, two jars of peanut butter for $8.5 each and six packs of Buns for $2.80 each. What is the total bill rounded to the nearest dollar. $40 Confidential

  38. 3) Joseph’s math paper is given below. • You be the teacher and check his paper. Explain his • mistakes to him. • 3.14 + 6.89 = 9.93 • 6.3 x 2.1 = 132.3 • 2,34,871 = 2.34x105 rounded to the nearest thousand • 6.82 ÷ 0.02 = 300 rounded to the nearest hundred • Wrong 10.03 Carry not done • Wrong 13.23 Did not place the decimal correctly • Wrong 2.35x 105 when rounded it will become 2,35,000 • Correct Confidential

  39. You had a GREAT lesson today! Be sure to practice what you learned! Confidential

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