ࡱ> 9;8@ b[bjbj ^uu%000040tJh1 2 2 2 2m3m3m3JJJJJJJ$KRM\CJim3K3"m3m3m3CJ 2 2+J888m3 2 2J8m3J88G|!I 2\1 4㖫03mHAIJ0JHVN7VN$!IVN!I m3m38m3m3m3m3m3CJCJ.0w80DECIMALS INSTRUCTION SHEET Addition and Subtraction Step 1 Line up the decimal points. Step 2 Put in zeros as placeholders, if necessary. Step 3 Add or subtract. Example #1: Example #2: Step 1- Line up the decimal points. 2.345 + 1.5 ( 2.345 14 5.6 ( 14. + 1.5__ - 5.6 Step 2 - Put in zeros as placeholders. 2.345 14.0 + 1.500 - 5.6 Step 3 - Add or subtract. 2.345 14.0 + 1.500 - 5.6 3.845 8.4 Multiplication Step 1 Multiply the numbers ignoring the decimals. Step 2 Add the number of decimal digits in the original numbers. Step 3 Move the decimal the same number of places to the left in your answer. Example: 3.2 x 0.41 = Step 1 - Multiply ignoring the decimal points. 32 X 41___ 32 128  1312 Step 2 - Add the number of decimal digits in each of the original numbers: 3.2 has one decimal digit, and 0.41 has two decimal digits. Therefore, the answer will have a total of three decimal digits. Step 3 - Move the decimal the same number of places to the left in your answer. 1312 will become 1.312 ( three places Division Step 1 Shift the decimal to the right to make the divisor (outside number) a whole number. Step 2 Move the decimal of the dividend (inside number) the same number of places to the right as the divisor. Add zeros, if needed. Step 3 Place the decimal point in your answer directly above the new decimal point in the dividend. Divide. Example: Step 1 - Shift the decimal to the right to make the divisor (.45) a whole number. .45  EMBED Equation.3  becomes 45 EMBED Equation.3  EMBED Equation.3  ( 2 places Step 2 - Move the decimal of the dividend (36) the same number of places to the right. Add zeros if needed. 45 EMBED Equation.3  becomes 45 EMBED Equation.3  Step 3 - Place the decimal point in your answer directly above the new decimal point in the dividend. Divide. 45 EMBED Equation.3  45 EMBED Equation.3  360 00 Rounding Step 1 Determine the place to which the number is to be rounded. Indicate it by circling it or underlining it. Step 2 If the digit to the right of the number to be rounded is less than 5, replace it and all the digits to the right of it by zeros. If the digit to the right of the underlined number is 5 or higher, increase the underlined number by 1 and replace all numbers to the right by zeros. If the zeros are decimal digits, you may eliminate them. Place value chart Ten thousandsThousandsHundredsTensOnesDecimal PointTenthsHundredthsThousandthsTen ThousandthsHundred Thousandths10,000 1,000 100 10 1 . .1 .01 .001  .0001.00001 Example #1: Round 2.832 to the nearest hundredth. Step 1 Determine the place to which the number is to be rounded. 2.832 Step 2 If the digit to the right of the number to be rounded is less than 5, replace it and all the digits to the right of it by zeros. If the digit to the right of the underlined number is 5 or higher, increase the underlined number by 1 and replace all numbers to the right by zeros. If the zeros are decimal digits, you may eliminate them. 2.832 = 2.830 = 2.83 Example #2: Round 43.5648 to the nearest thousandth. 43.5648 = 43.5650 = 43.565 Example #3: Round 5,897,000 to the nearest hundred thousand. 5,897,000 = 5,900,000 Decimal Fractions To convert a number from fraction form to decimal form, simply divide the numerator (the top number) by the denominator (the bottom number) of the fraction. Example: 5 8 8 EMBED Equation.3  ( Add as many zeros as needed. 48 20 16 40 40 0 Converting a decimal to a fraction To change a decimal to a fraction, determine the place value of the last number in the decimal. This becomes the denominator. The decimal number becomes the numerator. Then reduce your answer. Example: .625 - the 5 is in the thousandths column, therefore, .625 =  EMBED Equation.3  = reduces to  EMBED Equation.3  (Hint: Your denominator will have the same number of zeros as there are decimal digits in the decimal number you started with - .625 has three decimal digits so the denominator will have three zeros) Order of Operations When more than one operation is to be performed in a problem, a specific order for solving the problem must be followed. 1. Solve anything in parentheses first 2. Solve anything with an exponent (52 the 2 is the exponent; it means the number times itself that many times, so 52 = 5 5 = 25) 3. Multiply/Divide from left to right in order 4. Add/Subtract from left to right in order 4.2 + 6(3.8 1.1) 4.5 +.09 = 4.2 + 6(2.7) 4.5 +.09 = 4.2 + 16.2 4.5 +.09 = 4.2 + 3.6 + .09 = 7.89 DECIMALS PRACTICE SHEET A. Put the following fractions into decimal form. 1. 1/16 4. 5/32 7. 1[! 2. 11/8 5. 2 11/32 8. 2 T! 3. 2 ^! 6. 9/10 9. 12/15 B. Write each of the following decimals in fraction form. 1. 0.5 4. 0.1875 7. 0.1125 2. 0.375 5. 0.88 8. 0.75 3. 0.875 6. 0.975 9. 0.6225 C. Add or subtract as shown. 1. 4.39 + 18.8 = 9. $7.52 + $11.77 = 2. 3.68 1.74 = 10. 104.06 15.80 = 3. 264.3 + 12.804 = 11. 165.4 + 73.61 = 4. 116.7 32.82 = 12. 14 6.52 = 5. 3 + 1.08 = 13. 45.3 15.273 = 6. 19.70 + 62.598 = 14. 0.42 + 1.452 + 31.8 = 7. 21 + 3.814 = 15. 3.045 1[! = 8. 90  25.397 = 16. 7.81  3.685 = D. Calculate the following equations. 1. 8.2 6.3 = 6. 24.71 6.4 = 2. 6.78 3.32 = 7. 8.85 2.79 = 3. 1.4 0.6 = 8. 75.82 6.71 = 4. 0.004 0.02 = 9. 0.2 0.6 0.9 = 5. 6.02 3.3 = 10. 0.6 3.15 2.04 = E. Calculate the following problems, then round to the place indicated. 1. 1.26 4.5 = 6. 0.424 0.5 = (tenth) (hundredth) 2. 3.834 2.13 = 7. 0.007 0.03 = (tenth) (two decimal digits) 3. 0.04 0.076 = 8. 18.76 4.05 = (three decimal places) (one decimal place) 4. 17.8 6.4 = 9. 0.08 0.053 = (ten thousandths) (tenth) 5. 17.6 0.082 = 10. 1 0.62 = (thousandth) (hundredth) F. Solve the problems below following the rules for order of operations. 1. 12.2 9.4 2.68 + 1.6 0.8 = 5. 2.4 + (0.5)2 0.35 = 2. 9.6 + 3.6 (0.4)2 = 6. (1.1)3 + 8.6 2.15 0.086 = 3. (0.76 + 4.24) 0.25 + 8.6 = 7. (0.6)3 + (7 6.3) 0.07 = 4. (32.16 32.02)2 (2.24 + 1.76) = 8. (0.6)3 + (2.4)2 + 18.6 3.05 + 4.8 = G. Solve the word problems below. 1. John needed to hang a picture he bought. He drilled a hole \! inch in diameter. The nail he intended to use was 0.5 inch in diameter. Was the hole too small or too large? By how much? 2. Elenas Hair Salon uses an average of 5.4 quarts of shampoo per month. 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