5.1 – Introduction to Decimals Decimal Notation and Writing Decimals. 2, 4 5 7, 8 3 2 . 8 3 0 9 4 tens ones millions tenths hundreds thousands hundredths thousandths ten-thousands ten-thousandths hundred-thousands hundred-thousandths

5.1 – Introduction to Decimals 4. – Solving Equations with Fractions Decimal Notation and Writing Decimals. Write each number in words. 0.06 Six hundredths -200.073 Negative two hundred and seventy-three thousandths 0.0829 Eight hundred twenty-nine ten-thousandths 87.31 Eighty-seven and thirty-one hundredths 52.1085 Fifty-two and one thousand eighty-five ten-thousandths 1493.62 One thousand four hundred ninety-three and sixty-two hundredths

5.1 – Introduction to Decimals 4. – Solving Equations with Fractions Decimal Notation and Writing Decimals. Write each decimal in standard form. Five hundred and ninety-six hundredths 500.96 Thirty-nine and forty-two thousandths 39.042 Negative eight hundred seven and twenty-five ten-thousandths -807.0025 Twelve thousand thirty-seven and two hundred ninety-eight thousandths 12,037.298

5.1 – Introduction to Decimals Decimal Notation and Writing Decimals. Write the following decimals as fractions/mixed numbers in simplest form. 0.51 0.241 0.032 29.97 64.8 -209.986

5.1 – Introduction to Decimals Comparing Decimals Compare digits in the same place, when determining which number is larger. When two digits are not the same value, the larger digit is the larger decimal. Use < or > to make a true statement 26.208 < 26.28 0.12 > 0.026 0.0065 > 0.00065 3.4251 > 3.4249 -0.562 > -0.652 -0.039 < -0.0309

5.1 – Introduction to Decimals Rounding Decimals Locate the digit to the right of the requested place value. If the digit to the right is 5 or greater, round the place value up one and drop remaining digits. If the digit to the right is less than 5, the place value remains and the remaining digits are dropped. 482.7817 Round to the nearest thousandth 482.782 0.7522 Round to the nearest tenth 0.8 3.141592 Round to the nearest hundredth 3.14 752.883 Round to the nearest tens 750

5.2 – Adding and Subtracting Decimals Are the values the same? 0.03 0.003 0.0030000 0.0003 0.003 0.003000 0.00300 0.003 0.0030 0.3 0.003 0.00300 NO YES YES Zeros placed at the end of the last digit in a decimal do not change the value of the decimal.

5.2 – Adding and Subtracting Decimals 1) Write the numbers so the decimal points line up vertically. 2) Place zeros after the last digit to assist in adding or subtracting the decimals. 3) Add or subtract the decimal places like whole numbers. Examples: 19.52 + 5.371 40.08 + 17.612 19.52 40.08 + 5.371 + 17.612 24.891 57.692

5.2 – Adding and Subtracting Decimals Examples: 0.125 + 422.8 19 + 26.47 0.125 19 .00 + 422.8 00 + 26.47 422.925 45.47 34.567 + 129.43 + 2.8903 11.21 + 46.013 + 362.526 34.567 11.21 129.43 00 46.013 + 2.8903 + 362.526 1 6 6 . 8 8 7 3 4 1 9 . 7 4 9

5.2 – Adding and Subtracting Decimals Examples: 6.7 – 3.92 73 – 29.31 6.7 73 .00 - 3.92 - 29.31 2 . 7 8 4 3 . 6 9 -5.4 – 9.6 7.12 + (-9.92) -5.4 -9.92 -9.6 7.12 - 15 . - 2 . 8

5.2 – Adding and Subtracting Decimals Examples: 19.204 from 25.91 25.91 - 19.204 6 . 7 6 Evaluate y – z if y = 11.6 and z = 10.87 11.6 - 10.87 . 7 3

5.2 – Adding and Subtracting Decimals Examples: Is 12.14 a solution of the equation y – 4.3 = 7.84? y – 4.3 = 7.84 12.14 – 4.3 = 7.84 12.14 - 4.3 7 . 8 4 = 7.84 12.14 is a solution.

5.2 – Adding and Subtracting Decimals Examples: -4.3y + 7.8 – 20.18y + 14.602 -4.30y 7.8 00 -20.18y 14.602 - 2 4 . 4 8 y 2 2 . 4 2 -24.48y + 22.402

5.2 – Adding and Subtracting Decimals Estimation – a process to check if an answer is reasonable. Actual (Exact) Estimate 58.1 + 326.97 60 + 330 58.1 60 + 326.97 330 3 8 5 . 7 390 Actual (Exact) Estimate 16.08 – 0.921 16 – 1 16.08 16 - 0.921 - 1 1 5 . 1 5 9 15

5.3 – Multiplying Decimals 1) Multiply the decimals as thought they are whole numbers. 2) Add the number of decimal places in each term. 3) From the last digit of the product, count to the left and place the decimal after that numbered term. Examples: 34.8 0.0641 x 0.62 x 27 696 4487 2088 1282 21576 17307 3 decimal places 4 decimal places 21.576 1.7307

5.3 – Multiplying Decimals Examples: 7.3 -0.9 x -0.9 x 7.3 657 27 63 2 decimal places 657 6.57 2 decimal places 6.57

5.3 – Multiplying Decimals Actual (Exact) Estimate 30.26 30 x 2.89 x 3 27234 90 24208 6052 874514 4 decimal places 87.4514

5.3 – Multiplying Decimals Examples: Is -5.5 a solution of the equation: – 6x = 33? -6 (-5.5) 5.5 x 6 330 1 decimal place 33.0 = 33 -5.5 is a solution.

5.3 – Multiplying Decimals A garden contains 60.5 square yards of space for planting. The fertilizer to be used on the garden suggests a spreading rate of 5.6 ounces per square yard. How many ounces of fertilizer are needed? 60.5 x 5.6 3630 3025 33880 2 decimal places 338.80 338.8 ounces

5.3 – Circumference of a Circle Blue line = Diameter r Red line = Radius d d = 2r Circumference – the length around the edge of a circle. C =  d or C = 2  r

5.3 – Circumference of a Circle C =  d or C = 2  r Find the circumference of a circle whose diameter is 7 meters. ( Use 3.14 as an approximation of .) C = 3.14 (7) 3.14 x 7 2198 2 decimal places 21.98 meters

5.3 – Circumference of a Circle C =  d or C = 2  r Find the circumference of a circle whose radius is 2.5 feet. ( Use 3.14 as an approximation of .) C =2 (3.14) (2.5) 3.14 6.28 x 2 x 2.5 628 3140 2 decimal places 1256 15700 6.28 3 decimal places 15.700 15.7 feet