hundredthousandths tenthousandths hundredths tenths ones tens hundreds thousands

hundred-thousandths ten-thousandths hundredths tenths ones tens hundreds thousands ten-thousands hundred-thousands millions 4. 1 – Introduction to Decimals Decimal Notation and Writing Decimals. 2, 4 5 7, 8 3 2. 8 3 0 9 4

– Introduction Decimals 4. – 4. 1 Solving Equationstowith Fractions Decimal Notation and Writing Decimals. Write each number in words. 0. 06 -200. 073 0. 0829 87. 31 52. 1085 1493. 62 Six hundredths Negative two hundred and seventy-three thousandths Eight hundred twenty-nine ten-thousandths Eighty-seven and thirty-one hundredths Fifty-two and one thousand eighty-five tenthousandths One thousand four hundred ninety-three and sixty-two hundredths

– Introduction Decimals 4. – 4. 1 Solving Equationstowith 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 twentyfive ten-thousandths Twelve thousand thirty-seven and two hundred ninety-eight thousandths -807. 0025 12, 037. 298

4. 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

4. 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

4. 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 3. 141592 Round to the nearest hundredth 0. 8 3. 14 750 752. 883 Round to the nearest tens

4. 2 – Adding and Subtracting Decimals Are the values the same? 0. 03 0. 00300 0. 3 NO 0. 0030000 0. 00300 YES Zeros placed at the end of the last digit in a decimal do not change the value of the decimal.

4. 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 0 + 5. 371 40. 08 0 + 17. 612 24. 891 57. 692

4. 2 – Adding and Subtracting Decimals Examples: 0. 125 + 422. 8 19 + 26. 47 0. 125 + 422. 800 19. 00 + 26. 47 422. 925 45. 47 34. 567 + 129. 43 + 2. 8903 34. 5670 129. 4300 + 2. 8903 16 6. 8873 11. 21 + 46. 013 + 362. 526 11. 210 46. 013 + 362. 526 41 9. 74 9

4. 2 – Adding and Subtracting Decimals Examples: 6. 7 – 3. 92 73 – 29. 31 6. 7 0 - 3. 92 73. 00 - 29. 31 5. 4 – 9. 6 7. 12 + 9. 92 5. 4 -9. 6 9. 92 +7. 12

4. 2 – Adding and Subtracting Decimals Examples: 19. 204 from 25. 91 0 - 19. 204 Evaluate y – z if y = 11. 6 and z = 10. 87

4. 2 – Adding and Subtracting Decimals Estimation – a process to check if an answer is reasonable. Actual (Exact) 58. 1 + 326. 97 58. 1 0 + 326. 97 Actual (Exact) Estimate 60 + 330 60 330 Estimate 16. 08 – 0. 921 16 – 1 16. 08 0 - 0. 921 16 - 1

4. 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 x 0. 62 696 2088 0. 0641 x 27 4487 1282 21576 17307 3 decimal places 21. 576 4 decimal places 1. 7307

4. 3 – Multiplying Decimals Examples: 7. 3 x -0. 9 657 2 decimal places 6. 57 -0. 9 x 7. 3 27 63 657 2 decimal places 6. 57

4. 3 – Multiplying Decimals Actual (Exact) 30. 26 x 2. 89 Estimate 30 x 3