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4. Example 1-5c Objective Find the product of decimals and whole numbers

5. Example 1-5c Vocabulary Scientific notation A way of expressing a number as the product of a number that is at least 1 but less than 10 and the power of 10

6. Lesson 1 Contents Example 1Multiply Decimals Example 2Multiply Decimals Example 3Annex Zeros in the Product Example 4Annex Zeros in the Product Example 5Scientific Notation

7. Example 1-1a 1/5 Find 18.9  4 Write the problem vertically line up digits, not place value Multiply 4  9 = 36 Put the one’s place value of 6 under the 4 Carry the ten’s place value of 3 3 Multiply 4  8 = 32 Add the carry of 3 to 32 = 35 Put the one’s place value of 5 under the 8 Carry the ten’s place value of 3 3

8. Example 1-1a 1/5 Find 18.9  4 Multiply 4  1 = 4 3 Add the carry of 3 to 4 = 7 Put the one’s place value of 7 under the 1 Count the decimal places in 18.9 3 1 Count the decimal places in 4 0 Add the place values 1 + 0 1 Beginning on the right of the 6, place a decimal 1 place to the left Answer: 75.6

9. Example 1-1c Answer: 100.8 1/5 Find 12.6  8

10. Example 1-2a 4 2/5 Find 0.56  7 Write the problem vertically line up digits, not place value Multiply 7  6 = 42 Put the one’s place value of 2 under the 7 Carry the ten’s place value of 4 Multiply 7  5 = 35 Add the carry of 4 to 35 = 39 Put the one’s place value of 9 under the 5 Carry the ten’s place value of 3 3

11. Example 1-2a 4 2/5 Find 0.56  7 Multiply 7  0 = 0 Add the carry of 3 to 0 = 3 Put the one’s place value of 3 under the 0 3 Count the decimal places in 0.56 2 Count the decimal places in 7 0 Add the place values 2 + 0 Beginning on the right of the 2, place a decimal 2 places to the left Answer: 3.92 2

12. Example 1-2c Answer: 3.32 2/5 Find 0.83  4

13. Example 1-3a 3/5 1 Find 3  0.016 Write the problem vertically line up digits, not place value Since 0.016 has more digits than 3, put it on top Multiply 3  6 = 18 Put the one’s place value of 8 under the 3 Carry the ten’s place value of 1 Multiply 3  1 = 3 Add the carry of 1 to 3 = 4 Put the one’s place value of 4 under the 1

14. Example 1-3a 3/5 1 Find 3  0.016 Multiply 3  0 = 0 Put the one’s place value of 0 under the 0 next to the 1 Multiply 3  0 = 0 Put the one’s place value of 0 under the 0 Count the decimal places in 0.016 3 Count the decimal places in 3 0 Add the place values 3 + 0 3 Beginning on the right of the 8, place a decimal 3 places to the left Answer: 0.048

15. Example 1-3b Answer: 0.092 3/5 Find 4  0.023

16. Example 1-4a ALGEBRA Evaluate 4/5 Write the algebraic expression5g Remember: 5g means 5  g Replace g with 0.0091 Bring down the 5 5 (0.0091) Write the problem vertically line up digits, not place value Since 0.091 has more digits than 5, put it on top 0.0091 x 5

17. Example 1-4a ALGEBRA Evaluate 4/5 0.0091 x 5 Multiply 5  1 = 5 Put the one’s place value of 5 under the 5 5 Multiply 5  9 = 45 Put the one’s place value of 5 under the 9 Carry the ten’s place value of 4 4 5

18. Example 1-4a ALGEBRA Evaluate 4/5 0.0091 x 5 Multiply 5  0 = 0 5 0 Put the one’s place value of 4 under the 0 next to the 9 4 5 Add the carry of 4 to 0 = 4 Put the one’s place value of 0 under the 0 4 0 Multiply 5  0 = 0 Put the one’s place value of 0 under the 0 0

19. Example 1-4a ALGEBRA Evaluate 4/5 0.0091 x 5 0 0455 4 Count the decimal places in 0.091 4 Count the decimal places in 5 0 Add the place values 4 + 0 Beginning on the right of the 5, place a decimal 4 places to the left. Answer: 0.0455 4

20. Example 1-4b ALGEBRA Evaluate Answer: 0.0186 4/5

21. Example 1-5a ASTRONOMY The average distance from Earth to the Sun is 1.5  10 8 kilometers. Write this distance in standard form. 5/5 Write the problem 1.5  10 8 Use the calculator Put 1.5 in calculator 1.5 Push the  sign  Put 10 in calculator 10 Push the exponent key [y x ] yxyx

22. Example 1-5a ASTRONOMY The average distance from Earth to the Sun is 1.5  10 8 kilometers. Write this distance in standard form. 5/5 1.5  10 8 1.5  10 yxyx Put the exponent 8 in calculator 8 Push the = sign = 150,000,000 Make sure to add the commas in the appropriate places Answer: The average distance is 150,000,000 kilometers

23. Example 1-5c Answer: 240,000 years ARCHAEOLOGY An archaeologist claims that a particular artifact is 2.4  10 5 years old. Write this age in standard form. * 5/5

24. End of Lesson 1 Assignment Lesson 4:1Multiplying Decimals15 - 38 All by Whole Numbers