The document discusses how to multiply decimals by powers of ten using place value. It shows that multiplying a decimal by 10 moves the decimal point one place to the right, multiplying by 100 moves it two places to the right, and multiplying by 1000 moves it three places to the right. Examples are provided with the decimals 2.38 and 0.78 being multiplied by 1, 10, 100, and 1000. The relationship between moving the decimal point and the power of ten being multiplied is then generalized.

1. 6-1 Mental Math:
Multiplying Decimals by
10, 100, and 1000
Math Notes
Number Sense 2.1

3. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000

4. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
2.38 x 1 = 2.38

5. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
2.38 x 1 = 2.38
2.38 x 10 = 23.8

6. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
2.38 x 1 = 2.38
2.38 x 10 = 23.8
2.38 x 100 = 238.0

7. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
2.38 x 1 = 2.38
2.38 x 10 = 23.8
2.38 x 100 = 238.0
2.38 x 1000 = 2380.0

8. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
2.38 x 1 = 2.38
2.38 x 10 = 23.8
2.38 x 100 = 238.0
2.38 x 1000 = 2380.0

9. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
2.38 x 1 = 2.38
2.38 x 10 = 23.8
2.38 x 100 = 238.0
2.38 x 1000 = 2380.0

10. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
2.38 x 1 = 2.38
2.38 x 10 = 23.8
2.38 x 100 = 238.0
2.38 x 1000 = 2380.0

11. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
2.38 x 1 = 2.38
2.38 x 10 = 23.8
2.38 x 100 = 238.0
2.38 x 1000 = 2380.0

12. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
2.38 x 1 = 2.38
2.38 x 10 = 23.8
2.38 x 100 = 238.0
2.38 x 1000 = 2380.0

13. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
2.38 x 1 = 2.38
2.38 x 10 = 23.8
2.38 x 100 = 238.0
2.38 x 1000 = 2380.0

14. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
2.38 x 1 = 2.38
2.38 x 10 = 23.8
2.38 x 100 = 238.0
2.38 x 1000 = 2380.0

15. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
2.38 x 1 = 2.38
2.38 x 10 = 23.8
2.38 x 100 = 238.0
2.38 x 1000 = 2380.0

16. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
2.38 x 1 = 2.38
2.38 x 10 = 23.8
2.38 x 100 = 238.0
2.38 x 1000 = 2380.0

18. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000

19. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
0.78 x 1 = 0.78

20. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
0.78 x 1 = 0.78
0.78 x 10 = 07.8

21. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
0.78 x 1 = 0.78
0.78 x 10 = 07.8
0.78 x 100 = 78.0

22. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
0.78 x 1 = 0.78
0.78 x 10 = 07.8
0.78 x 100 = 78.0
0.78 x 1000 = 780.0

23. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
0.78 x 1 = 0.78
0.78 x 10 = 07.8
0.78 x 100 = 78.0
0.78 x 1000 = 780.0

24. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
0.78 x 1 = 0.78
0.78 x 10 = 07.8
0.78 x 100 = 78.0
0.78 x 1000 = 780.0

25. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
0.78 x 1 = 0.78
0.78 x 10 = 07.8
0.78 x 100 = 78.0
0.78 x 1000 = 780.0

26. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
0.78 x 1 = 0.78
0.78 x 10 = 07.8
0.78 x 100 = 78.0
0.78 x 1000 = 780.0

27. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
0.78 x 1 = 0.78
0.78 x 10 = 07.8
0.78 x 100 = 78.0
0.78 x 1000 = 780.0

28. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
0.78 x 1 = 0.78
0.78 x 10 = 07.8
0.78 x 100 = 78.0
0.78 x 1000 = 780.0

29. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
0.78 x 1 = 0.78
0.78 x 10 = 07.8
0.78 x 100 = 78.0
0.78 x 1000 = 780.0

30. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
0.78 x 1 = 0.78
0.78 x 10 = 07.8
0.78 x 100 = 78.0
0.78 x 1000 = 780.0

31. Basic facts and patterns of zeros can help
you multiply decimals by 10, 100, and 1000
0.78 x 1 = 0.78
0.78 x 10 = 07.8
0.78 x 100 = 78.0
0.78 x 1000 = 780.0

32. Algebra. Find each n
6.59 x n = 65.9

33. Algebra. Find each n
6.59 x n = 65.9
The decimal moved to the right ONE place value.

34. Algebra. Find each n
6.59 x n = 65.9
The decimal moved to the right ONE place value.

35. Algebra. Find each n
6.59 x n = 65.9
The decimal moved to the right ONE place value.
What would cause the decimal to move
ONE over: 10 100 1000?

36. Algebra. Find each n
6.59 x n = 65.9
The decimal moved to the right ONE place value.
What would cause the decimal to move
ONE over: 10 100 1000?

37. Algebra. Find each n
6.59 x n = 65.9
The decimal moved to the right ONE place value.
What would cause the decimal to move
ONE over: 10 100 1000?

38. Algebra. Find each n
6.59 x n = 65.9
The decimal moved to the right ONE place value.
What would cause the decimal to move
ONE over: 10 100 1000?

39. Algebra. Find each n
6.59 x n = 65.9
The decimal moved to the right ONE place value.
What would cause the decimal to move
ONE over: 10 100 1000?

40. Algebra. Find each n
6.59 x n = 65.9
The decimal moved to the right ONE place value.
What would cause the decimal to move
ONE over: 10 100 1000?
n = 10

41. Algebra. Find each n
0.5 x 1000 = n

42. Algebra. Find each n
0.5 x 1000 = n
How many decimal places will the decimal point
move by multiplying by 1000?

43. Algebra. Find each n
0.5 x 1000 = n
How many decimal places will the decimal point
move by multiplying by 1000?
10 100 1000?

44. Algebra. Find each n
0.5 x 1000 = n
How many decimal places will the decimal point
move by multiplying by 1000?
10 100 1000?

45. Algebra. Find each n
0.5 x 1000 = n
How many decimal places will the decimal point
move by multiplying by 1000?
10 100 1000?

46. Algebra. Find each n
0.5 x 1000 = n
How many decimal places will the decimal point
move by multiplying by 1000?
10 100 1000?

47. Algebra. Find each n
0.5 x 1000 = n
How many decimal places will the decimal point
move by multiplying by 1000?
10 100 1000?
0. 5

48. Algebra. Find each n
0.5 x 1000 = n
How many decimal places will the decimal point
move by multiplying by 1000?
10 100 1000?
05 .

49. Algebra. Find each n
0.5 x 1000 = n
How many decimal places will the decimal point
move by multiplying by 1000?
10 100 1000?
0 50 .

50. Algebra. Find each n
0.5 x 1000 = n
How many decimal places will the decimal point
move by multiplying by 1000?
10 100 1000?
0 5 0 0.

51. Algebra. Find each n
0.5 x 1000 = n
How many decimal places will the decimal point
move by multiplying by 1000?
10 100 1000?
0 5 0 0 .0

52. Algebra. Find each n
0.5 x 1000 = n
How many decimal places will the decimal point
move by multiplying by 1000?
10 100 1000?
5 0 0 .0

53. Algebra. Find each n
n x 0.216 = 21.6

54. Algebra. Find each n
n x 0.216 = 21.6
The decimal moved to the right TWO place values.

55. Algebra. Find each n
n x 0.216 = 21.6
The decimal moved to the right TWO place values.

56. Algebra. Find each n
n x 0.216 = 21.6
The decimal moved to the right TWO place values.
What would cause the decimal to move
TWO over: 10 100 1000?

57. Algebra. Find each n
n x 0.216 = 21.6
The decimal moved to the right TWO place values.
What would cause the decimal to move
TWO over: 10 100 1000?

58. Algebra. Find each n
n x 0.216 = 21.6
The decimal moved to the right TWO place values.
What would cause the decimal to move
TWO over: 10 100 1000?

59. Algebra. Find each n
n x 0.216 = 21.6
The decimal moved to the right TWO place values.
What would cause the decimal to move
TWO over: 10 100 1000?

60. Algebra. Find each n
n x 0.216 = 21.6
The decimal moved to the right TWO place values.
What would cause the decimal to move
TWO over: 10 100 1000?

61. Algebra. Find each n
n x 0.216 = 21.6
The decimal moved to the right TWO place values.
What would cause the decimal to move
TWO over: 10 100 1000?
n = 100