This document provides examples for converting numbers between standard decimal notation and scientific notation. It begins with examples of expressing numbers in scientific notation, such as expressing 49,200 as 4.9x104, and 1,230,000 as 1.23x106. It then gives examples of expressing numbers in scientific notation in standard decimal form, such as writing 5.2x103 as 5,200 and 7.8x105 as 780,000. The document demonstrates how to convert numbers between the two notations.

1. ☺

2. GUESS THE MATHEMATICAL WORD GIVEN

3. M m sa t h e a t i c

4. p te x o n e n

5. N ge a t i v e

6. p to i n

7. p ro w e

8. s tp o i i v e

9. d ti g i s

10. d le c i m a

11. m rn u b e

12. r sa i e

13. b sa e

14. REVIEW

15. Powers of 10
base 10n
exponent
102
= 10 x 10 = 100
103
104
= 10 x 10 x 10 = 1000
= 10 x 10 x 10 x 10 = 10000
10101
=10

16. 10−1
=
1
101 = 0.1
10−2
10−3
=
1
10
x
1
10
= 0.01
=
1
10
x
1
10
x
1
10
= 0.001
=
1
102
=
1
103
=
1
100
=
1
1000
=
1
10

17. • Pluto’s average distance from the sun is
approximately 3,670,000,000 miles.
• The radius of a hydrogen atom is
0.000000000053meters.

18. 𝑀 𝑥 10 𝑛
𝑤ℎ𝑒𝑟𝑒 1 ≤ 𝑀 < 10
𝐒𝐂𝐈𝐄𝐍𝐓𝐈𝐅𝐈𝐂 𝐍𝐎𝐓𝐀𝐓𝐈𝐎𝐍
Scientific notation is a special way of writing too
big or too small numbers.

19. 5,000
x10 x 10 x 10
5,240,000
. 𝑥103
25,000
𝑀 𝑥 10 𝑛
𝑥104
239,000 = 2.39
= 5.24𝑥106
=5 x 1000
=5
= 5 𝑥10
= 2.5 𝑥10
𝑥10𝑥105

20. 𝑥10−1
0.000065
𝑀 𝑥 10 𝑛
𝑥10−5
= 3.56
=8.2
0.25
0.00356
0.0000082
= 2.5𝑥10
= 6.5
𝑥10−3
x10
𝑥10−6𝑥10

21. 5𝑥103 = 5 0 0 0 = 5 000
= 2.52.5𝑥104
0 0 0 = 25 000
= 2.392.39𝑥105
0 0 0 = 239 000
SCIENTIFIC TO STANDARD FORM
. .
9𝑥109
=9.0000 0 0 000 = 9 000 000 000

22. 2.5𝑥10−1 = 2.5 = 0.25
3.56𝑥10−3 = 3.56 = 0.00356.0 0
.
8.2𝑥10−6 = 0 8.2 = 0.0000082.0 0 0 0

23. EXPRESS IN SCIENTIFIC NOTATION AND VICE VERSA
A rocket ship accelerates to a speed of
48,000 km/hr.
THE NUMBERS INVOLVED IN THE STATEMENT

24. 4.8 𝑥 104 km/hr

25. EXPRESS IN SCIENTIFIC NOTATION AND VICE VERSA
The speed of light is about 300,000 km/s.
THE NUMBERS INVOLVED IN THE STATEMENT

26. 3 𝑥 105 km/s

27. The wave length of red light is 0.000 065 cm.
EXPRESS IN SCIENTIFIC NOTATION AND VICE VERSA
THE NUMBERS INVOLVED IN THE STATEMENT

28. 6.5𝑥 10−5 cm

29. A certain star is about 97,000,000,000 light years away
from earth.
EXPRESS IN SCIENTIFIC NOTATION AND VICE VERSA
THE NUMBERS INVOLVED IN THE STATEMENT

30. 9.7 𝑥 1010

31. The distance of the moon to the earth is
about 239,000 km.
THE NUMBERS INVOLVED IN THE STATEMENT
EXPRESS IN SCIENTIFIC NOTATION AND VICE VERSA

32. 2.39 𝑥 105
km

33. The radius of an atom of hydrogen is
about 0.000 000 005 cm.
EXPRESS IN SCIENTIFIC NOTATION AND VICE VERSA
THE NUMBERS INVOLVED IN THE STATEMENT

34. 5 𝑥 10−9 cm

35. The wave length of gamma rays is 2𝑥10−10
cm.
EXPRESS IN SCIENTIFIC NOTATION AND VICE VERSA
THE NUMBERS INVOLVED IN THE STATEMENT

36. 0.000 000 000 2 cm

37. The image of each picture remains on the
screen approximately 6𝑥10−2
seconds.
EXPRESS IN SCIENTIFIC NOTATION AND VICE VERSA
THE NUMBERS INVOLVED IN THE STATEMENT

38. 0.06 seconds

39. A car traveled 100,000 meters in 2 hours.
EXPRESS IN SCIENTIFIC NOTATION AND VICE VERSA
THE NUMBERS INVOLVED IN THE STATEMENT

40. 1x105

41. Jeminae received a luxurious car from his
boyfriend worth 8,000,000 pesos.
EXPRESS IN SCIENTIFIC NOTATION AND VICE VERSA
THE NUMBERS INVOLVED IN THE STATEMENT

42. 8x106

44. A. Express in Scientific
Notation
1. 49,200
2. 1,230,000
3. 0.000 005 8
4. 0.000 008 15
5. 0.000 000 061 5
B. Express in Decimal
Notation
1. 5.2x103
2. 7.8x105
3. 6.45x107
4. 4.5x10−3
5. 3.9x10−6

45. B.
1. 5,200
2. 780 000
3. 64 500 000
4. 0.0045
5. 0.0000039
A.
1. 4.9x104
2. 1.23x106
3. 5.8x10−6
4. 8.15x10−6
5. 6.15x10−8

46. ☺By: Maria Theresa Bicar - Edar