The document discusses scientific notation, which is a way to write very large or small numbers in a standardized form. It explains that in scientific notation, any number can be written as A x 10N, where 1 < A < 10 and N is an exponent that represents powers of 10. Positive exponents mean the decimal is moved to the right, and negative exponents mean it is moved to the left. The document provides examples of writing numbers in scientific notation and changing them back to standard form by moving the decimal according to the exponent N.

1. Scientific Notation

2. Scientific Notation
An important application for exponents is the use of the
powers of 10 in calculation of very large or very small numbers.

3. 100 = 1
Scientific Notation
An important application for exponents is the use of the
powers of 10 in calculation of very large or very small numbers.
Powers of 10:

4. 100 = 1
101 = 10
Scientific Notation
An important application for exponents is the use of the
powers of 10 in calculation of very large or very small numbers.
Powers of 10:

5. 100 = 1
101 = 10
102 = 100
Scientific Notation
An important application for exponents is the use of the
powers of 10 in calculation of very large or very small numbers.
Powers of 10:

6. 100 = 1
101 = 10
102 = 100
103 = 1000
Scientific Notation
An important application for exponents is the use of the
powers of 10 in calculation of very large or very small numbers.
Powers of 10:
The number of “0’s”
is the exponent.
Note:

7. 100 = 1
101 = 10
102 = 100
103 = 1000
10–1 = 0.1
Scientific Notation
An important application for exponents is the use of the
powers of 10 in calculation of very large or very small numbers.
Powers of 10:
The number of “0’s”
is the exponent.
Note:

8. 100 = 1
101 = 10
102 = 100
103 = 1000
10–1 = 0.1
10–2 = 0.01
Scientific Notation
An important application for exponents is the use of the
powers of 10 in calculation of very large or very small numbers.
Powers of 10:
The number of “0’s”
is the exponent.
Note:

9. 100 = 1
101 = 10
102 = 100
103 = 1000
10–1 = 0.1
10–2 = 0.01
10–3 = 0.001
10–4 = 0.0001
Scientific Notation
An important application for exponents is the use of the
powers of 10 in calculation of very large or very small numbers.
Powers of 10:
The number of “0’s”
is the exponent.
Note:
The number of “0’s”
in the front matches
the exponent.

10. 100 = 1
101 = 10
102 = 100
103 = 1000
10–1 = 0.1
10–2 = 0.01
10–3 = 0.001
10–4 = 0.0001
Scientific Notation
Scientific Notation
An important application for exponents is the use of the
powers of 10 in calculation of very large or very small numbers.
Powers of 10:
The number of “0’s”
is the exponent.
Note:
The number of “0’s”
in the front matches
the exponent.

11. 100 = 1
101 = 10
102 = 100
103 = 1000
10–1 = 0.1
10–2 = 0.01
10–3 = 0.001
10–4 = 0.0001
Scientific Notation
Scientific Notation
Any number can be written in the form
A x 10N
where 1 < A < 10.
An important application for exponents is the use of the
powers of 10 in calculation of very large or very small numbers.
Powers of 10:
The number of “0’s”
is the exponent.
Note:
The number of “0’s”
in the front matches
the exponent.

12. 100 = 1
101 = 10
102 = 100
103 = 1000
10–1 = 0.1
10–2 = 0.01
10–3 = 0.001
10–4 = 0.0001
Scientific Notation
Scientific Notation
Any number can be written in the form
A x 10N
where 1 < A < 10. This form is called the scientific notation of
the number.
An important application for exponents is the use of the
powers of 10 in calculation of very large or very small numbers.
Powers of 10:
The number of “0’s”
is the exponent.
The number of “0’s”
in the front matches
the exponent.
Note:

13. Scientific Notation
To write a number in scientific notation, we move the decimal
point behind the first nonzero digit.

14. Scientific Notation
To write a number in scientific notation, we move the decimal
point behind the first nonzero digit.
i. If the decimal point moves to the left N spaces, then the
exponent over 10 is positive N,

15. Scientific Notation
To write a number in scientific notation, we move the decimal
point behind the first nonzero digit.
i. If the decimal point moves to the left N spaces, then the
exponent over 10 is positive N, i.e. if after moving the
decimal point we get a smaller number A, then N is positive.

16. Scientific Notation
To write a number in scientific notation, we move the decimal
point behind the first nonzero digit.
i. If the decimal point moves to the left N spaces, then the
exponent over 10 is positive N, i.e. if after moving the
decimal point we get a smaller number A, then N is positive.
Example A. Write the following numbers in scientific
notation.
a. 12300.

17. Scientific Notation
To write a number in scientific notation, we move the decimal
point behind the first nonzero digit.
i. If the decimal point moves to the left N spaces, then the
exponent over 10 is positive N, i.e. if after moving the
decimal point we get a smaller number A, then N is positive.
Move left 4 places.
Example A. Write the following numbers in scientific
notation.
a. 12300. = 1 2300 .

18. Scientific Notation
To write a number in scientific notation, we move the decimal
point behind the first nonzero digit.
i. If the decimal point moves to the left N spaces, then the
exponent over 10 is positive N, i.e. if after moving the
decimal point we get a smaller number A, then N is positive.
Move left 4 places.
Example A. Write the following numbers in scientific
notation.
a. 12300. = 1 2300 . = 1. 23 x 10 +4

19. Scientific Notation
To write a number in scientific notation, we move the decimal
point behind the first nonzero digit.
i. If the decimal point moves to the left N spaces, then the
exponent over 10 is positive N, i.e. if after moving the
decimal point we get a smaller number A, then N is positive.
ii. If the decimal point moves to the right N spaces, then the
exponent over 10 is negative,
Move left 4 places.
Example A. Write the following numbers in scientific
notation.
a. 12300. = 1 2300 . = 1. 23 x 10 +4

20. Scientific Notation
To write a number in scientific notation, we move the decimal
point behind the first nonzero digit.
i. If the decimal point moves to the left N spaces, then the
exponent over 10 is positive N, i.e. if after moving the
decimal point we get a smaller number A, then N is positive.
ii. If the decimal point moves to the right N spaces, then the
exponent over 10 is negative, i.e. if after moving the decimal
point we get a larger number A, then N is negative.
Move left 4 places.
Example A. Write the following numbers in scientific
notation.
a. 12300. = 1 2300 . = 1. 23 x 10 +4

21. Scientific Notation
To write a number in scientific notation, we move the decimal
point behind the first nonzero digit.
i. If the decimal point moves to the left N spaces, then the
exponent over 10 is positive N, i.e. if after moving the
decimal point we get a smaller number A, then N is positive.
ii. If the decimal point moves to the right N spaces, then the
exponent over 10 is negative, i.e. if after moving the decimal
point we get a larger number A, then N is negative.
Move left 4 places.
Example A. Write the following numbers in scientific
notation.
a. 12300. = 1 2300 . = 1. 23 x 10 +4
b. 0.00123

22. Scientific Notation
To write a number in scientific notation, we move the decimal
point behind the first nonzero digit.
i. If the decimal point moves to the left N spaces, then the
exponent over 10 is positive N, i.e. if after moving the
decimal point we get a smaller number A, then N is positive.
ii. If the decimal point moves to the right N spaces, then the
exponent over 10 is negative, i.e. if after moving the decimal
point we get a larger number A, then N is negative.
Move left 4 places.
Move right 3 places
Example A. Write the following numbers in scientific
notation.
a. 12300. = 1 2300 . = 1. 23 x 10 +4
b. 0.00123 = 0. 001 23

23. Scientific Notation
To write a number in scientific notation, we move the decimal
point behind the first nonzero digit.
i. If the decimal point moves to the left N spaces, then the
exponent over 10 is positive N, i.e. if after moving the
decimal point we get a smaller number A, then N is positive.
ii. If the decimal point moves to the right N spaces, then the
exponent over 10 is negative, i.e. if after moving the decimal
point we get a larger number A, then N is negative.
Move left 4 places.
Move right 3 places
Example A. Write the following numbers in scientific
notation.
a. 12300. = 1 2300 . = 1. 23 x 10 +4
b. 0.00123 = 0. 001 23 = 1. 23 x 10 –3

24. Scientific Notation
To change a number in scientific notation back to the standard
form, we move the decimal point according to N.

25. Scientific Notation
To change a number in scientific notation back to the standard
form, we move the decimal point according to N.
i. If N is positive, move the decimal point in A to the right,

26. Scientific Notation
To change a number in scientific notation back to the standard
form, we move the decimal point according to N.
i. If N is positive, move the decimal point in A to the right,
i.e. make A into a larger number.

27. Scientific Notation
To change a number in scientific notation back to the standard
form, we move the decimal point according to N.
i. If N is positive, move the decimal point in A to the right,
i.e. make A into a larger number.
Example B. Write the following numbers in the standard form.
a. 1. 23 x 10 +4

28. Scientific Notation
To change a number in scientific notation back to the standard
form, we move the decimal point according to N.
i. If N is positive, move the decimal point in A to the right,
i.e. make A into a larger number.
Move right 4 places,
Example B. Write the following numbers in the standard form.
a. 1. 23 x 10 +4 = 1 2300 . = 12300.

29. Scientific Notation
To change a number in scientific notation back to the standard
form, we move the decimal point according to N.
i. If N is positive, move the decimal point in A to the right,
i.e. make A into a larger number.
ii. If N is negative, move the decimal point in A to the left,
Move right 4 places,
Example B. Write the following numbers in the standard form.
a. 1. 23 x 10 +4 = 1 2300 . = 12300.

30. Scientific Notation
To change a number in scientific notation back to the standard
form, we move the decimal point according to N.
i. If N is positive, move the decimal point in A to the right,
i.e. make A into a larger number.
ii. If N is negative, move the decimal point in A to the left,
i.e. make A into a smaller number.
Move right 4 places,
Example B. Write the following numbers in the standard form.
a. 1. 23 x 10 +4 = 1 2300 . = 12300.

31. Scientific Notation
To change a number in scientific notation back to the standard
form, we move the decimal point according to N.
i. If N is positive, move the decimal point in A to the right,
i.e. make A into a larger number.
ii. If N is negative, move the decimal point in A to the left,
i.e. make A into a smaller number.
Move right 4 places,
Example B. Write the following numbers in the standard form.
a. 1. 23 x 10 +4 = 1 2300 . = 12300.
b. 1. 23 x 10 –3

32. Scientific Notation
To change a number in scientific notation back to the standard
form, we move the decimal point according to N.
i. If N is positive, move the decimal point in A to the right,
i.e. make A into a larger number.
ii. If N is negative, move the decimal point in A to the left,
i.e. make A into a smaller number.
Move right 4 places,
Move left 3 places
Example B. Write the following numbers in the standard form.
a. 1. 23 x 10 +4 = 1 2300 . = 12300.
b. 1. 23 x 10 –3 = 0. 001 23 = 0.00123

33. Scientific Notation
To change a number in scientific notation back to the standard
form, we move the decimal point according to N.
i. If N is positive, move the decimal point in A to the right,
i.e. make A into a larger number.
ii. If N is negative, move the decimal point in A to the left,
i.e. make A into a smaller number.
Move right 4 places,
Move left 3 places
Example B. Write the following numbers in the standard form.
a. 1. 23 x 10 +4 = 1 2300 . = 12300.
b. 1. 23 x 10 –3 = 0. 001 23 = 0.00123
Scientific notation simplifies multiplication and division of
very large and very small numbers.

34. Example C. Calculate. Give the answer in both scientific
notation and the standard notation.
a. (1.2 x 108) x (1.3 x 10–12)
Scientific Notation

35. Example C. Calculate. Give the answer in both scientific
notation and the standard notation.
a. (1.2 x 108) x (1.3 x 10–12)
= 1.2 x 1.3 x 108 x 10 –12
Scientific Notation

36. Example C. Calculate. Give the answer in both scientific
notation and the standard notation.
a. (1.2 x 108) x (1.3 x 10–12)
= 1.2 x 1.3 x 108 x 10 –12
= 1.56 x 108 –12
Scientific Notation

37. Example C. Calculate. Give the answer in both scientific
notation and the standard notation.
a. (1.2 x 108) x (1.3 x 10–12)
= 1.2 x 1.3 x 108 x 10 –12
= 1.56 x 108 –12
= 1.56 x 10 –4
Scientific Notation

38. Example C. Calculate. Give the answer in both scientific
notation and the standard notation.
a. (1.2 x 108) x (1.3 x 10–12)
= 1.2 x 1.3 x 108 x 10 –12
= 1.56 x 108 –12
= 1.56 x 10 –4
= 0.000156
Scientific Notation

39. Example C. Calculate. Give the answer in both scientific
notation and the standard notation.
a. (1.2 x 108) x (1.3 x 10–12)
= 1.2 x 1.3 x 108 x 10 –12
= 1.56 x 108 –12
= 1.56 x 10 –4
= 0.000156
b.
6.3 x 10-2
2.1 x 10-10
Scientific Notation

40. Example C. Calculate. Give the answer in both scientific
notation and the standard notation.
a. (1.2 x 108) x (1.3 x 10–12)
= 1.2 x 1.3 x 108 x 10 –12
= 1.56 x 108 –12
= 1.56 x 10 –4
= 0.000156
b.
6.3 x 10-2
2.1 x 10-10
=
6.3
2.1
x 10 – 2 – ( – 10)
Scientific Notation

41. Example C. Calculate. Give the answer in both scientific
notation and the standard notation.
a. (1.2 x 108) x (1.3 x 10–12)
= 1.2 x 1.3 x 108 x 10 –12
= 1.56 x 108 –12
= 1.56 x 10 –4
= 0.000156
b.
6.3 x 10-2
2.1 x 10-10
=
6.3
2.1
x 10 – 2 – ( – 10)
= 3 x 108
Scientific Notation

42. Example C. Calculate. Give the answer in both scientific
notation and the standard notation.
a. (1.2 x 108) x (1.3 x 10–12)
= 1.2 x 1.3 x 108 x 10 –12
= 1.56 x 108 –12
= 1.56 x 10 –4
= 0.000156
b.
6.3 x 10-2
2.1 x 10-10
=
6.3
2.1
x 10 – 2 – ( – 10)
= 3 x 108
= 300,000,000
Scientific Notation

43. Example D. Convert each numbers into scientific notation.
Calculate the result. Give the answer in both scientific
notation and the standard notation.
Scientific Notation

44. Example D. Convert each numbers into scientific notation.
Calculate the result. Give the answer in both scientific
notation and the standard notation.
240,000,000 x 0.0000025
0.00015
Scientific Notation

45. Example D. Convert each numbers into scientific notation.
Calculate the result. Give the answer in both scientific
notation and the standard notation.
240,000,000 x 0.0000025
=
0.00015
2.4 x 108
Scientific Notation

46. Example D. Convert each numbers into scientific notation.
Calculate the result. Give the answer in both scientific
notation and the standard notation.
240,000,000 x 0.0000025
=
0.00015
2.4 x 108 x 2.5 x 10–6
Scientific Notation

47. Example D. Convert each numbers into scientific notation.
Calculate the result. Give the answer in both scientific
notation and the standard notation.
240,000,000 x 0.0000025
=
0.00015
2.4 x 108 x 2.5 x 10–6
1.5 x 10–4
Scientific Notation

48. Example D. Convert each numbers into scientific notation.
Calculate the result. Give the answer in both scientific
notation and the standard notation.
240,000,000 x 0.0000025
=
0.00015
2.4 x 108 x 2.5 x 10–6
1.5 x 10–4
= 2.4 x 2.5 x 108 x 10–6
1.5 x 10–4
Scientific Notation

49. Example D. Convert each numbers into scientific notation.
Calculate the result. Give the answer in both scientific
notation and the standard notation.
240,000,000 x 0.0000025
=
0.00015
2.4 x 108 x 2.5 x 10–6
1.5 x 10–4
=
2.4 x 2.5
1.5
x 10 8 + (–6) – ( – 4)
= 2.4 x 2.5 x 108 x 10–6
1.5 x 10–4
Scientific Notation

50. Example D. Convert each numbers into scientific notation.
Calculate the result. Give the answer in both scientific
notation and the standard notation.
240,000,000 x 0.0000025
=
0.00015
2.4 x 108 x 2.5 x 10–6
1.5 x 10–4
=
2.4 x 2.5
1.5
x 10 8 + (–6) – ( – 4)
= 2.4 x 2.5 x 108 x 10–6
1.5 x 10–4
= 4 x 108 – 6 + 4
Scientific Notation

51. Example D. Convert each numbers into scientific notation.
Calculate the result. Give the answer in both scientific
notation and the standard notation.
240,000,000 x 0.0000025
=
0.00015
2.4 x 108 x 2.5 x 10–6
1.5 x 10–4
=
2.4 x 2.5
1.5
x 10 8 + (–6) – ( – 4)
= 2.4 x 2.5 x 108 x 10–6
1.5 x 10–4
= 4 x 108 – 6 + 4
= 4 x 106 = 4,000,000
Scientific Notation