Scientific notation is used to write very large or small numbers in a condensed form. It expresses numbers as the product of a number between 1 and 10 and a power of 10. For example, the distance to the nearest star can be written as 24,700,000,000,000 miles, which in scientific notation is 2.47 × 1013 miles. A single bacteria is about 0.00000075 meters in diameter, which is 7.5 × 10-7 meters in scientific notation. The document then provides examples and steps for converting numbers between standard decimal form and scientific notation.

4. Scientists deal with extremely large and extremely
small numbers like:
• The distance from the sun to the nearest star,
Proxima Centauri, is about 24 700 000 000 000
miles
• A single bacteria is about 0.00000075 meters
in diameter.

5. That’s why scientific notation was created for
the large number of zeros in these numbers
makes them difficult to read and makes them
tedious to write.

6. gives a convenient way to
write very large numbers or very small
numbers.

7. The is written as
a
multiplied by a .
4.35 × 106

8. 4.35 × 106
= 4 350 000
Scientific Notation Standard Form

9. To change a decimal notation to a scientific notation:
1. Place the decimal point after the first nonzero digit
2. Count the number of places the decimal place is
moved, and use that number as the number exponent
3. If the original number is greater than 10, the exponent
is positive. If the original number is between 1 and 10,
the exponent is zero
4. If the original number is between 0 and 1, the
exponent is negative.

10. Example 1 – Write each in scientific notation
937000
Place the to the right of the .
.
Count the to the right of this
decimal.
5 decimal
places
Write the scientific notation. Delete all the 0s to the right of the
and write the as the .
= 9. 3 7 × 10510

11. Example 2 – Write each in scientific notation
7000000
Place the to the right of the .
.
Count the to the right of this
decimal.
6 decimal
places
Count the to the right of this
decimal.
Write the scientific notation. Delete all the 0s to the right of the
and write the as the .
= 7 × 106
10

12. Example 3 – Write each in scientific notation
−2 98
Place the to the right of the .
.
Count the to the right of this
decimal.
2 decimal
places
Count the to the right of this
decimal.
Write the scientific notation. Delete all the 0s to the right of the
and write the as the .
= -2 × 10102
. 9 8

13. Example 4 – Write each in scientific notation
317.8
Place the to the right of the .
.
Count the moved.
2 decimal
places
Write the scientific notation. Delete all the 0s to the right of the
and write the as the .
= 3. 1 7 × 10102
8

14. Example 5 – Write each in scientific notation
1516.2
Place the to the right of the .
.
Count the moved.
3 decimal
places
Write the scientific notation. Delete all the 0s to the right of the
and write the as the .
= 5. 1 6 × 10103
21

15. Example 6 – Write each in scientific notation
0.0000503
Move the to the right of the first non
zero digit.
.
Count the to the right of this
decimal.
5 decimal
places
Write the scientific notation.
= 5. 0 3 × 10−510

16. Example 7 – Write each in scientific notation
0.0000009
Move the to the right of the first non
zero digit.
.
Count the to the right of this
decimal.
7 decimal
places
Write the scientific notation.
= 9 × 10−7
10

17. question
s?

19. Express each in scientific notation.
1. 420000 = 4.2 × 105
2. 928.1 = 9.281 × 102
3. −1870.9 = −1.8709 × 103

20. question
s?

21. E-Math 7
Practice and Application
Test I and II
Page 71

23. Each digit in a number that gives the degree of precision of
measurement is called a . The following are
significant digits.
1. All are significant.

24. All are significant.
Three significant digits: 2, 3, and 5
235

25. All are significant.
Seven significant digits: 1 487 692
1 487 692

26. All are significant.
Four significant digits: 7 829
7 829

27. All are significant.
Six significant digits: 929 282
929 282

28. Each digit in a number that gives the degree of precision of
measurement is called a . The following are
significant digits.
1. All are significant.
2. All located between significant digits.

29. All located between significant digits.
Three significant figures
205

30. All located between significant digits.
Four significant figures
4005

31. All located between significant digits.
Seven significant figures
2904005

32. All located between significant digits.
Four significant figures
100900000

33. Each digit in a number that gives the degree of precision of
measurement is called a . The following are
significant digits.
1. All are significant.
2. All located between significant digits.
3. All zeros at the end of a decimal

34. All zeros at the end of a decimal
Four significant figures
21.30

35. All zeros at the end of a decimal
Four significant figures
5.250

36. All zeros at the end of a decimal
Six significant figures
0.0300070

37. All zeros at the end of a decimal
Two significant figures
0.00010

38. Each digit in a number that gives the degree of precision of
measurement is called a . The following are
significant digits.
1. All are significant.
2. All located between significant digits.
3. All zeros at the end of a decimal
4. All digits of the first factor when a number is
expressed in scientific notation.

39. All digits of the first factor when a number is
expressed in scientific notation
Three significant figures
8.43 × 107

40. All digits of the first factor when a number is
expressed in scientific notation
Four significant figures
2.050 × 10−3

41. Each digit in a number that gives the degree of precision of
measurement is called a . The following are
significant digits.
1. All are significant.
2. All located between significant digits.
3. All zeros at the end of a decimal
4. All digits of the first factor when a number is
expressed in scientific notation.
5. Underscored or specified zeroes of a whole number
ending zeroes

42. Underscored or specified zeroes of a whole
number ending zeroes
Two significant
figures
27 000
Four significant
figures
27 000

43. Underscored or specified zeroes of a whole
number ending zeroes
One significant
figure
800
Three significant
figures
800

45. State the numbers of significant figure in each
number.
1. 0.07
2. 8.043
3. 0.00030500
4. 3 402
5. 81000
One significant figure
Four significant figures
Five significant figures
Four significant figures
Two significant figures

46. question
s?

47. E-Math 7
Practice and Application
Test VI
Page 72