conversion between decimals, fractions and percentages

1. Conversion Between Decimals, Fractions and Percentages

2. Conversion Between Decimals, Fractions and Percentages
Fractions, decimals and percentages are three different ways to express answers
to the question “How much?”.

3. Conversion Between Decimals, Fractions and Percentages
Fractions, decimals and percentages are three different ways to express answers
to the question “How much?”.
A fraction gives the instruction for obtaining a quantity,

4. Conversion Between Decimals, Fractions and Percentages
Fractions, decimals and percentages are three different ways to express answers
to the question “How much?”.
A fraction gives the instruction for obtaining a quantity, for example
3
4

5. Conversion Between Decimals, Fractions and Percentages
Fractions, decimals and percentages are three different ways to express answers
to the question “How much?”.
A fraction gives the instruction for obtaining a quantity, for example
3
4
Divide the unit (1), i.e. the whole, into 4 equal parts

6. Conversion Between Decimals, Fractions and Percentages
Fractions, decimals and percentages are three different ways to express answers
to the question “How much?”.
A fraction gives the instruction for obtaining a quantity, for example
3
4
Divide the unit (1), i.e. the whole, into 4 equal parts
then take 3 parts.

7. Conversion Between Decimals, Fractions and Percentages
Fractions, decimals and percentages are three different ways to express answers
to the question “How much?”.
A fraction gives the instruction for obtaining a quantity, for example
3
4
Divide the unit (1), i.e. the whole, into 4 equal parts
then take 3 parts.
Fractions are easy to understand conceptually so it’s important for mathematics
which emphasis the study of relations among numbers.

8. Conversion Between Decimals, Fractions and Percentages
Fractions, decimals and percentages are three different ways to express answers
to the question “How much?”.
A fraction gives the instruction for obtaining a quantity, for example
3
4
Divide the unit (1), i.e. the whole, into 4 equal parts
then take 3 parts.
Fractions are easy to understand conceptually so it’s important for mathematics
which emphasis the study of relations among numbers. However, it’s cumbersome
to add or subtract fractions because searching for the least common denominator
is difficult for a lengthy list of fractions.

9. Conversion Between Decimals, Fractions and Percentages
Fractions, decimals and percentages are three different ways to express answers
to the question “How much?”.
A fraction gives the instruction for obtaining a quantity, for example
3
4
Divide the unit (1), i.e. the whole, into 4 equal parts
then take 3 parts.
Fractions are easy to understand conceptually so it’s important for mathematics
which emphasis the study of relations among numbers. However, it’s cumbersome
to add or subtract fractions because searching for the least common denominator
is difficult for a lengthy list of fractions.
One way to over come the difficulty of adding or subtracting fractions is to
standardize the denominators to powers of 10, which leads to the decimal system.

10. Conversion Between Decimals, Fractions and Percentages
Fractions, decimals and percentages are three different ways to express answers
to the question “How much?”.
A fraction gives the instruction for obtaining a quantity, for example
3
4
Divide the unit (1), i.e. the whole, into 4 equal parts
then take 3 parts.
Fractions are easy to understand conceptually so it’s important for mathematics
which emphasis the study of relations among numbers. However, it’s cumbersome
to add or subtract fractions because searching for the least common denominator
is difficult for a lengthy list of fractions.
One way to over come the difficulty of adding or subtracting fractions is to
standardize the denominators to powers of 10, which leads to the decimal system.
For example, the decimal number 0.75
means

11. Conversion Between Decimals, Fractions and Percentages
Fractions, decimals and percentages are three different ways to express answers
to the question “How much?”.
A fraction gives the instruction for obtaining a quantity, for example
3
4
Divide the unit (1), i.e. the whole, into 4 equal parts
then take 3 parts.
Fractions are easy to understand conceptually so it’s important for mathematics
which emphasis the study of relations among numbers. However, it’s cumbersome
to add or subtract fractions because searching for the least common denominator
is difficult for a lengthy list of fractions.
One way to over come the difficulty of adding or subtracting fractions is to
standardize the denominators to powers of 10, which leads to the decimal system.
For example, the decimal number 0.75
means 7
10
5
100+ denominators are powers of 10.

12. To convert fractions to decimals, we attach 0’s after the decimal point and
perform long division.
Conversion Between Decimals, Fractions and Percentages

13. Example A. Convert the fractions into a decimal.
8
1
Conversion Between Decimals, Fractions and Percentages
To convert fractions to decimals, we attach 0’s after the decimal point and
perform long division.

14. Example A. Convert the fractions into a decimal.
8
1
)8 1.
Perform long division,
Conversion Between Decimals, Fractions and Percentages
To convert fractions to decimals, we attach 0’s after the decimal point and
perform long division.
attach 0’s
0 0 0

15. Example A. Convert the fractions into a decimal.
4 0
8
1
)8 1.
Perform long division,
.
0 0 0
1
8
2 0
2 5
1 6
Conversion Between Decimals, Fractions and Percentages
4 0
0
0
To convert fractions to decimals, we attach 0’s after the decimal point and
perform long division.
attach 0’s

16. Example A. Convert the fractions into a decimal.
4 0
8
1
)8 1.
Perform long division, we obtain that
.1
8
2 0
2 5
1 6
Conversion Between Decimals, Fractions and Percentages
4 0
0
0
8
1
= 0.125.
To convert fractions to decimals, we attach 0’s after the decimal point and
perform long division.
0 0 0
attach 0’s

17. Example A. Convert the fractions into a decimal.
4 0
8
1
)8 1.
Perform long division, we obtain that
.1
8
2 0
2 5
1 6
Conversion Between Decimals, Fractions and Percentages
4 0
0
0
8
1
= 0.125.
=2
1
Here is a list of common fractions and their decimal expansions:
0.50 =4
1 0.25 =5
1 0.20 =
10
1
0.10
=
20
1 0.05 =
25
1 0.04 =
50
1
0.02 =
100
1 0.01
8
1
= 0.125 8
2
= 0.250 8
3
= 0.375 8
4
= 0.500= 4
1 = 2
1
8
5
= 0.625 8
6 = 0.750 = 4
3
8
7
= 0.875
To convert fractions to decimals, we attach 0’s after the decimal point and
perform long division.
0 0 0
attach 0’s

18. Example A. Convert the fractions into a decimal.
4 0
8
1
)8 1.
Perform long division, we obtain that
.1
8
2 0
2 5
1 6
Conversion Between Decimals, Fractions and Percentages
4 0
0
0
8
1
= 0.125.
=2
1
Here is a list of common fractions and their decimal expansions:
0.50 =4
1 0.25 =5
1 0.20 =
10
1
0.10
=
20
1 0.05 =
25
1 0.04 =
50
1
0.02 =
100
1 0.01
8
1
= 0.125 8
2
= 0.250 8
3
= 0.375 8
4
= 0.500= 4
1 = 2
1
8
5
= 0.625 8
6 = 0.750 = 4
3
8
7
= 0.875
It’s easy to add or subtract decimals numbers–we don’t need to look for common
denominators as the case with fractions.
To convert fractions to decimals, we attach 0’s after the decimal point and
perform long division.
0 0 0
attach 0’s

19. Example B. Calculate the 0.375 x 1600 using fractions.
Conversion Between Decimals, Fractions and Percentages
Some problems are easier to do using fractions.

20. Example B. Calculate the 0.375 x 1600 using fractions.
Conversion Between Decimals, Fractions and Percentages
8
3
0.375 =
Some problems are easier to do using fractions.

21. Example B. Calculate the 0.375 x 1600 using fractions.
8
3
so 0.375 x 1600 =
Conversion Between Decimals, Fractions and Percentages
8
3
0.375 = x 1600 =
Some problems are easier to do using fractions.

22. Example B. Calculate the 0.375 x 1600 using fractions.
8
3
so 0.375 x 1600 =
Conversion Between Decimals, Fractions and Percentages
8
3
0.375 = x 1600 = 600
Some problems are easier to do using fractions.
200

23. Example B. Calculate the 0.375 x 1600 using fractions.
Conversion Between Decimals, Fractions and Percentages
Some problems are easier to do using fractions.
Fact About Shifting the Decimal Points in a Fraction
Given a fraction, if the decimal points of the numerator and the denominator are
shifted in the same direction with the same number of spaces,
the resulting fraction is an equivalent fraction, i.e. it’s the same.
8
3
so 0.375 x 1600 =
8
3
0.375 = x 1600 = 600
200

24. Example B. Calculate the 0.375 x 1600 using fractions.
Conversion Between Decimals, Fractions and Percentages
Some problems are easier to do using fractions.
Fact About Shifting the Decimal Points in a Fraction
Given a fraction, if the decimal points of the numerator and the denominator are
shifted in the same direction with the same number of spaces,
the resulting fraction is an equivalent fraction, i.e. it’s the same.
To change a decimal number of the form 0 . # # # # to a fraction:
1. Put “1.” in the denominator and line up the decimal points.
8
3
so 0.375 x 1600 =
8
3
0.375 = x 1600 = 600
200

25. Example B. Calculate the 0.375 x 1600 using fractions.
Conversion Between Decimals, Fractions and Percentages
Some problems are easier to do using fractions.
Fact About Shifting the Decimal Points in a Fraction
Given a fraction, if the decimal points of the numerator and the denominator are
shifted in the same direction with the same number of spaces,
the resulting fraction is an equivalent fraction, i.e. it’s the same.
To change a decimal number of the form 0 . # # # # to a fraction:
1. Put “1.” in the denominator and line up the decimal points.
0 . # # # #
1 .
8
3
so 0.375 x 1600 =
8
3
0.375 = x 1600 = 600
200

26. Example B. Calculate the 0.375 x 1600 using fractions.
Conversion Between Decimals, Fractions and Percentages
Some problems are easier to do using fractions.
Fact About Shifting the Decimal Points in a Fraction
Given a fraction, if the decimal points of the numerator and the denominator are
shifted in the same direction with the same number of spaces,
the resulting fraction is an equivalent fraction, i.e. it’s the same.
To change a decimal number of the form 0 . # # # # to a fraction:
1. Put “1.” in the denominator and line up the decimal points.
0 . # # # #
1 .
8
3
so 0.375 x 1600 =
8
3
0.375 = x 1600 = 600
200
2. Slide the decimal point of the
numerator to end of the number.

27. Example B. Calculate the 0.375 x 1600 using fractions.
Conversion Between Decimals, Fractions and Percentages
Some problems are easier to do using fractions.
Fact About Shifting the Decimal Points in a Fraction
Given a fraction, if the decimal points of the numerator and the denominator are
shifted in the same direction with the same number of spaces,
the resulting fraction is an equivalent fraction, i.e. it’s the same.
To change a decimal number of the form 0 . # # # # to a fraction:
1. Put “1.” in the denominator and line up the decimal points.
0 . # # # #
1 .
0 . # # # #
1 .
.=
Drag the decimal point
to the end of the number2. Slide the decimal point of the
numerator to end of the number.
8
3
so 0.375 x 1600 =
8
3
0.375 = x 1600 = 600
200

28. Example B. Calculate the 0.375 x 1600 using fractions.
Conversion Between Decimals, Fractions and Percentages
Some problems are easier to do using fractions.
Fact About Shifting the Decimal Points in a Fraction
Given a fraction, if the decimal points of the numerator and the denominator are
shifted in the same direction with the same number of spaces,
the resulting fraction is an equivalent fraction, i.e. it’s the same.
To change a decimal number of the form 0 . # # # # to a fraction:
1. Put “1.” in the denominator and line up the decimal points.
0 . # # # #
1 .
0 . # # # #
1 .
.=
Drag the decimal point
to the end of the number2. Slide the decimal point of the
numerator to end of the number.
3. Pack a “0” for
each move to the right.
8
3
so 0.375 x 1600 =
8
3
0.375 = x 1600 = 600
200

29. Example B. Calculate the 0.375 x 1600 using fractions.
Conversion Between Decimals, Fractions and Percentages
Some problems are easier to do using fractions.
Fact About Shifting the Decimal Points in a Fraction
Given a fraction, if the decimal points of the numerator and the denominator are
shifted in the same direction with the same number of spaces,
the resulting fraction is an equivalent fraction, i.e. it’s the same.
To change a decimal number of the form 0 . # # # # to a fraction:
1. Put “1.” in the denominator and line up the decimal points.
0 . # # # #
1 .
0 . # # # #
1 .
.
.0 0 0 0
=
Drag the decimal point
to the end of the number
then fill in a “0” for each move.
2. Slide the decimal point of the
numerator to end of the number.
3. Pack a “0” for
each move to the right.
8
3
so 0.375 x 1600 =
8
3
0.375 = x 1600 = 600
200

30. Example C. Convert the following decimals to fractions.
a. 0.023
Conversion Between Decimals, Fractions and Percentages

31. Example C. Convert the following decimals to fractions.
a. 0.023
1. Insert “1.” in the denominator
and line up the decimal points.
Conversion Between Decimals, Fractions and Percentages

32. Example C. Convert the following decimals to fractions.
a. 0.023
0 . 0 2 3
1 .
1. Insert “1.” in the denominator
and line up the decimal points.
Conversion Between Decimals, Fractions and Percentages

33. Example C. Convert the following decimals to fractions.
a. 0.023
0 . 0 2 3
1 .
1. Insert “1.” in the denominator
and line up the decimal points.
2. Slide the pair of points in to
the back of the last non-zero digit
in the numerator, and pack 0’s in
the skipped slots in the
denominator.
Conversion Between Decimals, Fractions and Percentages

34. 1. Insert “1.” in the denominator
and line up the decimal points.
2. Slide the pair of points in to
the back of the last non-zero digit
in the numerator, and pack 0’s in
the skipped slots in the
denominator.
Example C. Convert the following decimals to fractions.
a. 0.023
0 . 0 2 3
1 .0 0 0
0 . 0 2 3
1 .
=
.
.
Conversion Between Decimals, Fractions and Percentages

35. 1. Insert “1.” in the denominator
and line up the decimal points.
2. Slide the pair of points in to
the back of the last non-zero digit
in the numerator, and pack 0’s in
the skipped slots in the
denominator.
Example C. Convert the following decimals to fractions.
a. 0.023
0 . 0 2 3
1 .0 0 0 1000
23=
0 . 0 2 3
1 .
=
.
.
Conversion Between Decimals, Fractions and Percentages

36. 1. Insert “1.” in the denominator
and line up the decimal points.
2. Slide the pair of points in to
the back of the last non-zero digit
in the numerator, and pack 0’s in
the skipped slots in the
denominator.
Example C. Convert the following decimals to fractions.
a. 0.023
0 . 0 2 3
1 .0 0 0 1000
23=
0 . 0 2 3
1 .
=
.
.
b. 37. 25
Conversion Between Decimals, Fractions and Percentages

37. 1. Insert “1.” in the denominator
and line up the decimal points.
2. Slide the pair of points in to
the back of the last non-zero digit
in the numerator, and pack 0’s in
the skipped slots in the
denominator.
Example C. Convert the following decimals to fractions.
a. 0.023
0 . 0 2 3
1 .0 0 0 1000
23=
0 . 0 2 3
1 .
=
.
.
b. 37. 25
we only need to convert the decimal 0.25 to a fraction.
Since 37.25 = 37 + 0.25
Conversion Between Decimals, Fractions and Percentages

38. 1. Insert “1.” in the denominator
and line up the decimal points.
2. Slide the pair of points in to
the back of the last non-zero digit
in the numerator, and pack 0’s in
the skipped slots in the
denominator.
Example C. Convert the following decimals to fractions.
a. 0.023
0 . 0 2 3
1 .0 0 0 1000
23=
0 . 0 2 3
1 .
=
.
.
b. 37. 25
0 . 2 5
1 .
we only need to convert the decimal 0.25 to a fraction.
Since 37.25 = 37 + 0.25
0. 2 5 =
Conversion Between Decimals, Fractions and Percentages

39. 1. Insert “1.” in the denominator
and line up the decimal points.
2. Slide the pair of points in to
the back of the last non-zero digit
in the numerator, and pack 0’s in
the skipped slots in the
denominator.
Example C. Convert the following decimals to fractions.
a. 0.023
0 . 0 2 3
1 .0 0 0 1000
23=
0 . 0 2 3
1 .
=
.
.
b. 37. 25
0 . 2 5
1 .
we only need to convert the decimal 0.25 to a fraction.
Since 37.25 = 37 + 0.25
0. 2 5 =
0 . 2 5
1 . 0 0
=
.
.
Conversion Between Decimals, Fractions and Percentages

40. 1. Insert “1.” in the denominator
and line up the decimal points.
2. Slide the pair of points in to
the back of the last non-zero digit
in the numerator, and pack 0’s in
the skipped slots in the
denominator.
Example C. Convert the following decimals to fractions.
a. 0.023
0 . 0 2 3
1 .0 0 0 1000
23=
0 . 0 2 3
1 .
=
.
.
b. 37. 25
0 . 2 5
1 .
we only need to convert the decimal 0.25 to a fraction.
Since 37.25 = 37 + 0.25
0. 2 5 =
0 . 2 5
1 . 0 0
=
.
. 100
25
=
Conversion Between Decimals, Fractions and Percentages

41. 1. Insert “1.” in the denominator
and line up the decimal points.
2. Slide the pair of points in to
the back of the last non-zero digit
in the numerator, and pack 0’s in
the skipped slots in the
denominator.
Example C. Convert the following decimals to fractions.
a. 0.023
0 . 0 2 3
1 .0 0 0 1000
23=
0 . 0 2 3
1 .
=
.
.
b. 37. 25
0 . 2 5
1 .
we only need to convert the decimal 0.25 to a fraction.
Since 37.25 = 37 + 0.25
0. 2 5 =
0 . 2 5
1 . 0 0
=
.
. 100
25
= =
Conversion Between Decimals, Fractions and Percentages
4
1

42. 1. Insert “1.” in the denominator
and line up the decimal points.
2. Slide the pair of points in to
the back of the last non-zero digit
in the numerator, and pack 0’s in
the skipped slots in the
denominator.
Example C. Convert the following decimals to fractions.
a. 0.023
0 . 0 2 3
1 .0 0 0 1000
23=
0 . 0 2 3
1 .
=
.
.
b. 37. 25
0 . 2 5
1 .
we only need to convert the decimal 0.25 to a fraction.
Since 37.25 = 37 + 0.25
0. 2 5 =
0 . 2 5
1 . 0 0
=
.
. 100
25
= = . Therefore 37.25 = 37
Conversion Between Decimals, Fractions and Percentages
4
1
4
1

43. 1. Insert “1.” in the denominator
and line up the decimal points.
2. Slide the pair of points in to
the back of the last non-zero digit
in the numerator, and pack 0’s in
the skipped slots in the
denominator.
Example C. Convert the following decimals to fractions.
a. 0.023
0 . 0 2 3
1 .0 0 0 1000
23=
0 . 0 2 3
1 .
=
.
.
b. 37. 25
0 . 2 5
1 .
we only need to convert the decimal 0.25 to a fraction.
Since 37.25 = 37 + 0.25
0. 2 5 =
0 . 2 5
1 . 0 0
=
.
. 100
25
= = . Therefore 37.25 = 37
4
1
Conversion Between Decimals, Fractions and Percentages
Percentages are fractions with 100 as the denominator. It’s useful to think
of 1% as 1¢ = $0.01 and that 30% as 30 ¢ = $0.30, etc..
4
1

44. The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages

45. The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
To change a decimal number into a #% # . # # #

46. The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert “1.” as the denominator,
To change a decimal number into a #% # . # # #
1 .

47. The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert “1.” as the denominator,
2. move the decimal points two places to the right
to make the denominator “100.”, write the result using the % notation.
To change a decimal number into a #% # . # # #
1 .

48. The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert “1.” as the denominator,
2. move the decimal points two places to the right
to make the denominator “100.”, write the result using the % notation.
To change a decimal number into a #% # . # # #
1 .
# . # # #
1 .
.
.0 0
=
move right, expand denom. to “100”

49. The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert “1.” as the denominator,
2. move the decimal points two places to the right
to make the denominator “100.”, write the result using the % notation.
Example D. a. Convert 4.5 to %. b. Convert 0.045 to %.
To change a decimal number into a #% # . # # #
1 .
# . # # #
1 .
.
.0 0
=
move right, expand denom. to “100”

50. 4.5 =
The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert “1.” as the denominator,
2. move the decimal points two places to the right
to make the denominator “100.”, write the result using the % notation.
Example D. a. Convert 4.5 to %. b. Convert 0.045 to %.
4.5
1.
To change a decimal number into a #% # . # # #
1 .
# . # # #
1 .
.
.0 0
=
move right, expand denom. to “100”

51. 4.5 =
The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert “1.” as the denominator,
2. move the decimal points two places to the right
to make the denominator “100.”, write the result using the % notation.
Example D. a. Convert 4.5 to %. b. Convert 0.045 to %.
4.5
1.
=
4.50.
1.00.
To change a decimal number into a #% # . # # #
1 .
# . # # #
1 .
.
.0 0
=
move right, expand denom. to “100”
move right, expand to “100”

52. 4.5 =
The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert “1.” as the denominator,
2. move the decimal points two places to the right
to make the denominator “100.”, write the result using the % notation.
Example D. a. Convert 4.5 to %. b. Convert 0.045 to %.
4.5
1.
=
4.50.
1.00.
= 450%
Hence 4.50 = 450.%.
To change a decimal number into a #% # . # # #
1 .
# . # # #
1 .
.
.0 0
=
move right, expand denom. to “100”
move right, expand to “100”

53. 4.5 =
The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert “1.” as the denominator,
2. move the decimal points two places to the right
to make the denominator “100.”, write the result using the % notation.
Example D. a. Convert 4.5 to %. b. Convert 0.045 to %.
4.5
1.
=
4.50.
1.00.
= 450% 0.045 = 1.
0.045
Hence 4.50 = 450.%.
To change a decimal number into a #% # . # # #
1 .
# . # # #
1 .
.
.0 0
=
move right, expand denom. to “100”
move right, expand to “100”

54. 4.5 =
The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert “1.” as the denominator,
2. move the decimal points two places to the right
to make the denominator “100.”, write the result using the % notation.
Example D. a. Convert 4.5 to %. b. Convert 0.045 to %.
4.5
1.
=
4.50.
1.00.
= 450% 0.045 = 1. =
0.04.50
1.00. = 4.50%
0.045
Hence 4.50 = 450.%. Hence 0.045 = 4.5%.
To change a decimal number into a #% # . # # #
1 .
# . # # #
1 .
.
.0 0
=
move right, expand denom. to “100”
move right, expand to “100”

55. 4.5 =
The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert “1.” as the denominator,
2. move the decimal points two places to the right
to make the denominator “100.”, write the result using the % notation.
Example D. a. Convert 4.5 to %. b. Convert 0.045 to %.
4.5
1.
=
4.50.
1.00.
= 450% 0.045 = 1. =
0.04.50
1.00. = 4.50%
0.045
Hence 4.50 = 450.%. Hence 0.045 = 4.5%.
To change a decimal number into a #%
To change a #% into a decimal number
# . # # #
1 .
# . # # #
1 .
.
.0 0
=
move right, expand denom. to “100”
move right, expand to “100”

56. 4.5 =
The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert “1.” as the denominator,
2. move the decimal points two places to the right
to make the denominator “100.”, write the result using the % notation.
Example D. a. Convert 4.5 to %. b. Convert 0.045 to %.
4.5
1.
=
4.50.
1.00.
= 450% 0.045 = 1. =
0.04.50
1.00. = 4.50%
0.045
Hence 4.50 = 450.%. Hence 0.045 = 4.5%.
To change a decimal number into a #%
1. write the #% as
To change a #% into a decimal number
#
100
# . # # #
1 .
# . # # #
1 .
.
.0 0
=
move right, expand denom. to “100”
# # #. #
1 0 0.
move right, expand to “100”

57. 4.5 =
The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert “1.” as the denominator,
2. move the decimal points two places to the right
to make the denominator “100.”, write the result using the % notation.
Example D. a. Convert 4.5 to %. b. Convert 0.045 to %.
4.5
1.
=
4.50.
1.00.
= 450% 0.045 = 1. =
0.04.50
1.00. = 4.50%
0.045
Hence 4.50 = 450.%. Hence 0.045 = 4.5%.
To change a decimal number into a #%
1. write the #% as
2. move the two decimal points two places to the left
so the denominator is 1 and the numerator is the answer.
To change a #% into a decimal number
#
100
# . # # #
1 .
# . # # #
1 .
.
.0 0
=
move right, expand denom. to “100”
move right, expand to “100”
# # #. #
1 0 0.

58. 4.5 =
The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert “1.” as the denominator,
2. move the decimal points two places to the right
to make the denominator “100.”, write the result using the % notation.
Example D. a. Convert 4.5 to %. b. Convert 0.045 to %.
4.5
1.
=
4.50.
1.00.
= 450% 0.045 = 1. =
0.04.50
1.00. = 4.50%
0.045
Hence 4.50 = 450.%. Hence 0.045 = 4.5%.
To change a decimal number into a #%
1. write the #% as
2. move the two decimal points two places to the left
so the denominator is 1 and the numerator is the answer.
To change a #% into a decimal number
#
100
# . # # #
1 .
# . # # #
1 .
.
.0 0
=
move right, expand denom. to “100”
# . # # #
1 .
# # #. #
1.
.
0 0. =
move left, reduce denom. to “1”
move right, expand to “100”

59. Conversion Between Decimals, Fractions and Percentages
Example E.
a. Convert 0.35% to a decimal number. b. Convert 3,000 % to a decimal number.

60. Conversion Between Decimals, Fractions and Percentages
Example E.
a. Convert 0.35% to a decimal number. b. Convert 3,000 % to a decimal number.
=
0.35
1 0 0.
0.35% move left to reduce to “1”

61. Conversion Between Decimals, Fractions and Percentages
Example E.
a. Convert 0.35% to a decimal number. b. Convert 3,000 % to a decimal number.
=
0.35
1 0 0.
0.35% move left to reduce to “1”

62. Conversion Between Decimals, Fractions and Percentages
Example E.
a. Convert 0.35% to a decimal number. b. Convert 3,000 % to a decimal number.
=
0.35
1 0 0.
0.35%
Hence 0.35% = 0.0035.
move left to reduce to “1”
= 0.00.35

63. Conversion Between Decimals, Fractions and Percentages
Example E.
a. Convert 0.35% to a decimal number. b. Convert 3,000 % to a decimal number.
=
0.35
1 0 0.
0.35%
Hence 0.35% = 0.0035.
move left to reduce to “1”
= 0.00.35
=
3 0 0 0.
1 0 0.
3,000%

64. Conversion Between Decimals, Fractions and Percentages
Example E.
a. Convert 0.35% to a decimal number. b. Convert 3,000 % to a decimal number.
=
0.35
1 0 0.
0.35%
Hence 0.35% = 0.0035.
move left to reduce to “1”
= 0.00.35
=
3 0 0 0.
1 0 0.
3,000%
= 30.00.
Hence 3,000% = 30.00 or 30.

65. Conversion Between Decimals, Fractions and Percentages
Example E.
a. Convert 0.35% to a decimal number. b. Convert 3,000 % to a decimal number.
=
0.35
1 0 0.
0.35%
Hence 0.35% = 0.0035.
move left to reduce to “1”
= 0.00.35
=
3 0 0 0.
1 0 0.
3,000%
= 30.00.
Hence 3,000% = 30.00 or 30.
Example F.
The cost of a dozen eggs changed from $2.40 to $3.00.
What is the increase in the price? What is the % of increase in the price?

66. Conversion Between Decimals, Fractions and Percentages
Example E.
a. Convert 0.35% to a decimal number. b. Convert 3,000 % to a decimal number.
=
0.35
1 0 0.
0.35%
Hence 0.35% = 0.0035.
move left to reduce to “1”
= 0.00.35
=
3 0 0 0.
1 0 0.
3,000%
= 30.00.
Hence 3,000% = 30.00 or 30.
Example F.
The cost of a dozen eggs changed from $2.40 to $3.00.
What is the increase in the price? What is the % of increase in the price?
The increase in the price is 3.00 – 2.40 = $0.60.

67. Conversion Between Decimals, Fractions and Percentages
Example E.
a. Convert 0.35% to a decimal number. b. Convert 3,000 % to a decimal number.
=
0.35
1 0 0.
0.35%
Hence 0.35% = 0.0035.
move left to reduce to “1”
= 0.00.35
=
3 0 0 0.
1 0 0.
3,000%
= 30.00.
Hence 3,000% = 30.00 or 30.
Example F.
The cost of a dozen eggs changed from $2.40 to $3.00.
What is the increase in the price? What is the % of increase in the price?
The increase in the price is 3.00 – 2.40 = $0.60.
The % of increase in the price is:
0.60the price hike
original price
=
2.40

68. Conversion Between Decimals, Fractions and Percentages
Example E.
a. Convert 0.35% to a decimal number. b. Convert 3,000 % to a decimal number.
=
0.35
1 0 0.
0.35%
Hence 0.35% = 0.0035.
move left to reduce to “1”
= 0.00.35
=
3 0 0 0.
1 0 0.
3,000%
= 30.00.
Hence 3,000% = 30.00 or 30.
Example F.
The cost of a dozen eggs changed from $2.40 to $3.00.
What is the increase in the price? What is the % of increase in the price?
The increase in the price is 3.00 – 2.40 = $0.60.
The % of increase in the price is:
0.60the price hike
original price
=
2.40
= =
1
4
= 0.25 = 25%
6.
24.

69. Conversion Between Decimals, Fractions and Percentages
Example E.
a. Convert 0.35% to a decimal number. b. Convert 3,000 % to a decimal number.
=
0.35
1 0 0.
0.35%
Hence 0.35% = 0.0035.
move left to reduce to “1”
= 0.00.35
=
3 0 0 0.
1 0 0.
3,000%
= 30.00.
Hence 3,000% = 30.00 or 30.
Example F.
The cost of a dozen eggs changed from $2.40 to $3.00.
What is the increase in the price? What is the % of increase in the price?
The increase in the price is 3.00 – 2.40 = $0.60.
The % of increase in the price is:
0.60the price hike
original price
=
2.40
= =
1
4
= 0.25 = 25%
So this is a 25 % increase in the price.
6.
24.

70. Conversion Between Decimals, Fractions and Percentages
Example E.
a. Convert 0.35% to a decimal number. b. Convert 3,000 % to a decimal number.
=
0.35
1 0 0.
0.35%
Hence 0.35% = 0.0035.
move left to reduce to “1”
= 0.00.35
=
3 0 0 0.
1 0 0.
3,000%
= 30.00.
Hence 3,000% = 30.00 or 30.
Example F.
The cost of a dozen eggs changed from $2.40 to $3.00.
What is the increase in the price? What is the % of increase in the price?
The increase in the price is 3.00 – 2.40 = $0.60.
The % of increase in the price is:
0.60the price hike
original price
=
2.40
= =
1
4
= 0.25 = 25%
So this is a 25 % increase in the price.
6.
24.
Question: If the price falls from $3.00 to $2.40, what is the % of price drop?
(Ans: 20%)