2. Conversion Between Decimals, Fractions and Percentages
Fractions, decimals and percentages are three different ways to express answers
to the question βHow much?β.
3. Conversion Between Decimals, Fractions and Percentages
Fractions, decimals and percentages are three different ways to express answers
to the question βHow much?β.
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 βHow much?β.
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 βHow much?β.
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 βHow much?β.
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 βHow much?β.
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 itβs 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 βHow much?β.
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 itβs important for mathematics
which emphasis the study of relations among numbers. However, itβs 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 βHow much?β.
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 itβs important for mathematics
which emphasis the study of relations among numbers. However, itβs 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 βHow much?β.
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 itβs important for mathematics
which emphasis the study of relations among numbers. However, itβs 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 βHow much?β.
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 itβs important for mathematics
which emphasis the study of relations among numbers. However, itβs 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 0βs 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 0βs 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 0βs after the decimal point and
perform long division.
attach 0βs
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 0βs after the decimal point and
perform long division.
attach 0βs
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 0βs after the decimal point and
perform long division.
0 0 0
attach 0βs
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 0βs after the decimal point and
perform long division.
0 0 0
attach 0βs
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
Itβs easy to add or subtract decimals numbersβwe donβt need to look for common
denominators as the case with fractions.
To convert fractions to decimals, we attach 0βs after the decimal point and
perform long division.
0 0 0
attach 0βs
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. itβs 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. itβs the same.
To change a decimal number of the form 0 . # # # # to a fraction:
1. Put β1.β 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. itβs the same.
To change a decimal number of the form 0 . # # # # to a fraction:
1. Put β1.β 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. itβs the same.
To change a decimal number of the form 0 . # # # # to a fraction:
1. Put β1.β 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. itβs the same.
To change a decimal number of the form 0 . # # # # to a fraction:
1. Put β1.β 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. itβs the same.
To change a decimal number of the form 0 . # # # # to a fraction:
1. Put β1.β 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 β0β 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. itβs the same.
To change a decimal number of the form 0 . # # # # to a fraction:
1. Put β1.β 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 β0β for each move.
2. Slide the decimal point of the
numerator to end of the number.
3. Pack a β0β 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 β1.β 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 β1.β 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 β1.β 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 0βs in
the skipped slots in the
denominator.
Conversion Between Decimals, Fractions and Percentages
34. 1. Insert β1.β 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 0βs 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 β1.β 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 0βs 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 β1.β 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 0βs 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 β1.β 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 0βs 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 β1.β 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 0βs 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 β1.β 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 0βs 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 β1.β 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 0βs 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 β1.β 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 0βs 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 β1.β 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 0βs 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 β1.β 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 0βs 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. Itβs useful to think
of 1% as 1Β’ = $0.01 and that 30% as 30 Β’ = $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 β1.β 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 β1.β as the denominator,
2. move the decimal points two places to the right
to make the denominator β100.β, 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 β1.β as the denominator,
2. move the decimal points two places to the right
to make the denominator β100.β, write the result using the % notation.
To change a decimal number into a #% # . # # #
1 .
# . # # #
1 .
.
.0 0
=
move right, expand denom. to β100β
49. The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert β1.β as the denominator,
2. move the decimal points two places to the right
to make the denominator β100.β, 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 β100β
50. 4.5 =
The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert β1.β as the denominator,
2. move the decimal points two places to the right
to make the denominator β100.β, 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 β100β
51. 4.5 =
The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert β1.β as the denominator,
2. move the decimal points two places to the right
to make the denominator β100.β, 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 β100β
move right, expand to β100β
52. 4.5 =
The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert β1.β as the denominator,
2. move the decimal points two places to the right
to make the denominator β100.β, 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 β100β
move right, expand to β100β
53. 4.5 =
The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert β1.β as the denominator,
2. move the decimal points two places to the right
to make the denominator β100.β, 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 β100β
move right, expand to β100β
54. 4.5 =
The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert β1.β as the denominator,
2. move the decimal points two places to the right
to make the denominator β100.β, 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 β100β
move right, expand to β100β
55. 4.5 =
The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert β1.β as the denominator,
2. move the decimal points two places to the right
to make the denominator β100.β, 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 β100β
move right, expand to β100β
56. 4.5 =
The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert β1.β as the denominator,
2. move the decimal points two places to the right
to make the denominator β100.β, 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 β100β
# # #. #
1 0 0.
move right, expand to β100β
57. 4.5 =
The conversion between decimal numbers and percentages is done by shifting
decimal points.
Conversion Between Decimals, Fractions and Percentages
1. insert β1.β as the denominator,
2. move the decimal points two places to the right
to make the denominator β100.β, 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 β100β
move right, expand to β100β
# # #. #
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 β1.β as the denominator,
2. move the decimal points two places to the right
to make the denominator β100.β, 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 β100β
# . # # #
1 .
# # #. #
1.
.
0 0. =
move left, reduce denom. to β1β
move right, expand to β100β
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 β1β
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 β1β
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 β1β
= 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 β1β
= 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 β1β
= 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 β1β
= 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 β1β
= 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 β 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 β1β
= 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 β 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 β1β
= 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 β 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 β1β
= 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 β 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 β1β
= 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 β 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%)