DECIMAL TO FRACTION or Fraction to Decimal VICE VERSA.pptx

Conversion of decimal to fraction

1. Converting fractions
into decimal form and
vise versa

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2. Warm Up
Write each fraction in the simplest form.

En |
1. 2/3 “a6 2
/

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3. |
Learn to write fractions as decimals, and
vice versa, and to determine whether a

cl is terminating or repeating.

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4. Vocabulary

Terminating decimal
Repeating decimal

Non-terminating decimal
Non-repeating decimal

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5. mA decimal that ends with a
specific digit

/ =Examples:

=2.6

= 5.3566

= 0.003

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6. = A decimal with one or more
repeating digit

= Examples:

= 0.33333......... or 0.3

m2 777 TT or 2.7

= 37.121212........ or 37.12

= 8.66666.........

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7. =A decimal that does not end or repeat

= Examples:

= / = Approximately
37[4159265358979323846 o:

= \5 = Approximately
2.236067976.........

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8. Non-repeating Decimal

=A decimal that does not repeat
= Examples:

= JU = Approximately
.14159265358979323846.........
2953133313333...

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9. Converting
Fraction
into decimal
Form (First Method)
\

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10. nvert a Fraceoe to a
lly, follow these step:

4 1: Find a number you can
ultiply by the bottom of the
fraction to make it 10, or 100, or
1000, or any 1 followed by Os.

Step 2: Multiply both top and bottom
by that number.

Ss En 3. Then write down just the top
mber, putting the decimal place in
e correct spot (one space from the
ht for every zero in the bottom
mber)

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11. Example 2: Using Mental Math to Write
Fractions as Decimals

Write each fraction as a decimal.

hg ite) Multiply to get a power of
10 ten in the denominator.

74 Multiply to get a power of
ten ín the denominator.

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12. Check It Out: Example 2

| Write each fraction as a decimal.

_6 Multiply to get a power of
10 ten in the denominator.
0

AZ Multiply to get a power of
100 ten ín the denominator.

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13. | Converting fractions
to decimals
( Second Method.)

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14. Example 1: Writing Fractions as Decimals

¡Write each fraction as a decimal. Round to the
nearest hundredth, if necessary.

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15. Check It Out: Example 1

| Write each fraction as a decimal. Round to the
nearest hundredth, if necessary.

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16. The decimals 0.75 and 1.2 in Example 1 are
| terminating decimals because the decimals

| comes to an end. The decimal 0.333...is a
repeating decimal because the decimal
repeats a pattern forever. You can also write a
repeating decimal with a bar over the repeating
part. /

0.333... = 0.3
0.8333... = 0.83
0.727272... = 0.72

\

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17. Example 3: Writing Decimals as Fractions

Write each decimal as a fraction in simplest
form.

A. 0.018 B. 1.55

18 155
~ 1,000 1.55 =100
noi _155 +5
=1,000 + 2 100 +5

9 _ 31 yal
= 500 =39 "5

Reading Math
\\You read the decimal 0.018 as “eighteen thousandths.” 1]

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18. Check It Out: Example 3

Write each decimal as a fraction in simplest
form.

A, 0.015 B. 1.30

£15 130
0.015,< _130
7,000 1.30 = {90
+ - 130+ 10
1,000 + 5 100 + 10
= 3 213 3
200 = à

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19. Terminating
Decimals as
Fractions

20. Th The terminating decimal with n 12.041 is

expressed as a fraction as follows:

12.041

_ 12(1000) + 41
i 1000

_ 12041
~ 1000

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21. An alternative way:

12.041

_ 12.041 x 1000
E 1000

_ 12041
~ 1000

\

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22. Example 2:

0.4689

_ 0.4689 x 10 000
L 10 000

_ 4689
10000

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23. Repeating
decimals as
fractions

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24. BE Steps:

Step 1: Multiply the given 10”
where n is the number of
| digits in the repeating block.

Given: 0.465 x 10° = 465.465
tep 2: Subtract the given

from the result. _
465.465 - 0.465=465

25. Step 3: The given
decimal is equal to the
fraction whose
numerator is the result
in the step 2 and whose
/denominator is 10”-1.

0 A65= 465 _ 465

103-1 999

26. Lesson Quiz (ASSIGNMENT)

| Write each fraction as a decimal.

1. Y 32 2% 2.625
3/4 0.7 4.3% 055
Write each decimal as a fraction in simplest

5.0.42 21 6. 8.625 Sor 82

If your soccer team wins 21 out of 30 games,
hat is your team’s winning rate? 0.70

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