# To convert a decimal to a fraction by vjg9WC

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```									Math 81                                                              Activity # 17

“Converting between Fractions and Decimals”

Your Name: ___________________ Team Member #1__________________

Team Member #2.______________ Team Member #3__________________

Task 1: Convert a decimal to a fraction.

Note: The Key is to read the decimal as you would write the decimal notation in
words.

Problem 1: Convert the decimal 0.6 to a    Problem 2: Convert the decimal 4.75 to a
fraction.                                  fraction.

Solution:   0.7 is read as seven-tenths,   Solution: 4.75 is read as four and
7
and in fraction form it is .               seventy-five hundredths, which refer
10                                          75
to the mixed number 4         . In simplest
7
Hence, 0.7                                                          100
10                                     75     25  3    3
form, 4      4         4 . As a
100     25  4    4
3 19              19
fraction 4  , so 4.75  .
4 4                4

Problem 3: Convert the decimal 0.42 to a fraction.

a) 0.42 is read as ____________________

b) Write it in fraction form _________

c) Can it be simplified? ________. If so, what is the fraction
in simplest form: __________(Show your work below)

d) Therefore, 0.42 
Convert each of the following decimals to a fraction in simplest form.
1)    0.17            2) 0.785                   3) 8.42

7
Problem 4: Convert the decimal 0.15             to a fraction
8
7
Solution:          0.15     is read as fifteen and seven eighths hundredths, and in fraction
8
form it is
7 127
15
8  8 Since the fraction bar representsdivision, we may rewrite it using the division symbol
100 100
127
      100
8
127 1
     
8 100
127

800

Convert the following decimal to a fraction.

2
4)       0.16
3
Task 2: Convert a fraction to a decimal.

Note: To convert a fraction to a decimal. The Key is to divide. Then, round the
decimal to the indicated place value.

7                                      8
Problem 5:Convert the fraction       to a Problem 6:Convert the fraction   to
40                                     3
decimal.                                  decimal. Round to the nearest
hundredth.

Solution:                                   Solution:
Since the fraction bar represents           Again since the fraction bar represents
7                                          8
division, we have     7  40 .             division, we have  8  3 . So we will take 5
40                                         3
So, we will take 7 divided by 40.           divided by 6. Using long division, we

Using long division, we have 40 7 , which   have 3 8 , which the same is
is the same as 40 7.000                                      2.666
3 8.000

0.175                                        6
40 7.000                                        20
40                                           18
300                                           20
28 0                                          18
200                                           20
200                                           18
0                                            2
7                                  Now rounding 2.666 to the nearest
Hence,       0.175
40                                                                8
hundredth, we get 2.67. Hence,  2.67
3
5
Problem 7: Convert the fraction 2       to a decimal. Round to the nearest
6
thousandths.

Solution:                                       Solution:
5 17                                            5      5
Method 1: Since 2            17  6 , using   Method 2: Since 2        2  , using long
6 6                                             6      6
long division we will take 17 divided by 6.     division we will take 5 divided by 6.
2.8333                                        0.8333
6 17.0000                                     6 5.0000
12                                             48
50                                             20
48                                           18
20                                             20
18                                            18
20                                              20
18                                               18
2                                               2
Now rounding 2.8333 to the nearest              Now rounding 0.8333 to the nearest
thousandth, we have 2.833 . Hence,              thousandth, we have 0.833 . Hence,
5                                               5     5
2  2.833                                       2  2   2  0.8333  2.8333
6                                               6     6

Tip: When converting a fraction to a decimal with a denominator that is a multiple
of 10 such as 10, 100, 1000, etc., division is not necessary. In other words, the
decimal notation can be obtained by reading as you would write the fraction in
words.
7
Example: Convert the fraction           to a decimal.
100
7
Solution:      is read as “seven hundredths”. In decimal form it is 0.07 .
100
Convert the following fractions to a decimal. Round to the nearest thousandth
when necessary.
23                                         27
5)                                        6)
1000                                        4

5                                             7
7)                                         8)    4
12                                             9

Task 3: To identify the order relation between a decimal and a fraction.
5
Problem 6: Place the correct symbol, < or >, between the numbers      and 0.312 .
16
Solution:
5                            5
Convert     to a decimal by dividing  0.3125 .
16                           16
Note that 0.312  0.3120 . So comparing the two decimals, we have
0.3125  0.3120
5
Hence,      0.312
16
Place the correct symbol, <, =, or >, between the numbers.
9) 3.08_____3.082                        10)    5.08_____5.80

7                                            5
11)       _____0.583                       12)          _____0.2083
12                                            24
Convert each of the following decimals to a fraction in simplest form.
13)      0.36                14)   4.125                   15)    0.270

16)   0.12
2                17)    0.025                  18)   0.09
2
3                                                           7

Convert each of the following fractions to a decimal. Round to the nearest
hundredth.
2                                          7
19)                                        20)
13                                          6

5                                       75
21)   12                                   22)
6                                      1000

```
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