Question

Represent the following decimals in rational ( p/q ) form.
1. 0.134 bar
2. 0.237 bar
3. 1.10125 bar
4. 8.325 bar
5. 0.123 bar
6. 0.357 bar
7. 0.0032 bar
8. 0.6315 bar
9. 2.015 bar
10. 1.0049 bar

Answer 1

Answer:

❤All the best❤

@RayyanKashan

Step-by-step explanation:

1.

0.134 bar

Let x = 0.134 bar

x = 0.134134... (1)

Here we have three repeating digits after decimal

so we will multiply both sides of equation one with 1000.

and we will get equation two.

1000x = 134.134134... (2)

Now subtract (1) from (2)

1000x - x = (134.134134...) - (0.134134..)

999x = 134

x = 134/999

Well

0.134 bar = 134/999 already simplest form

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2. 0.237 bar

Let x = 0.237 bar

x = 0.237237... (1)

Here we have three repeating digits after decimal

so we will multiply both sides of equation one with 1000.

and we will get equation two.

1000x = 237.237237... (2)

Now subtract (1) from (2)

1000x - x = (237.237237...) - (0.237237...)

999x = 237

x = 237/999

x = 237/999 ÷ 3/3

x = 79/333

Well

0.237 bar = 237/999 or 79/333 Simplest form

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3.

1.10125

Let x = 1.10125 bar

x = 1.1012510125... (1)

Here we have five repeating digits after decimal

so we will multiply both sides of equation one with 100000.

and we will get equation two.

100000x = 110125.1012510125... (2)

Now subtract (1) from (2)

100000x - x = (110125.1012510125...) - (1.1012510125...)

99999x = 110124

x = 110124/99999

Well

1.10125 bar = 110124/99999

110124/99999 ÷ 9/9

= 12236/11111

Well

1.10125 = 12236/11111

Or

1 and 1125/11111 mixed fraction

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4.

8.325

Let x = 8.325 bar

x = 8.325325... (1)

Here we have three repeating digits after decimal

so we will multiply both sides of equation one with 1000.

and we will get equation two.

1000x = 8325.325325... (2)

Now subtract (1) from (2)

1000x - x = (8325.325325...) - (0.325325...)

999x = 8317

x = 8317/999

Well

8.325bar = 8317/999 simplest form

or

8 and 325/999 mixed fraction

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5.

0.123bar

According to above method we will get

0.123 bar = 123/999

123/999 ÷ 3/3 = 41/333 simplest form

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6.

.357bar

According to the above method we will get

.357bar = 357/999

357/999 ÷ 3/3 = 119/333 in simplest form

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7.

0.0032bar

According to the above method we will get

0.0032bar = 32/9999

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8.

.6315bar

According to above method we will get

0.6315 bar = 6315/9999

6315/9999 ÷ 3/3 = 2105/3333 simplest form

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9.

2.015bar

According to above method we will get

2.015bar = 2013/999

2013/999 ÷ 3/3 = 671/333 Answer

or

2 and 5/333 mixed fraction

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10.

1.0049bar

According to above method we will get

1.0049bar = 10048/9999

or

1 and 49/9999 Mixed fraction

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Note: 1 and 2/3 means 1 2/3 Mixed fraction

❤All the best❤

@RayyanKashan