Nasleyidn
Answered

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Change
2.215(1 and 5 are recurring/repeating decimals)
in form of​ a/b

Sagot :

Aroojumair2005idn

Answer:

Answer:

2.215=2 43/200

Step-by-step explanation:

Showing the work

Rewrite the decimal number as a fraction with 1 in the denominator

2.215=2.215/1

Multiply to remove 3 decimal places. Here, you multiply top and bottom by 103 = 1000

2.215/1×1000/1000=2215/1000

Find the Greatest Common Factor (GCF) of 2215 and 1000, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 5,

2215÷5/1000÷5=443/200

Simplify the improper fraction,

=2 43/200

In conclusion,

2.215=2 43/200

Answer:

[tex]\frac{731}{330}[/tex]

Step-by-step explanation:

We require 2 equations with the repeating numbers placed after the decimal point.

let x = 2.2151515... ( multiply both sides by 10 and 1000 )

10x = 22.1515.... → (1)

1000x = 2215.1515.... → (2)

Subtract (1) from (2) thus eliminating the repeating decimal

990x = 2193 ( divide both sides by 990 )

x = [tex]\frac{2193}{990}[/tex] = [tex]\frac{731}{330}[/tex]

Thus

2.2151515..... = [tex]\frac{731}{330}[/tex]

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