Question

After how many decimal places will the decimal representation of the rational number 229 / 2²x5³ terminate ?
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Answer 1

Answer:

after three places it will terminate

Answer 2

Answer:

To find : After how many decimal places will the decimal representation of the rational number 22922×57\frac{229}{2^2\times 5^7}

2

2

×5

7

229

terminate ?

Solution :

The rational number is represented as 22922×57\frac{229}{2^2\times 5^7}

2

2

×5

7

229

Multiply the numerator and denominator by 252^52

5

,

=229×2522×25×57=\frac{229\times 2^5}{2^2\times 2^5\times 5^7}=

2

2

×2

5

×5

7

229×2

5

=229×3227×57=\frac{229\times 32}{2^7\times 5^7}=

2

7

×5

7

229×32

=7328(2×5)7=\frac{7328}{(2\times 5)^7}=

(2×5)

7

7328

=7328(10)7=\frac{7328}{(10)^7}=

(10)

7

7328

=0.0007328=0.0007328=0.0007328

After 7 decimal places will the decimal representation of the rational number 22922×57\frac{229}{2^2\times 5^7}

2

2

×5

7

229

terminate.

#Learn more

The decimal representation of 6/1250 will terminate after how many places of decimals

Step-by-step explanation:

please brainlist me if this helps