Question

After how many decimal places the decimal expansion of 51/150 will terminate

Answer 1

Answer:

51/150

17/50

0.34

2 place

Answer 2

The decimal expansion  $\frac{51}{150}$  will terminate after 2 decimal places.

Step-by-step explanation:

To find : After how many decimal places the decimal expansion of 51/150 will terminate ?

Solution :

The decimal expansion is terminating when the denominator is in the form of $2^n\times 5^m$ otherwise it is non-terminating.

Factor the denominator,

$\dfrac{51}{150}=\dfrac{51}{2\times3\times 5 \times5}$

$\dfrac{51}{150}=\dfrac{17}{2\times 5^2}$

The denominator is in the required form so it is terminating.

$\dfrac{51}{150}=\dfrac{17\times 2}{2^2\times 5^2}$

$\dfrac{51}{150}=\dfrac{34}{10^2}$

$\dfrac{51}{150}=0.34$

The decimal expansion  $\frac{51}{150}$  will terminate after 2 decimal places.

#Learn more

The decimal expansion of the rational number 33/22.5 will terminates after How many places of decimal

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