Courses
Courses for Kids
Free study material
Offline Centres
More Last updated date: 09th Dec 2023
Total views: 279.9k
Views today: 4.79k

# The decimal expansion of $\dfrac{{51}}{{{2^3} \times {5^2}}}$ will terminate after how many decimal places? Verified
279.9k+ views
Hint: In the given integer, if the factors of denominator of the given rational number (p/q) is in the form of ${2^m}{5^n}$, where m and n are non-negative integer, then the decimal expression of the rational number is terminating otherwise they will not terminating and they repeat continuously.

Complete step by step solution:
Euclid Division Lemma: It states that if we have two positive integers a and b, then there exist unique integers q and r which satisfies the condition $a = bq + r$, where $\text{0 < r < b}$.
Given
$= \dfrac{{51}}{{{2^3} \times {5^2}}}$
Or we can write as
$= \dfrac{{51}}{{8 \times 25}}$
$= \dfrac{{51}}{{200}}$
Further solving it. we get,
$= 0.255$
Hence, $\dfrac{{51}}{{{2^3} \times {5^2}}}$ will terminate after three decimals.