The decimal representation of 345679 /2²× 5⁵ Will be terminated after how many decimals places ??
Please don't post invalid answer please..!!
Answers
Answer:
27.65432
Step-by-step explanation:
345679/4×3125
345679/12500
27.65432
terminating
Given : 345679 / (2² × 5⁵)
To Find : The decimal representation will terminate after how many decimal places
Solution:
345679 / (2² × 5⁵)
Multiply numerator and denominator by 2³
= 345679 × 2³ / (2³ × 2² × 5⁵)
= 345679 × 2³ / (2³ ⁺² × 5⁵)
= 345679 × 2³ / (2⁵ × 5⁵)
= 345679 × 2³ / (2× 5)⁵
= 345679 × 2³ / (10)⁵
= 345679 × 2³ / 100000
The decimal representation will terminate after 5 decimal places.
345679 × 2³ / 100000
= 345679 × 8 / 100000
= 2765432 / 100000
= 27.65432
The decimal representation will terminate after 5 decimal places.
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