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May 09, 2023 2:15 pm
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Difficulty:
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81% (01:07) correct
19%
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Which of the following is the smallest value of n such that \(\frac{n}{420}\) is a terminating decimal?
A. 18
B. 21
C. 24
D. 30
E. 42
A. 18
B. 21
C. 24
D. 30
E. 42
May 09, 2023 2:25 pm
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We need n/420 to be a terminating decimal.
A terminating decimal has an end digit (1/2=0.5; 1/8=0.125; 1/5=0.2), where as non terminating decimal has repetitive pattern (1/3=0.3333; 1/7=14.28571).
420=2X2X3X5X7
Considering smallest values:
n=18, n/420= 3/70 or 0.3/7. (Non terminating).
n=21, n/420= 1/20=0.05. (Terminating). Hence, n=21 is the smallest value.
A terminating decimal has an end digit (1/2=0.5; 1/8=0.125; 1/5=0.2), where as non terminating decimal has repetitive pattern (1/3=0.3333; 1/7=14.28571).
420=2X2X3X5X7
Considering smallest values:
n=18, n/420= 3/70 or 0.3/7. (Non terminating).
n=21, n/420= 1/20=0.05. (Terminating). Hence, n=21 is the smallest value.
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