Question

Выберите из дробей те, которые можно записать в виде конечной десятичной дроби.Покажите, как это сделать:10/14 ,141/60 , 21/75 , 255/136 , 108/45 , 200/6 , 150/780 , 207/920 , 33/375 , 210/560 , 13/3000

Answer 1

10/14;141/60;21/75;255/136;108/45;200/6;150/780;33/357;210/560

Answer 2

Fractions that can be written as finite decimal fractions:

To determine which fractions can be written as finite decimal fractions, we need to check if the denominator of each fraction is divisible by only 2 and/or 5. If the denominator has any other prime factors, the fraction cannot be expressed as a finite decimal fraction.

Let's go through each fraction and check if it can be written as a finite decimal fraction:

1. 10/14: The denominator 14 is divisible by 2, so this fraction can be written as a finite decimal fraction. To convert it, we divide 10 by 14: 10 ÷ 14 = 0.7142857... (repeating decimal). 2. 141/60: The denominator 60 is divisible by 2 and 5, so this fraction can be written as a finite decimal fraction. To convert it, we divide 141 by 60: 141 ÷ 60 = 2.35. 3. 21/75: The denominator 75 is divisible by 5, so this fraction can be written as a finite decimal fraction. To convert it, we divide 21 by 75: 21 ÷ 75 = 0.28. 4. 255/136: The denominator 136 is divisible by 2, so this fraction can be written as a finite decimal fraction. To convert it, we divide 255 by 136: 255 ÷ 136 = 1.875. 5. 108/45: The denominator 45 is divisible by 5, so this fraction can be written as a finite decimal fraction. To convert it, we divide 108 by 45: 108 ÷ 45 = 2.4. 6. 200/6: The denominator 6 is divisible by 2, so this fraction can be written as a finite decimal fraction. To convert it, we divide 200 by 6: 200 ÷ 6 = 33.333333... (repeating decimal). 7. 150/780: The denominator 780 is divisible by 2 and 5, so this fraction can be written as a finite decimal fraction. To convert it, we divide 150 by 780: 150 ÷ 780 = 0.1923076923076923... (repeating decimal). 8. 207/920: The denominator 920 is divisible by 2 and 5, so this fraction can be written as a finite decimal fraction. To convert it, we divide 207 by 920: 207 ÷ 920 = 0.225. 9. 33/375: The denominator 375 is divisible by 5, so this fraction can be written as a finite decimal fraction. To convert it, we divide 33 by 375: 33 ÷ 375 = 0.088. 10. 210/560: The denominator 560 is divisible by 2 and 5, so this fraction can be written as a finite decimal fraction. To convert it, we divide 210 by 560: 210 ÷ 560 = 0.375. 11. 13/3000: The denominator 3000 is divisible by 2 and 5, so this fraction can be written as a finite decimal fraction. To convert it, we divide 13 by 3000: 13 ÷ 3000 = 0.004333333... (repeating decimal).

Based on the above analysis, the fractions that can be written as finite decimal fractions are: - 10/14 - 141/60 - 21/75 - 255/136 - 108/45 - 200/6 - 150/780 - 207/920 - 33/375 - 210/560 - 13/3000

Please note that some of the fractions result in repeating decimals, while others are non-repeating decimals.