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Our next fraction, 1/4, will not quite be so easy to convert. This fraction has unlimited equivalents starting with 2/8, 3/12, and 4/16; but none of them has a 10 in the denominator. The equivalent fraction whose denominator is closest to 10 is 2/8. We need a fraction whose denominator is 10 to go into the 1/10 position. The fraction we are looking for should be closest to, but not higher than 2/8. Beginning with 1/10, this fraction is clearly smaller than 2/8, but it is not the closest. 2/10 is also smaller (because its numerator is the same and its denominator is larger). 3/10, on the other hand, is a larger fraction. How do we know this? 1/4 is equivalent to 3/12, which also has 3 as its numerator, and the denominator 12 is larger than 10, making the fraction smaller. From this, we know that the fraction 1/4 is larger than 2/10 but smaller than 3/10. The closest-under denominator-10 fraction that we seek is thereby 2/10. This gives us 2 for the digit in the 1/10 position.

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