Math Reflection, Fractions and Decimals

When is it more useful to use fraction or decimal notation?

You should fraction notation over decimal notation when the fraction notation is more convenient or when the decimal notation isn't easy to work with, or has many digits. For example, the 1/9 in decimal notation is 0.11111111111 which is much harder to work with, an 1/3 in 0.33333333333. You should use decimals when there are many digits, like .132435 instead of 132435/1000000.

When comparing two positive whole numbers with different numbers of digits, such as 115 and 37, the one with more digits is greater. Does this rule work for comparing decimals?

No, because 115 > 37, and .115 < .37