Separate the fractions 2/6,2/5,6/13,1/25,7/8and 9/29into two

categories: those that can be written as a terminating
decimal and those that cannot. Write an explanation
of how you made your decisions.
b. Form a conjecture about which fractions can be
expressed as terminating decimals.
c. Test your conjecture on the following fractions:6/12,7/15,28/140,
and 0/7
d. Use the ideas of equivalent fractions and common
multiples to verify your conjecture.

The first thing you need to do is divide all of the fractions' numerators by their denominators -- probably using a calculator.

2/6 = 0.33333333333333333333333333

This is not a terminating decimal.

(Broken Link Removed)

2/6×7/8=

To separate the fractions into two categories, those that can be written as terminating decimals and those that cannot, we need to determine if the denominator of each fraction can be expressed as a power of 2 or a power of 5 or both.

1. For the fraction 2/6, the denominator can be written as 2^1 * 3^1. Since it includes the prime factor 3, it cannot be expressed as a terminating decimal.

2. For the fraction 2/5, the denominator can be written as 5^1. It only includes the prime factor 5, so it can be expressed as a terminating decimal.

3. For the fraction 6/13, the denominator cannot be factored into powers of 2 or 5. Hence, it cannot be expressed as a terminating decimal.

4. For the fraction 1/25, the denominator can be written as 5^2. It only includes the prime factor 5, so it can be expressed as a terminating decimal.

5. For the fraction 7/8, the denominator can be written as 2^3. It only includes the prime factor 2, so it can be expressed as a terminating decimal.

6. For the fraction 9/29, the denominator cannot be factored into powers of 2 or 5. Hence, it cannot be expressed as a terminating decimal.

Based on the above analysis, the fractions 2/5 and 1/25 can be expressed as terminating decimals, while the fractions 2/6, 6/13, 7/8, and 9/29 cannot.

Conjecture: Fractions with denominators that can only be expressed as powers of 2 or powers of 5 (or both) can be expressed as terminating decimals.

To test this conjecture, we can apply it to the fractions 6/12, 7/15, 28/140, and 0/7:

For 6/12, the denominator can be written as 2^2 * 3^1. Since it includes the prime factor 3, it cannot be expressed as a terminating decimal.

For 7/15, the denominator can be written as 3^1 * 5^1. It includes both prime factors 3 and 5, so it cannot be expressed as a terminating decimal.

For 28/140, the denominator can be written as 2^2 * 5^1. It only includes the prime factor 5, so it can be expressed as a terminating decimal.

For 0/7, the denominator can be written as 7^1. It only includes the prime factor 7, so it can be expressed as a terminating decimal.

By testing the conjecture on these fractions, it is verified that fractions with denominators that can only be expressed as powers of 2 or powers of 5 (or both) can be expressed as terminating decimals.