Separate the fractions 2/6, 2/5, 6/13, 1/25, 7/8, and 9/29 into two categories. The two categories are those that can be written as a terminating decimal and those that cannot. I don't understand what a terminating decimal is.
This site has an excellent explantion.
http://www.icoachmath.com/(S(nlrru2551nwvji45sscr2tej))/SiteMap/DictionaryDefinition.aspx?process=sitemap/terminatingdecimal&
A terminating decimal ends after a certain finite number of decinal places, and does not have to be rounded off. An example would be 378 = 0.875
Your selfterminating decimal fractions are: 2/5, 1/25, and 7/8
Yes! That was a perfect explanation. And then what about conjectures?
Thank you both. So how would I form a conjecture of the terminating decimals
A terminating decimal is a decimal number that ends, or terminates, after a certain number of digits. In other words, it has a finite number of digits after the decimal point. For example, the fraction 1/4 is a terminating decimal because it is equal to 0.25, which ends after two decimal places. On the other hand, a fraction like 1/3 is a non-terminating decimal because it can be written as 0.3333..., with the digit 3 repeating endlessly.
To determine whether a fraction can be written as a terminating decimal, you need to examine the denominator (the bottom number). In decimal form, any fraction with a denominator of a power of 10 (e.g., 10, 100, 1000, etc.) can be expressed as a terminating decimal.
Now, let's categorize the given fractions into two groups: those that can be written as a terminating decimal and those that cannot.
1. 2/6: To determine if it can be a terminating decimal, simplify the fraction. Here, 2/6 simplifies to 1/3, which we know is a non-terminating decimal.
2. 2/5: This fraction cannot be simplified any further. The denominator is not a power of 10, so it cannot be a terminating decimal.
3. 6/13: This fraction also cannot be simplified. The denominator is not a power of 10, so it cannot be a terminating decimal.
4. 1/25: This fraction does not simplify further. The denominator is a power of 10 (i.e., 25 = 5^2), so it can be written as a terminating decimal.
5. 7/8: This fraction is in its simplest form. The denominator is not a power of 10, so it cannot be a terminating decimal.
6. 9/29: This fraction does not simplify. The denominator is not a power of 10, so it cannot be a terminating decimal.
In summary:
Terminating decimals: 1/25
Non-terminating decimals: 2/6, 2/5, 6/13, 7/8, 9/29