For instance, the number 0.4444 has a repeating decimal of 4. It is a basic repeating decimal in the sense that there's no non-repeating portion to the decimal number. Count how many repeating digits there are in the pattern. Once your equation is written, you will multiply it by 10^y, where y equals the number of repeating digits in the pattern. In the example of 0.4444, there is one digit that repeats, so you will multiply the equation by 10^1. For a repeating decimal of 0.4545, there are two digits that repeat, and you would, therefore, multiply your equation by 10^2. For three repeating digits, multiply by 10^3, etc. Write it out so that x equals the original number. In this instance, the equation is x = 0.4444. Since there's only one digit in the repeating decimal, multiply the equation by 10^1 (which equals 10). In the example where x = 0.4444, then 10x = 4.4444. With the example x = 0.4545, there are two repeating digits, so you multiply both sides of the equation by 10^2 (which equals 100), giving you 100x = 45.4545. You accomplish this by subtracting x from 10x. Remember that whatever you do to one side of the equation must be done to the other, so: 10x 1x = 4.4444 0.4444 On the left side, you have10x - 1x = 9x. On the right side, you have 4.4444 0.4444 = 4 Therefore, 9x = 4 Once you know what 9x equals, you can determine what x equals by dividing both sides of the equation by 9: On the left side of the equation you have 9x 9 = x. On the right side of the equation you have 4/9 Therefore, x = 4/9, and the repeating decimal 0.4444 can be written as the fraction 4/9. Put the fraction in its simplest form (if applicable) by dividing both the numerator and denominator by the greatest common factor. In the example of 4/9, that is the simplest form.
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One-sentence summary -- Locate the repeating decimal. Rewrite the decimal as an equation. Remove the repeating decimal. Solve for x. Reduce the fraction.

In addition to the basic supplies you should already have for your birds, you will need a large cage for the canaries to breed in, a nest for the female to lay its eggs in, and nesting material the female will use to build up the nest. You may also need a light to shine on the cage if your region is getting less than 14 hours of light each day. There are special breeding cages available that first allow the male and female canary to become accustomed to one another without allowing contact. These cages have a divider down the middle that can be removed when you are ready to allow your canaries to mate. Nests for breeding canaries are available from specialty pet supply providers. If you buy a pre-made nest, you will also need to buy your canaries some nesting material that they can add to the pre-made nest. Unless actively breeding, canaries must be kept in their own cages. Males tend to fight and a male might kill the female if she is not ready to breed. Their cages can, however, be kept in the same room. Breeding usually occurs in the Spring. Canaries like to breed when the temperature is around 70 degrees and there are about 14 hours of light. These conditions can be replicated indoors, in order to promote breeding. Male and female canaries act differently when they are ready to breed. Male canaries will usually come into condition before the female. Signs that they're ready to mate include dropping their wings when they sing and singing harsher and louder songs. They may also dance around on their perch and be more territorial when other males are nearby. Females will most often begin to tear paper, as if readying a nest, when they come into condition. The most certain sign of their readiness, however, is when their vent appears red and swollen. They may also raise their tails and appear to squat when males are nearby. Put their cages side by side or place both birds in a special breeding cage that has a central divider. This will get the birds used to each other and their behavior with each other will tell you if they are ready to mate. If you are just using a large cage instead of a breeding cage, simply place the nest in the female's cage. Once the female has begun adding nesting material to her nest, it is a sign that she is getting ready to mate. Nesting canaries should be fed a proper diet that consists of pelleted food, enriched seed, soft food, and additional calcium from a few weeks before breeding until they are done feeding their chicks. A cuttle-bone or grit is recommended to give the hen the additional calcium required for producing healthy eggs. These specialty foods are available through pet supply companies.
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One-sentence summary -- Purchase breeding supplies. Keep canaries separated until time to breed. Watch for signs that the canaries are in "condition," or ready to breed. Place the male and female canaries near each other, but not in the same cage. Add a nest to the female's side of the breeding cage. Feed a proper diet.

Before you can develop an apology, you need to identify what you did to upset the person. It is important to know which of your specific actions led to the person being upset with you. If you are uncertain about why the person is mad at you, you should ask what specific things upset them. Example scenario 1: I embarrassed my friend by making a scene at his party. Example scenario 2: I snapped at my spouse and was irritable and short all day In addition to understanding what you did to upset someone, you also need to understand why you did it. While you don't want to use your intentions as an excuse, your reasons may help you develop your apology by helping you to take responsibility for your actions. Example scenario 1: I made a scene at the party because I was feeling left out and wanted more attention. Example scenario 2: I treated my spouse this way because I did not sleep well the night before and I had a lot of things on my mind. It is important to develop a sense of empathy for the person to whom you are apologizing. Having empathy means that you understand why your actions hurt the other person because you have put yourself in their shoes and imagined their pain. Without empathy, your apology may end up sounding empty and insincere.Before apologizing to someone, take the time to develop your empathy for the person. Imagine if the same thing had happened to you. How would you feel? What would you do? Example scenario 1: If my friend made a scene at a party I was giving, I would feel angry and betrayed. Example scenario 2: If my spouse had snapped at me for no reason and treated me badly all day, I would feel hurt and confused. Apologizing can be hard because it requires you to admit that you have done something wrong. Just remember that by apologizing, you are not admitting to being a bad person. One study found that taking a few moments to affirm your good qualities (in private, before you apologize to someone) can make the apology easier. Try taking a moment to yourself before your next apology, look at yourself in the mirror, and say three things that you like about yourself. If you have many things that you need to say to the person, you may want to write out your apology before you apologize. By writing your apology out, you will have an easier time knowing what you need to say. You can also keep the notes with you when you actually apologize to remind yourself. By taking the time to write out your apology, you will demonstrate to the other person that you have thought long and hard about your mistake. Your apology will be understood as even more sincere as a result. Apologizing in person is preferable. But if you cannot reach the person by phone or in person, you can still email or snail mail your apology to the person.
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One-sentence summary --
Think about what you did to upset the person. Understand why you did what you did. Empathize with the person you wronged. Remember that your mistake does not make you a bad person. Write out your apology.