4/19/2023 0 Comments Fraction converter infinite![]() The number of 9 is consistent with the number of trailing decimal places to be repeated, and the number of 0 is consistent with the number of non-recurring decimal places. Through the above 4 examples, we can see that the denominator is composed of 9 and 0. Example 4Ĩ.1233 153, the decimal point is followed by four non-recurring decimal places of 1233, and then followed by three repeating trailing decimal places of 153. 13Ģ3278 9900 is the initial fraction form of decimal 2.35 13. Example 3Ģ.35 13, the decimal point is followed by two non-recurring decimal places of 35, and then followed by two repeating trailing decimal places of 13. 3ġ92 900 is the initial fraction form of decimal 0.21 3. Example 2Ġ.21 3, the decimal point is followed by two non-recurring decimal places of 21, and then followed by a repeating trailing decimal place of 3. ![]() 3ġ2 90 is the initial fraction form of decimal 0.1 3. Example 1:Ġ.1 3, the decimal point is followed by an non-recurring decimal place of 1, and then followed by a repeating trailing decimal place of 3. If there are other non-recurring decimal places after the decimal point, can the above general formula be used? Similarly, let’s analyze through several examples. Wait a moment, the above three examples are all trailing decimal places to be repeated immediately after the decimal point. N represents the number of trailing decimal places to be repeated. Numerator: Number composed of the integer part and the trailing decimal places to be repeated minus the integer part Denominator: N 9s Therefore, when the decimal point is immediately followed by the trailing decimal places to be repeated, the general formula for converting infinite loop decimals to fractions can be described as: 102, the whole number part is 3, the trailing decimal place to be repeated is 102. 23, the whole number part is 1, the trailing decimal place to be repeated is 23. 6, the whole number part is 0, the trailing decimal place to be repeated is 6. So, what about the numerator? The numerator is equal to the number consisting of the whole number part and the trailing decimal places to be repeated minus the whole number part. By analogy, repeat with N trailing decimal places, the denominator is contained N 9s. Repeat with 3 trailing decimal places, the denominator is 999. Repeat with 2 trailing decimal places, the denominator is 99. Repeat with 1 trailing decimal place, the denominator is a 9. Yes, the number of digits in the denominator is related to the number of trailing decimal places to repeat. 102, and the next step is to simplify the fraction.ĭid you find any rules through observation? 102, soģ099 999 is the initial fraction form of decimal 3. 102, repeat with 3 trailing decimal places. Now, find the greatest common divisor and simplify it to complete the conversion. 23, soġ22 99 is the initial fraction form of decimal 1. 23, repeat with 2 trailing decimal places. Next, find the greatest common divisor and simplify it to complete the conversion. 6.Ħ 9 is the initial fraction form of decimal 0. 6, there is 1 trailing decimal place is repeated. ![]() ![]() So, how to convert an infinite recurring decimal into an integer? Let’s start with a few examples. Usually, decimals and fractions can be converted to each other, let’s see how they are converted.įollow the first step above to convert fractions to integers. For example, 2 5 means that a whole number is divided into five equal parts, and 2 of them are taken. The numerator at the top and the denominator at the bottom. Here, we mainly discuss two kinds of more commonly used decimals, finite decimals and infinite recurring decimals.įraction refers to the fraction of a number to another number, or the ratio of an event to all events. The mathematical symbols π and e are infinite non-recurring decimals. Infinite decimals include: infinite recurring decimals and infinite non-recurring decimals. For example, 0.25 is a pure decimal, 1.53 is a mixed decimal.Īccording to the length of the decimal part, it can be divided into finite decimals and infinite decimals. Numbers whose integer part is not zero are called mixed decimals. The decimal point is in the middle of integer and decimal.Īmong them, the number whose integer part is zero is called pure decimal. Before conversion, we should understand what is a decimal and what is a fraction?ĭecimal is a special form of real number, usually composed of 3 parts: integer part, decimal point and decimal part. ![]()
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