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Elementary Mathematical Olympiad: How to Turn Recurring Decimals into Fraction
1 answer
2024-09-20 17:19
Recurring decimals refer to decimals with a repeating fraction, such as 06666 and 314159265358979323846. If you want to convert such decimals into scores, you can follow the following steps: 1 determines the position of the loop section, that is, the difference between the first number and the last number of the decimal part is usually the number sequence of the decimal part when the two numbers are equal. For example, 06666's repeating period is between the 6th and 7th digits of the decimal part, which means 6-7=1, so it can be expressed as 1/2. 2. The number where the loop section is located and the numbers after it are all omitted, and only the decimals are retained to obtain the fraction form. For example, 06666 could be expressed as 1/2(6/6=2/2=1+1/2). 3. If there are multiple cycles after a certain number in the decimal part, you need to first determine the last cycle and then follow the above steps. For example, the loop section of 314159265358979323846 is between the 26th and 27th digits of the decimal part, which is 26-27=-1. Therefore, you need to first determine whether the last loop section is 1 or-1 and then simplify it accordingly. The method of converting a repeating decimal into a fraction needed to determine the last loop section according to the position of the loop section and then simplify it according to the above steps.
Illustrate how to convert a mixed loop decimals into a fraction! thanks
1 answer
2024-09-20 17:17
Mixed repeating decimals referred to decimals with a repeating structure. For example, 1/314159 could be written as 1/3(where 3 is a loop) or 1/314159(where 14159 is a loop). If you wanted to convert the mixed loop decimals into a fraction, you needed to find the loop section where the decimal loop part was located and then divide the loop section into several parts and express it as a fraction. For example, 1/314159 could be written as a fraction: 1/3 = 3/3 = 1 1/314159 = 3/314159 = 114159 Here, the fraction 3 and the 14159 were divided into three parts, which were represented by the fraction 1 and 114159 respectively. Continuing example: 1/520303 can be written as a fraction: 1/5 = 2/5 = 040203 1/520303 = 2/520303 = 040203 Here, the fraction 5 and the 20303 were divided into five parts, which were represented by the scores 040203 and 20303 respectively. By analogy, one could find the loop section where the loop part was located and then divide it into several parts and express it with scores.
How to turn a mixed loop decimals into a fraction Give me an example! thanks
1 answer
2024-09-20 17:11
Mixed repeating decimals meant that the decimals were repeating, such as 066666 or 314159265358979323846. To turn it into a fraction, one needed to find the loop and then split it into two fraction. Here is an example of converting 06666 into a score: ``` 066666 = 02 * 10^(n-1) + 03 * 10^(n-2) + + 06 * 10^(n-n+1) = 2/10 + 3/10 + + 6/10 ``` where n represents the number of loop nodes. In this example, n=4, so: ``` 066666 = 2/10 + 3/10 + 4/10 = 2(1/10) + 3(1/10) + 4(1/10) = 2 + 3 + 4 = 9 ``` Therefore, the mixed loop decimals 066666 could be converted into a fraction of 9.
Why did Shintaro bring Bunno back to Megahiko City as a performer? What had they done in Yang Blaze?
1 answer
2024-09-13 11:11
" Mr. Xiu's Little Jiaoyang " is a modern romance novel written by Qinxue Feiwu. It's a novel about urban life. The general plot of this novel is as follows: Mu Xinyang always thought that there were not so many romance novel plots in this world. He never thought that he would have all of them. Whether it was luck or destiny, the road ahead was unknown. It was right to move forward. Ming Xiu was a man with a higher EQ and IQ than ordinary people. His talent meant that his life would be extraordinary. However, he did not expect that he would be tripped by a small wild grass that was as hot as the sun, and from then on, his fate would change. His dark life had become warm and ordinary because of this blazing sun. Later, someone asked him,"Why did you fall for her in the first place?" He smiled faintly." Mu Xinyang is my only salvation. She is the meaning of my existence." The gaze he gave the camera was gentle and loving, as if it was filled with eternal gentleness…At that time, she, who was sitting at home watching the interview live broadcast, felt her heart skip a beat. He knew, so he knew everything… ---------------------------- " The Ultimate Fairy Doctor of the City " was a novel about urban life written by the author Xia Tiandeng. The general plot of the novel was: He possessed the primeval power of the vast universe, but because of the battle between his family, he had to bear the name of being abandoned. His legs were broken and he had to leave Huahai! When he was on the verge of death, a mysterious old man activated his primordial power to fight on the battlefield! Seven years later, he became the cold and aloof young master who controlled everything and was respected by tens of thousands of people! He returned with a cold and ruthless attitude! ---------------------------- " Return to the World of Quick Transference " was a novel about urban life written by the author who lost his keychain. The general plot of the novel was: After going through countless reincarnations, a male supporting character who had played the role of a bitter love, a crazy villain, a protagonist in a tragedy…Xiang Yang felt that she could bear the word "dedicated". When doing quests, they would always follow the plot and never deviate from the plot. When the character died, they would die without hesitation. The protagonist could not bear to kill him, so he pulled the protagonist's hand and poked himself. The protagonist didn't poke too deeply, but he deliberately moved forward. He had to ensure that he died thoroughly. The missions were all fine, and the Lord God's rating was very high. Why did a bug appear in the mission world after a period of time? Xiang Yang wanted to cry as she looked at the mission score that was dropping like crazy. No, he wouldn't allow it. He wanted to accept the re-engagement and go back to see what was going on! It was definitely the system's suppression. His score could not be so low. What was wrong with this world? Was it finally going to make a move on him, this drama queen? ---------------------------- " The Arrival of the Medical Concubine: Where Did the Tsundere Prince Escape to " was an ancient romance novel written by the author. The general plot of this novel was: How did death taste? He fell into endless darkness, without light or salvation. How did it feel to be resurrected? Her life that should have been a cheat fell into a sweet trap again. If you were the light of a candle, I would fly. But why did you let me know the cruel truth... ---------------------------- " I'm the Sun Emperor in the Mysterious Revival " was a suspense-mystery mystery novel written by the troubled pig-headed teenager. The general plot of the novel was: The Sun Monarch was the Sun God of the Sun, Moon, and Stars Gods. His full name was the Sun Palace Grand Pill Flaming Light Yu Ming Sun Monarch, or the Sun Palace Sun Monarch Xiao Xiao Immortal King. It was also known as the "Thunder Lord of the Sun" and had the saying that "the might of thunder"! In his previous life, the young Taoist boy accidentally reincarnated into the mysterious world of revival and became Yang Jian's high school classmate. He awakened the power of the sun during the ghost knocking on the door. It's the sun!" Gao Yang replied,"The sun cannot be seen! Unforgettable! Unimaginable!" Gao Yang said,"Look at me, do you want to kill me?!" Die!" "Haha, Yang Jian, you're not that good." At night, Gao Yang said,"Brother Legs, save me!" ---------------------------- " The King of City Cultivation Doctors " was a novel about urban life written by one of the authors. The general plot of the novel was: The Godly King of a generation has returned. If you obey me, you will have a revered status and an endless lifespan. If you resist me, you will perish and turn into ashes. ---------------------------- The Utsunomiya Kexue Case Book was a light novel by the author, Shanshui Chaxiang. The general plot of the novel was as follows: In this world where humans and monsters coexisted, Utsunomiya Feiyo was adopted by the Fujiwara family as the last member of the monster-slaying family, the Utsunomiya family. He had a younger brother called Takashi Natsume, and the two were good friends from junior high school. One was called Shizuji Nakamura, and the other was called Monday. He had opened a Utsunomiya Detective Agency in Tokyo, which was opposite his colleague, Maori Detective Agency. There was a barbershop rented downstairs, and Fei Shi often went there to get a haircut. She heard that the boss was a top student who graduated from Lily of the Valley. She wondered if it was true. There was a snack shop in Mi Hua Town that he liked called " Green Pine " and " Fruit ". The little girl in the shop seemed to be looking for her father. The angelic Xiaolan, the gentle Takashi Natsume, the naturally deaf Shouko, the understanding, gentle, and kind Akimi... They were all changing Fei Shi's heart, making him gradually treat the world with gentleness. Damn it, he clearly said that he would hate this world. " Brother Utsunomiya, why did you quit your job as a police officer?" Conan asked Utsunomiya Feishi. "Probably…You don't earn money, right?" Finally, he hated sad endings. 。 ---------------------------- " Smoke and Clouds Scattered Ashes in White Clothes " was an ancient romance novel written by the author, Yanyu Yangui. The general plot of this novel was: In the 15th year of Yuanzhen, Liu Shuying sold the family's fertile land and brought her seriously ill mother to the city to see a doctor. That day, the sun was slanted at the edge of the city wall, and a faint red sprinkled on the passers-by. It was originally a quiet and peaceful scene, but Liu Shuying only saw darkness. The darkness that was like a bottomless abyss made her heart tighten. She shook her head and laughed. Why did she suddenly have such a thought? Shaking her head, Liu Shuying helped her mother into the city. She didn't know that this city would be… Liu Shuying: If you were wrong from the beginning, would you continue? Unfortunately, no one told me the answer. Liu Hanyan thought to herself, What is the purpose of living in this life? ---------------------------- " Love Begins After Losing Feelings in Kyoto " was a light novel written by Vcri. It was a fantasy novel. The general plot of the novel was: "Every time I encounter danger, I meet you. As expected, you like me, right? So, if you don't like me, then why did you appear in my world... If it really didn't work…Can I like you?" " Brother, I can always be with you. I can't see any admiration in your eyes. Even though they are full of affection, it's just to match your facial features." The silhouettes of the white birds gradually intersected with each other. The sun gradually set, and the shadows overlapped and fused together. This was the story of a young man who had lost his feelings for beautiful girls in the capital. ---------------------------- " The Sun Angel of the Full-time Mage's End " was a light novel by the author, Frozen Heavens. The general plot of the novel was: He had traveled across the entire magical plane and lived in this world for fifteen years since he was a baby. Ren Xiu awakened light magic and came to the City of the Undead to unfold his story. He was the leader of the Three Heavenly Kings of Northern City No.1 Middle School, the defender of the city when the sun rose in the night, the executor of the national pillar plan, the proud son of the Miao tribe who awakened the power of the sun, the human god who received the inheritance of the first generation of angels... He was also the deputy leader of the Dark Alliance, the strongest priest of the Saintess, the reformist of the Holy City system, the founder of the Wheel of Finality, and the leader who led the humans to launch a counterattack. Demons ran amok in this world, and humans could only survive in the cracks. "If there's no torch in the future, I'll be the only light!" The light of the Sun Angel kindled hope. Group ID: 1070876293.
How to convert the infinite loop decimals into a fraction? And summarize the general law of converting infinite loop decimals into scores
1 answer
2024-09-13 23:18
The process of converting the infinite loop decimals into a fraction was more complicated and usually required the help of a calculator or other tools. The following is the general rule for converting infinite repeating decimals into fraction forms: 1: Truncated the fraction into a number and then took the module to get a small fraction. For example, for the infinite loop of 1/365249, we can intercept the decimal part into 1, 36524, and 9 and then take the quotient of them to get 1/365249. 2 divided the fraction of a fraction by itself until the quotient was 1 or 0. For example, for the infinite loop fraction 1/365249, we can divide it by 365249 to get the quotient 1/36524, 1/36525, 1/36526, and so on. 3 Multiply the fraction of the loop segment by a number smaller than it until the loop segment no longer appears. For example, for the infinite loop fraction 1/365249, we can multiply it by 365249/365249 to get 1/365250. 4 Multiply the fraction of the loop by a number smaller than it until the loop no longer appears and then convert the result to fraction. For example, for the infinite loop fraction 1/365249, we can multiply it by 365249/365249 to get 1/365250. We can convert it to a fraction of 1/(365249 * 365249). It should be noted that the above rules are only the general method of converting infinite repeating decimals into fraction forms. The specific conversion process may vary according to the position of the repeating fraction, precision requirements, and other factors.
Three fifths of a book has been read, and there are 15 pages left. The number of pages read is a fraction of the number of pages not read
1 answer
2024-09-18 15:44
If a book has been read three-fifths of the way and there are 15 pages left, then the number of pages read is the number of pages not read: Number of pages seen/number of pages not seen = 3/5/4/5 = 3/4 Therefore, the number of pages that had been read was four-thirds of the number of pages that had not been read.
What was the meaning of the ending of the performer of the hidden city? How did Wen Nai revive? Why is Yao back? In the previous episode, Shintaro committed suicide with scissors. What was going on?
1 answer
2024-09-10 10:42
What does the ending of the performer of the hidden city mean? How did Wen Nai revive? Why is Yao back? In the last episode, Shintaro committed suicide with scissors. What happened? In the ending of " The Actor of Megaigin City ", Hano was successfully resurrected and had a thrilling showdown with Shintaro. Haruka returned to reality and reunited with Shintaro. Together, they solved a series of problems in the city. As for the plot of Shintaro committing suicide with scissors, it was because he realized his mistake and decided to give up his life in the process of solving the problem of Megaigin City, but he was finally saved by Yao.
Xiao Ming had read 80 pages of a science and technology book, and there were 31 pages left. The pages that he had read and the pages that he had not read each accounted for a fraction of the total pages of the book.
1 answer
2024-09-11 02:54
The total number of pages in this book is 101. Xiao Ming has read 80 pages and has not read the remaining 31 pages. Therefore, the number of pages that Xiao Ming has read accounts for the total number of pages:80 pages/101 pages =08(copies) The number of pages that have not been read accounts for the total number of pages:31 pages/101 pages =03(copies) Therefore, there were 08 copies and 03 copies for those that Xiao Ming had seen and those that he had not seen.
Excuse me, I bought a jade bracelet worth more than 1,000 yuan from the Tengchong Jade Public Plate Shop today. There's no certificate. Is it true? thanks
1 answer
2024-09-24 15:32
We cannot confirm whether the jade bracelet you purchased is authentic or not because we did not provide the relevant certificate information. The certificate of the jade bracelet was usually...
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