• Title/Summary/Keyword: terminating decimal

Search Result 3, Processing Time 0.017 seconds

Problems and Alternatives on Teaching for Repeating Decimal (순환소수 지도에서의 문제점과 해결방안)

  • Lee, Kang-Sup;Uhm, Gyu-Yeon
    • School Mathematics
    • /
    • v.9 no.1
    • /
    • pp.1-12
    • /
    • 2007
  • The purpose of this study is searching for the problems and alternatives on teaching for repeating decimal. To accomplish the purpose, we have analyzed the fifth, sixth, and seventh Korean national curriculums, textbooks and examinations for the eighth grade about repeating decimal. W also have analyzed textbooks from USA to find for alternatives. As the results, we found followings. First, the national curriculums blocked us verifying the relation between rational number and repeating decimal. Second, definitions of terminating decimal, infinite decimal, and repeating decimal are slightly different in every textbooks. This leads seriously confusion for students examinations. The alternative on these problems is defining the terminating decimal as following; decimal which continually obtains only zeros in the quotient. That is, we have to avoid the representation of repeating decimal repeated nines under a declared system which apply an infinite decimal continually obtaining only zeros in the quotient. Then, we do not have any problems to verify the following statement. A number is a rational number if and only if it can be represented by a repeating decimal.

  • PDF

A Thought on Dealing with Repeating Decimals and Introducing Irrational Numbers (in the Middle School Mathematics) (중학교에서 순환소수 취급과 무리수 도입에 관한 고찰)

  • 김흥기
    • Journal of Educational Research in Mathematics
    • /
    • v.14 no.1
    • /
    • pp.1-17
    • /
    • 2004
  • According to the 7-th curriculum, irrational number should be introduced using repeating decimals in 8-th grade mathematics. To do so, the relation between rational numbers and repeating decimals such that a number is rational number if and only if it can be represented by a repeating decimal, should be examined closely Since this relation lacks clarity in some text books, irrational numbers have only slight relation with repeating decimals in those books. Furthermore, some text books introduce irrational numbers showing that $\sqrt{2}$ is not rational number, which is out of 7-th curriculum. On the other hand, if we use numeral 0 as a repetend, many results related to repeating decimals can be represented concisely. In particular, the treatments of order relation with repeating decimals in 8-th grade text books must be reconsidered.

  • PDF

Consideration on Shielding Effect Based on Apron Wearing During Low-dose I-131 Administration (저용량 I-131 투여시 Apron 착용여부에 따른 차폐효과에 대한 고찰)

  • Kim, Ilsu;Kim, Hosin;Ryu, Hyeonggi;Kang, Yeongjik;Park, Suyoung;Kim, Seungchan;Lee, Guiwon
    • The Korean Journal of Nuclear Medicine Technology
    • /
    • v.20 no.1
    • /
    • pp.32-36
    • /
    • 2016
  • Purpose In nuclear medicine examination, $^{131}I$ is widely used in nuclear medicine examination such as diagnosis, treatment, and others of thyroid cancer and other diseases. $^{131}I$ conducts examination and treatment through emission of ${\gamma}$ ray and ${\beta}^-$ ray. Since $^{131}I$ (364 keV) contains more energy compared to $^{99m}Tc$ (140 keV) although it displays high integrated rate and enables quick discharge through kidney, the objective of this study lies in comparing the difference in exposure dose of $^{131}I$ before and after wearing apron when handling $^{131}I$ with focus on 3 elements of external exposure protection that are distance, time, and shield in order to reduce the exposure to technicians in comparison with $^{99m}Tc$ during the handling and administration process. When wearing apron (in general, Pb 0.5 mm), $^{99m}Tc$ presents shield of over 90% but shielding effect of $^{131}I$ is relatively low as it is of high energy and there may be even more exposure due to influence of scattered ray (secondary) and bremsstrahlung in case of high dose. However, there is no special report or guideline for low dose (74 MBq) high energy thus quantitative analysis on exposure dose of technicians will be conducted based on apron wearing during the handling of $^{131}I$. Materials and Methods With patients who visited Department of Nuclear Medicine of our hospital for low dose $^{131}I$ administration for thyroid cancer and diagnosis for 7 months from Jun 2014 to Dec 2014 as its subject, total 6 pieces of TLD was attached to interior and exterior of apron placed on thyroid, chest, and testicle from preparation to administration. Then, radiation exposure dose from $^{131}I$ examination to administration was measured. Total procedure time was set as within 5 min per person including 3 min of explanation, 1 min of distribution, and 1 min of administration. In regards to TLD location selection, chest at which exposure dose is generally measured and thyroid and testicle with high sensitivity were selected. For preparation, 74 MBq of $^{131}I$ shall be distributed with the use of $2m{\ell}$ syringe and then it shall be distributed after making it into dose of $2m{\ell}$ though dilution with normal saline. When distributing $^{131}I$ and administering it to the patient, $100m{\ell}$ of water shall be put into a cup, distributed $^{131}I$ shall be diluted, and then oral administration to patients shall be conducted with the distance of 1m from the patient. The process of withdrawing $2m{\ell}$ syringe and cup used for oral administration was conducted while wearing apron and TLD. Apron and TLD were stored at storage room without influence of radiation exposure and the exposure dose was measured with request to Seoul Radiology Services. Results With the result of monthly accumulated exposure dose of TLD worn inside and outside of apron placed on thyroid, chest, and testicle during low dose $^{131}I$ examination during the research period divided by number of people, statistics processing was conducted with Wilcoxon Signed Rank Test using SPSS Version. 12.0K. As a result, it was revealed that there was no significant difference since all of thyroid (p = 0.345), chest (p = 0.686), and testicle (p = 0.715) were presented to be p > 0.05. Also, when converting the change in total exposure dose during research period into percentage, it was revealed to be -23.5%, -8.3%, and 19.0% for thyroid, chest, and testicle respectively. Conclusion As a result of conducting Wilcoxon Signed Rank Test, it was revealed that there is no statistically significant difference (p > 0.05). Also, in case of calculating shielding rate with accumulate exposure dose during 7 months, it was revealed that there is irregular change in exposure dose for inside and outside of apron. Although the degree of change seems to be high when it is expressed in percentage, it cannot be considered a big change since the unit of accumulated exposure dose is in decimal points. Therefore, regardless of wearing apron during high energy low dose $^{131}I$ administration, placing certain distance and terminating the administration as soon as possible would be of great assistance in reducing the exposure dose. Although this study restricted $^{131}I$ administration time to be within 5 min per person and distance for oral administration to be 1m, there was a shortcoming to acquire accurate result as there was insufficient number of N for statistics and it could be processed only through non-parametric method. Also, exposure dose per person during lose dose $^{131}I$ administration was measured with accumulated exposure dose using TLD rather than through direct-reading exposure dose thus more accurate result could be acquired when measurement is conducted using electronic dosimeter and pocket dosimeter.

  • PDF