Converting decimals into fractions is a common mathematical problem, and mastering the mantra for converting between decimals and fractions is the key to solving this problem. The following is the explanatory copy about the decimal fraction formula:
Decimal fractions, the method to keep in mind.
The denominator is fixed at one and the decimal point is shifted backward.
Integers are added and parentheses multiplied.
Fractionalized decimals, non-decimal decimals.
In special cases, the decimal point is moved backward.
Let's explain in detail what this mantra means:
The denominator is fixed at one": in the process of decimalizing fractions, we usually take the number after the decimal point as a whole, which is equivalent to the denominator in a fraction. This whole is often referred to as "1", which means that we need to find an integer that is equal to the decimal number by multiplying the decimal number so that it can be converted into fractional form.
Decimal point backward": When we convert decimal to fraction, the decimal point needs to be shifted to the right until the number after the decimal point becomes an integer. This process can be achieved by multiplying with the appropriate denominator. For example, 03 can be converted to fractional form 3 10, here we move the decimal point one place to the right.
Integers to be added": In the process of converting decimals to fractions, if the number after the decimal point is greater than or equal to 5, we need to carry the whole number. This process is equivalent to adding 1 to the numerator, and the denominator needs to be increased accordingly. For example, 075 can be converted to 75 100, here we add 1 to the integer part to get 75, and the denominator is increased to 100 accordingly.
Multiply parentheses": When the integer part of the decimal is a non-decimal number, we need to convert the integer part to a decimal number. This process can be achieved by multiplying by the appropriate decimal number. For example, 012 can be converted to 12 100, here we multiply the integer part by 10 to get 12, and the denominator is increased to 100 accordingly.
Fractionalize decimals, non-decimal decimals": When we convert fractions to decimals, we need to convert fractions to decimal numbers if the denominator of the fraction is not a multiple of 10 (i.e. a non-decimal number). This process can be achieved by dividing by the appropriate decimal number. For example, 2 3 can be converted to 0666……Here we divide the numerator by the denominator to get the result 0666……。
Special case note, decimal point backward": In some special cases, the number after the decimal point cannot be multiplied by the appropriate denominator to get an integer, in which case we can move the decimal point backward by one or more places until we get an acceptable integer result. For example, 001 can be converted to 1 100, here we move the decimal point back two places to get the whole number 1.
By mastering the skills and methods of the above formulas, we can quickly convert decimals into fractions, and at the same time, we can easily convert fractions into decimals. This method is not only suitable for basic mathematical calculations, but also for situations that require the processing of numerical data in various fields of scientific computing and engineering. Therefore, mastering the skills of decimal fractions is of great significance for improving mathematical literacy and solving practical problems.
In practical application, we can master the technique of decimal fractions through continuous practice. For example, we can try to convert some common decimal forms into fractions, or take care to use these techniques to simplify the calculation process when solving practical problems. In addition, we can also use modern technology to assist in calculations and verify results, such as using mathematical software or conversion tools to verify that our results are correct.
In conclusion, converting decimal numbers into fractions is an important skill in math calculations. By mastering the skills and methods of the above formulas, we can easily complete this conversion process and improve our mathematical literacy and ability to solve practical problems. Whether in study, work, or daily life, this skill will bring us many conveniences and advantages.
Of course, for a deeper understanding of the conversion between decimal and fraction, it is a good choice to read related books. Here are some books on decimal vs. fraction conversion for your reference:
The Book of Mathematics
This book is an introduction to the history of mathematics, introducing the importance and application of decimals and fractions in the history of mathematics. By reading this book, you can learn about the development of decimals and fractions, as well as their place and role in mathematics. The language of this book is easy to understand, making it suitable for beginners and math enthusiasts alike.
Fundamentals of Mathematics: Decimals and Fractions
This book is a basic tutorial dedicated to decimals and fractions, detailing the concepts, properties, operations, and other aspects of decimals and fractions. By reading this book, you can systematically learn about decimals and fractions, and master the skills of converting between decimals and fractions. This book is suitable for elementary and middle school students and beginners in mathematics.
Math Problem Solving Skills: Decimals and Fractions
This book is a guide to math problem-solving techniques, focusing on how to solve problems and techniques for decimals and fractions. By reading this book, you can learn how to use the knowledge of decimals and fractions to solve various math problems and improve your problem-solving skills. This book is suitable for students with some foundation in mathematics and mathematics enthusiasts.
These books provide basic knowledge and problem-solving skills about decimals and fractions, and by reading these books, you will gain a deeper understanding of the conversion between decimals and fractions, improve your mathematical literacy and problem-solving skills. Whether you are an elementary, middle, or college student, these books will provide you with valuable reference and guidance.