China
Africa
Explore chapters and articles related to this topic
Rational Numbers
Published in Nita H. Shah, Vishnuprasad D. Thakkar, Journey from Natural Numbers to Complex Numbers, 2020
Nita H. Shah, Vishnuprasad D. Thakkar
For addition and subtraction, numbers with a fixed number of digits after the decimal point (same for both the operands) can be done like integers, and the decimal point can be inserted at the result at an appropriate place. For example, 1·5 and 2·75 can be added by first converting them to the same number of digits after the decimal place. The numbers get converted to 1·50 and 2·75. Ignoring the decimal point, they become 150 and 275. Integer addition of these numbers gives 425, which after inserting back the decimal point becomes 4·25. For multiplication, numbers are multiplied as if they do not have a decimal point and the decimal point is added at an appropriate place (the sum of the number of digits after the decimal point in both numbers). To multiply 1·5 and 2·75 numbers without the decimal point, 15 and 275 are multiplied to get the result 4125, which becomes 4·125 after inserting the decimal point at three (1+2) places from the rightmost position. Proofs of these processes are left to the reader.
Decimals
Published in Joanne Kirkpatrick Price, Basic Math Concepts, 2018
To convert a decimal to a mixed number: Write the whole number (the number to the left of the decimal point).The number to the right of the decimal point is the numerator of the fraction.The position (place value) of the last number to the right of the decimal point indicates the denominator of the fraction.Reduce the fraction, if possible.
Decimals
Published in John Bird, Bird's Basic Engineering Mathematics, 2021
When multiplying decimal fractions: the numbers are multiplied as if they were integers, andthe position of the decimal point in the answer is such that there are as many digits to the right of it as the sum of the digits to the right of the decimal points of the two numbers being multiplied together.
CGSA optimized LSTM auto encoder for outlier detection
Published in International Journal of Computers and Applications, 2023
Chigurupati Ravi Swaroop, K. Raja
Before outlier detection, pre-processing approaches such as data cleansing and data scaling are applied. In data cleansing, missing or null values are replaced with zero. However, the possibility of null values is lower for the standard benchmark dataset. Data scaling is applied to make data to the common scale. The data is scaled to the common range between 0 and 1 using the min–max approach. It is described as follows: where represents the input value, is the minimum value from the dataset and is the higher value from the dataset. Using the border range minimizes the outlier effect by minimizing the standard deviation. The decimal point of values is shifted by normalizing the decimal scale. It is applied with the following equation. where , represents the input, and represents the integer value. In Z-score normalization, rescaling is applied based on the properties of a standard normalization. In the z-score approach, data is scaled to the standard distribution. The scaled values are obtained with the following equation. where is the standard deviation and represents the sample mean of attribute.