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Multiplying Decimals. Multiply without the decimal point, then re-insert it in the correct spot! Just follow these steps: Multiply normally, ignoring the decimal points. Then put the decimal point in the answer - it will have as many decimal places as the two original numbers combined.
To multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.
How to Multiply Decimals - Steps Line up the numbers on top of each other. Multiply the numbers while ignoring the decimal points. Count up all of the numbers of digits that are located at the right side of the decimal points of the factors. Move the decimal point of the whole number to the left ...
To multiply decimal numbers: Multiply the numbers just as if they were whole numbers. Line up the numbers on the right - do not align the decimal points. Starting on the right, multiply each digit in the top number by each digit in the bottom number, just as with whole numbers. Add the products.
This math introduction video tutorial discusses the process of multiplying decimals that are in the tenths and hundredths place in columns. It explains how to perform simple decimal multiplication ...
Each time we multiply by a power of 10, the decimal point is moved one place to the right. In Table 2, we are dividing the whole number 265,800. by powers of 10. Each time we divide by a power of 10, the decimal point is moved one place to the left.
A binary multiplier is an electronic circuit used in digital electronics, such as a computer, to multiply two binary numbers. It is built using binary adders. A variety of computer arithmetic techniques can be used to implement a digital multiplier. Most techniques involve computing a set of partial products, and then summing the partial products together. This process is similar to the method taught to primary schoolchildren for conducting long multiplication on base-10 integers, but has been modified here for application to a base-2 (binary) numeral system.
The repeating decimal continues with infinitely many nines. In mathematics, 0.999... (also written 0., among other ways), denotes the repeating decimal consisting of infinitely many 9s after the decimal point (and one 0 before it). This repeating decimal represents the smallest number no less than every decimal number in the sequence (0.9, 0.99, 0.999, ...). This number is equal to 1. In other words, "0.999..." and "1" represent the same number. There are many ways of showing this equality, from intuitive arguments to mathematically rigorous proofs. The technique used depends on target audience, background assumptions, historical context, and preferred development of the real numbers, the system within which 0.999... is commonly defined. (In other systems, 0.999... can have the same meaning, a different definition, or be undefined.) More generally, every nonzero terminating decimal has two equal representations (for example, 8.32 and 8.31999...), which is a property of all base representations. The utilitarian preference for the terminating decimal representation contributes to the misconception that it is the only representation. For this and other reasons—such as rigorous proofs relying on non-elementary techniques, properties, or disciplines—some people can find the equality sufficiently counterintuitive that they question or reject it. This has been the subject of several studies in mathematics education.
A repeating or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero. It can be shown that a number is rational if and only if its decimal representation is repeating or terminating (i.e. all except finitely many digits are zero). For example, the decimal representation of becomes periodic just after the decimal point, repeating the single digit "3" forever, i.e. 0.333…. A more complicated example is , whose decimal becomes periodic at the second digit following the decimal point and then repeats the sequence "144" forever, i.e. 5.8144144144…. At present, there is no single universally accepted notation or phrasing for repeating decimals. The infinitely repeated digit sequence is called the repetend or reptend. If the repetend is a zero, this decimal representation is called a terminating decimal rather than a repeating decimal, since the zeros can be omitted and the decimal terminates before these zeros. Every terminating decimal representation can be written as a decimal fraction, a fraction whose divisor is a power of 10 (e.g. ); it may also be written as a ratio of the form (e.g. ). However, every number with a terminating decimal representation also trivially has a second, alternative representation as a repeating decimal whose repetend is the digit 9. This is obtained by decreasing the final non-zero digit by one and appending a repetend of 9. and are two examples of this. (This type of repeating decimal can be obtained by long division if one uses a modified form of the usual division algorithm.) Any number that cannot be expressed as a ratio of two integers is said to be irrational. Their decimal representation neither terminates nor infinitely repeats but extends forever without regular repetition. Examples of such irrational numbers are the square root of 2 and .