Operations on Decimal Fractions-Multiplication of a Decimal Fraction by a Power of 10

In mathematics, figures can be categorized into various types such as natural number, real number, rational number, and whole number. The decimal number is one of them. The point in between the practitioner part and the whole number is known as the decimal point. This article examines in detail regarding “multiplication of a decimal fraction by a power of 10”.

Relationship between fractions and decimals

Using fractions in daily life has become common, it can be easily described as a part of a whole such as the third quarter of the game, one-third of sugar, half an hour, and so on. The whole part can be denoted as a/b where “a” is a part of b and b denotes the whole part. Similarly, ⅜ indicates that the numerator 3 is a portion of the whole denominator 8. Fractional values of denominators having values like 10, 100, 1000 can be written as a decimal by simply removing the zeros of the denominator and placing a decimal followed by zeros left to the numerator. This is the actual process when it comes to the concern of how to do a “multiplication of a decimal fraction by a power of 10”. In fact, Decimals can be multiplied, divided, added, and subtracted.

Multiplying fraction

When a fractional value gets multiplied by another fractional value, the result is often in the form of a whole number or fraction. A fraction consists of numerator and denominator, thus during fractional multiplication, numerator and denominator are multiplied respectively, for instance, multiplication of fractional value ⅘ * ⅔ is equivalent to (4*2)/(5*3) = 8/15. The multiplication of fractions is not similar to the addition and subtraction of fractions since in multiplication it is not necessary to have a similar denominator. The same is applicable to multiplication of a decimal fraction by a power of 10. Any of the two fractional values can be easily multiplied even if they don’t have a similar denominator.

Moving the decimal point is one of the major parts of learning the decimal system. The relation between decimal and fraction is vital to comprehend to build a strong basis in mathematics. When a figure is expressed in the form of a/b, where a and b are related to whole numbers and b is not equivalent to 0, it is called a fraction. During the multiplication of decimal fractions by the power of 10, the number is getting bigger. Similarly, when the number is getting divided by 10 it is getting smaller. A major concern during the multiplication of fractions is that it can be in proper or improper fractions but it cannot be performed on mixed fractions.

Procedure to multiply a fraction

When the question is “multiplication of a decimal fraction by a power of 10”, one has to determine whether the numeric values are in the form of the proper or improper fraction. Multiplication of fractional values can be denoted as a product of fraction with another faction or an integer with variables. The process of multiplication can be illustrated as follow:

• The numerator must be multiplied with another numerator
• The denominator must be multiplied with another numerator.
• Evaluate the faction in a simpler form if required.

Multiplication in proper fractions

A proper fraction indicates a fractional value in mathematical expression whose numerator is smaller than the denominator. During the “multiplication of a decimal fraction by a power of 10” having two proper fractions, the numerators of both fractions are simply multiplied. Similarly, the denominators of both fractions are multiplied. The resulted value can be further simplified or remain in a faction, for example, multiplication of ⅗ and ⅘ can be expressed as (3*10)/(5*20) = 15/200 =  3/40

Multiplication in improper fractions

An improper fraction indicates a fractional value in mathematical expression whose numerator is larger than the denominator. During the multiplication of two improper fractions, the numerator of both fractions is simply multiplied. Similarly, the denominator of both fractions is multiplied. While the multiplication process of the improper fraction the final result will also come out as an improper fraction.

Properties of multiplication of a decimal fraction by a power of 10

The following attributes are illustrated for the “multiplication of a decimal fraction by a power of 10”

• When the given fraction is multiplied in any order, the result remains the same.

(3/10)*(8/100) = 24/1000 = 3/125

Similarly, (8/1000)*(3/10) = 24/1000 = 3/125

Conclusion

From the above discussion, it can be concluded that both decimals and fractions are two different forms of way to represent numeric values. Fractions can be represented in the form of a/b and b is not equivalent to 0. Decimals and fractions both represent the connection of a portion by the whole. Multiplication of decimal fractions by a power of 10 is one of the various procedures required to evaluate mathematical equations.