Decimal

We’ll use a “.” to differentiate a whole integer from fraction, known as a decimal point. For an example, assume you’re going to get a burger. The vendor informs the burger cost as $5 & 70 cents. If you start to describe this sum in a single statistic, you can say the burger costs $5.70. You may be utilizing decimals & not recognizing them in various real-life scenarios. 

Decimals:

On a number line, decimals are the numbers that fall between integers. In mathematics, they are simply an alternative option to signify fractions. We may express more exact result for quantifiable things such as height, mass, length, and financial resources, and so on using decimals. Whole numbers will be to the decimal point’s left side, while decimal fractions are to the right. If we travel from one place to the next, the following position would be (1/12) orders of magnitude lower, resulting in a value of (1/12)th or twelfth value of the place. 

Place Value Table for Decimals

In the occurrence of decimals, the place value framework is similar to that of the representation of whole number for the whole integer component. However, just later the decimal point, a new set of numbers emerges, in which decimal fractions are used to express the value. Each place value is ten times higher than the preceding place value as we move to the left. So, we have tenths (1/10) to the right of one’s position, hundredths (1/100) to the right of tenths. For a better understanding, consider some illustrations of decimal place values. Each digit in the digits 84.654, 7.139, and 23.09 is represented by its place value.

Reading the Decimal Numbers:

A decimal number can be read in two ways. The first method is to read the complete number along with “point,” then read the fractional part’s digits separately. It’s a more relaxed approach to reading decimals. 55.34, for example, is fifty-five plus three-four. The other method would be to read first, the whole number, then the fractional part, which is read in the similar way as whole numbers but also with the last digit’s place value.  We can read 55.34 as fifty-five and thirty-four hundredths, for example. 

Expanded Decimal Form:

Expanded Decimals are decimals that have been multiplied by a factor of ten Decimals, like whole numbers, can be expressed in expanded form. As you may be aware, to express any integer in an expanded view, we must first type the face value. It is then multiplied by the place value of all of the integers in the number, with an additional sign in between. We’ll use the same method to express decimals in expanded form. Let’s use the enlarged form of 34.674 as an example. The very first stage is to list the supplied number’s digits in the decimal place value table, as reflected below.

The place values and face values from each of the numbers in the figure 34.674. As a result, the extended form of 34.674 could be written as follows: 

34.674 = 3 × 10 + 4 × 1 + 6 × 1/10 + 7 × 1/100 + 4 × 1/1000

OR

34.674 = 30 + 3 + 0.6 + 0.07 + 0.004

Rounding Decimals:

When rounding a decimal number towards the closest tenths, the number present in the hundredth place is considered. There are two possibilities for the digit at the hundredth position. Eliminate all the numbers to the right of the tenth place digit if the number is 4 or less, and the remainder is our desired result. If the digit in the hundredth place is 5 or higher, we must first raise the tenth place digit with 1, then eliminate all the digits to its right. 

Consider rounding the decimals for the number 684.8876 to the tenth decimal place. As we can see, the place digit of the hundredth value in 684.8876 is 8. Because 8>5, if we add 1 to the tenths place digit and disregard the remainder to round this number to the next tenth place. As a result, if we round 684.8876 to the tenth decimal place, the result is 684.9.

Conclusion 

We discussed Decimals, Rounding Decimals to the Nearest Tenth, Decimals in Expanded Form, Reading Decimal Numbers, and other related topics through the study material notes on Decimals. We also discussed the Place Value table for Decimals to give you proper knowledge. 

The prefix word “deci” in “decimal” signifies ten. The decimal point should be placed after the one’s place to indicate where the fraction begins. Always consider one digit at the moment from the right of the decimal point for comparing the decimal or fractional component of any decimal value.