Decimal Numbers in standard form

Introduction: On a number line, decimals are a group of numbers that fall between integers. We can write more precise values of quantifiable things such as length, weight, distance, money, and so on using decimals. The integers or whole numbers to the left of the decimal point are integers, while the decimal fractions to the right of the decimal point are decimal fractions. If we travel from one place to the next, the following place will be (1/10) times smaller, resulting in a value of (1/10)th or tenth place.

Reading Decimal Numbers: There are 2 ways to read a decimal number. The first approach is to read the whole number first, then “point,” and then read the digits of the fractional part separately. It’s a more laid-back approach to decimal reading. For instance, 85.64 equals eighty-five plus six-four. The second method is to read the whole number part first, followed by the fractional part, which is read in the same way as whole numbers but with the last digit’s place value. For example, we can read 85.64 as eighty-five and sixty-four hundredths.

Different Decimal Types

Decimals can be classified into different sorts based on the type of digits after the decimal point. The outcome will be determined by whether the numbers are repeating, non-repeating, or ending. Let’s look at how decimals are categorized into several types.

Terminating decimals are those that do not repeat themselves and end after a certain number of decimal places. For instance, 543.534234, 27.2, and so on.

Non-terminating decimals are those that have an endless number of digits following the decimal point. 54543.23774632439473747…, 827.79734394723…, and so on. Non-terminating decimal numbers can be broken further into two parts:

Recurring decimal numbers: Recurring decimal numbers have digits that repeat at a predetermined interval. For instance, 94346.374374374, 573.636363, and so on.

Non-recurring decimal numbers have digits that never repeat after a set interval. For instance, 743.872367346…, 7043927.78687564…

=> Scientific notation refers to the standard form of a decimal number. It entails expressing a decimal number by its initial digit, followed by a decimal point, and the following digits, multiplied by a power of ten to get the original value. In the usual form of a decimal, the number 4359.892 would be expressed as:

4.359892 × 103

What is the procedure for converting a decimal number to a standard form?

Understanding the decimal numeration system is all that is required to convert a decimal number to a standard form. All we have to do now is multiply by the exact power of ten. Follow the instructions below to accomplish this:

Make a mental note of where the decimal point is in the number. If the value is a full number, after the last digit, add the decimal point. If the number is less than zero, the decimal point must be moved to the right.

Rewrite the decimal point immediately after the first digit in the number if the value is greater than 0, or after the first non-zero digit if the number is less than 0. After the decimal point, write all non-zero digits (include 0s between non-zero digits).

Count how many decimal places the decimal point had to be shifted.

Write the result of step 2 multiplied by 10 to the power of n, where n is the number of decimal places where the decimal point has to be shifted. If the number is less than 0, multiply it by 10 to the power of -n.

Example:

In standard form, write 0.00001467 as follows:

Because this number is less than zero, we must move the decimal point to the right.

After the first non-zero value, we write the decimal point, followed by the rest of the non-zero digits: 1.467

Then we count how many decimal places the decimal point has shifted:

We know the power must be negative because the number is less than 0:

1.467 × 10-5 

Conclusion:

A decimal number is defined as a number that has a decimal point dividing the whole number from the fractional portions in algebra. A value less than one is represented by the digits after the decimal point. To begin, move the decimal separator point n places to place the number’s value within a given range, such as 1 to 10 in normalized notation. If the decimal was moved to the left, add 10n; if the decimal was moved to the right, add 10-n.