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Decimals are used to express fractions and whole numbers simultaneously. In the concept of decimals, we will separate the whole number from the fraction by inserting “.” It is called a decimal point. For example, you are going to take a can of juice. The seller tells you the price of a can of juice is $4 and 50 cents. In this case, you will say that the price of juice’s can is $4.50
In this article, we will discuss decimal numbers, real-life situations of decimal numbers and their type.
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What are Decimals?
Decimals on the number line are also a set of numbers that lie between the whole numbers. Decimals are also another form of writing fractions. It is because of the decimals that we can express more such quantities like measurement, money, distance, and weight more accurately. The numbers on the left of the decimal point are called integers or whole numbers while those on the right of the decimal point are called decimal fractions. If we move to the right of one’s count place the next place will be (1/10)th or tenth place of value.
Decimal Number System Under Place Value
The place value system under study for decimals concerning the whole number part remains the same as the normal whole number place value system. However, beyond the decimal point it is a different format which has numbers that are denoted using decimal fractions. It is seen that as we go towards the left, each place is 10 times of the previous place value. Thus, it is seen that to the right of one’s place, students have tenths (1/10) and to the right of tenths other hundredths (1/100) etc.
Let us look at some examples of decimal place values for better understanding of this topic. The place values and the numerals of the numbers 67.876, 3.660 and 1.06 are analysed in detail.
| Tens | Ones | Decimal point | Tenths | Hundreds | Thousandth |
| 6 | 7 | . | 8 | 7 | 6 |
| 3 | . | 6 | 6 | 0 | |
| 3 | 1 | . | 0 | 6 |
Reading Decimal Numbers
A decimal number may be read in two possible manners. One way is first to read all of the numbers before the decimal then say a verbal ‘point’ and then read each of the digits in the decimal’s fractional triples one by one. This is the more comfortable way to express decimals. An example of this way is described below. Let us consider the number 85.64, it can be expressed as eighty-five point six-four. The second or even more reasonable way is to say first the large whole number followed by the word ‘and’ and then the fraction part just the same but having the last digit as a numerator and telling where the denominator belongs. For example, this reading is also possible: eighty-five and sixty-four hundredths.
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Decimal in Expanded Form
As we have seen whole numbers, decimals can be written in expanded form. We all know that to obtain any number’s expanded form, we only need to write its face value multiplied by place value and sum it with an additional sign. For example, let’s write 71.532 in expanded form. We just put the digits of the given number on the Place value chart and we will write it in decimal form as shown below:
| Tens | Ones | Decimal points | Tenths | Hundredth | Thousandths |
| 7 | 1 | . | 5 | 3 | 2 |
As we can observe, the place values are clearly marked along with the face values of each of the digits of the number 71.532. So, the expanded form 71.532 can be expressed in the following way:
71.532 = 7 × 10 + 1 × 1 + 5 × 1/10 + 3 × 1/100 + 2 × 1/1000
OR
71.532 = 7× 10 + 1 × 1 + 1+ 0.5 + 0.03 + 0.002.
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Rounding Decimal to the Nearest Tenths
When a decimal number has to be rounded to the nearest tenths, then we take the digit at the hundredth place into consideration. The digit which is at the hundredth place can at most have two possible variations. To start with, if that number is 4 or less, then just take away the other digits to the right of the tenth place digit and the remaining part is our desired result.
If the 0.01 value has a figure of 5 or more, there will be a need to add one extra to the tenth place figure because of numbers rounded upwards and then all other values located on the right of this tenths value will not exist anymore. In 864.27446, eight is the hundredth number. This is known as “the hundredths number” and it denotes the hundredth place quantity found in the number. Since 8>4, let us round this off at the nearest tenth part. Accordingly, the tenth figure will be incremented by 1 and everything else will be eliminated. Thus, 864.27446 can be rounded up to its closest tenth which is thereby 864.3.
Comparing decimals
To compare decimal numbers, follow these simple steps:
- Compare the Whole Numbers: Start by comparing the whole number parts of the decimals. The number with the larger whole number is automatically greater. If the whole numbers are different, there’s no need to compare further.
- Compare Decimal Places: If the whole numbers are equal, move to the decimal part. Start by comparing the digits at the tenth place (the first digit after the decimal). If they are equal, continue to the next place value (hundredths, thousandths, etc.), comparing each digit until you find a difference.
Example: Let’s compare 23.789 and 23.759.
- First, compare the whole numbers: 23 = 23, so they are equal.
- Next, compare the tenth place: both have 7, so they are still equal.
- Move to the hundredth place: compare 8 and 5. Since 8 > 5, we conclude that 23.789 is greater than 23.759.
Thus, 23.789 > 23.759.
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Types of Decimals
Decimals can be classified into different categories based on the pattern of digits that appear after the decimal point. Here’s a breakdown of the main types of decimals:
- Terminating Decimals: These decimals have a finite number of digits after the decimal point and eventually come to an end. They do not repeat.
Examples: 543.534234, 27.2.
- Non-Terminating Decimals: These decimals have an infinite number of digits after the decimal point and never end. Non-terminating decimals can be further divided into two subtypes:
- Recurring Decimals: In these decimals, one or more digits repeat in a fixed pattern indefinitely.
Examples: 94346.374374374…, 573.636363…
- Non-Recurring Decimals: These decimals do not have a repeating pattern. The digits continue without repeating in any set order.
Examples: 743.872367346…, 7043927.78687564…
Interesting Facts about Decimals
- The term “decimal” comes from the prefix “deci,” which means ten, indicating the base-10 number system that decimals use.
- Always place the decimal point right after the ones place to clearly separate the whole number from the fractional part. This helps identify where the fractional values begin.
- To compare the fractional part of any decimal, evaluate one digit at a time starting from the first digit after the decimal point (tenths, hundredths, etc.). For example, in comparing 4.109 and 4.2, observe the tenth place: since 1 < 2, we conclude that 4.109 < 4.2.
FAQs on Decimals
What are decimals?
Decimals are numbers that consist of a whole number part and a fractional part separated by a decimal point. They are used to represent fractions in a base-10 system, making it easier to work with values less than one, such as 0.5, 3.14, and 7.89.
How do you compare decimal numbers?
To compare decimals, start by comparing the whole number of parts. If they are equal, compare the digits after the decimal point one by one, beginning with the tenth place, until you find a difference.
What is the difference between terminating and non-terminating decimals?
Terminating decimals have a finite number of digits after the decimal point and come to an end (e.g., 4.25). Non-terminating decimals continue infinitely and can either have repeating patterns (recurring) or no repeating pattern (non-recurring).
