A fraction of the denominator in the multiples of ten gives us a decimal number. When we learn about these numbers, we take into consideration the place value of numbers after the decimal. As an essential part of Arithematics, decimals find immense importance in every calculation. Here we shall understand the system of writing numbers.

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## Decimal Numbers and Place Values

Decimals denote those numbers which are smaller than one. To understand this, you need to remember the smallest thing used by you. For example, consider the smallest pencil used by you. When you measure this pencil on a scale, what do you notice?

It measures some points greater than 3 cm and less than 4 cm. For accuracy when we measure it on a scale we find it to measure 3.6 cm. See in the figure below:

When we see a scale we see that 1 cm has 10 parts, and our pencil lies between these parts. So, from the scale, we know that 1 cm = 10 parts! These 10 parts are said to be millimetres. Therefore, 1 cm = 10 millimeters or 10 mm. To understand the concept of decimals, see the following figure:

Decimals are a representation of fractions. This can be illustrated by the figure. In the above figure, the first square represents a unit number while the third denotes the same square divided into parts. Every square in the third square is a representation of decimals. The decimal system is mostly used in currency or measurement denotations.

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Understanding Tenth and Hundredth Part of a Number

## Tenths and Hundredths

When we write a number, the place value of such decimal starts from tenths place reason being the theory of denominator. When a non-divisible number is divided by 10 the answer that we get is a decimal number with tenths place value. For example: 23/10 = 2.3

Similar is the situation with hundredths and thousandths place value in decimal numbers. The place value of the decimal depends on the number it is divided by. Suppose a number is divided by hundred, then the place value of the decimal is a hundredth, likewise is the case of thousandths. For example: 421/100 = 4.21

For example in, 5321/1000= 5.321, can you guess the place value of 1?Â The place value of 1 here is at thousandths.

## Decimal’s Place Values

Have you noticed the difference in analyzing place values in whole numbers and decimal numbers. In whole numbers, the place value is examined from the right to left of the number. But, in decimals, the place value analysis follows the opposite direction. The decimal point (.) here is the ones place while the following decimals start from tenths, hundredths and so on.

The point to be noted here is that in whole numbers the greater the place values the larger is the number. But in decimals the larger the place value of the smaller is the decimal number. This means that the farther a number from the decimal point on the left, the lower is its value.

One more thing to be noted here is that while verbal expression we speak of the whole numbers denoting their place values, but in the decimals part we express each number as an individual. Expressing them like whole numbers is a wrong way of denoting decimals.

For example: In a number, 121.75 when we have to express the number verbally we say it to be One HUNDRED and Twenty-oneÂ point (decimal) Seven Five. This case, however, does not fit in with currencies! For currencies, we speak both whole number and decimal numbers with their place values.

## Uses of Decimals

Decimals are used in place of fractions. When weÂ intend to write any part of a unit object, instead of writing it in fractional form, we write it in the decimal form.

### In Temperature

For example, how do you write 25 and 1/2 degree in decimal form?Â We write it as 25.5Â°. Writing temperature in decimals is easier than writing the same in fractionals. Here we need to remember that 1Â° temperature is divisible in 10 parts.

### In Money

Similar is the case with money. When we write the cost of an object we write it as Rs 30.50. Here the number afterÂ decimal point denotes paise. We already know that Re 1 = 100 paise. This means that 100 paiseÂ make Re 1. So when we write .50 we mean it to be half of one Rupee.

Guess the denotation for .25 Ps. For .25 Ps we mean one-quarter of 100 paise i.e 1Re. Do you now understand why a decimal is put between Rupees and Paises?Â This is not just the case with the Indian currency, rather decimal’s are used in currency throughout the world.

### In Measurement

Now let’s come to measurements. As discussed earlier 1cm = 10 mm, this we see every day on the scale, but with larger measurements, the unit system stands as follows:

- 1 meter = 100 cm
- 1 kilometer = 1000 meter

So when we write 23.46 cm we intend to write 23 m 46 cm. As 1 m = 100 cm, the measurement in decimals here is in tenths and hundredths place value. Expressing a number in decimal’s form needs understanding. The only thing to remember here is that the place values in decimals signify part that these numbers make.

## Solved Examples for You

**Question 1: Which of the following shows the correct order of ascending numbers:**

**0.004, 0.04, 0.4, 4.0****4.0, 0.4, 0.04, 0.004****0.4, 0.4, 4.0, 0.004****None**

**Answer:** Option A. 0.004, 0.04, 0.4, 4.0, The farther is the digit from the decimal point the smaller it becomes.

**Question 2: Define the working of the decimals.**

**Answer:** Decimals are the shorthand method for writing the fractions and mixed numbers with denominators which generally are the powers of 10, such as 10, 100, 1000, etc.

**Question 3: Define decimal numbers.**

**Answer:** The decimal numbers are used for representing the numbers that are lesser than 1 unit. The decimals are written at the right side of the unit having a separation of a period in between.

**Question 4: Is a decimal also an integer?**

**Answer:** Each and every single integer is expressible as a decimal. However, most of the numbers that are expressible as a decimal are not generally integers. If each and every digit after the decimal point is zero (0) then, the number is surely an integer.

**Question 5: What is the decimal form?**

**Answer:** The decimals are based upon the preceding powers of the number â€˜10â€™. Therefore, as we are moving from left to the right, the place value of the digit gets divided by the number â€˜10â€™, this means that the decimal place value controls the value of tenths, hundredths and even thousandths. A tenth means (one-tenth) or â€˜1/10â€™. And in the decimal form, it is 0.1.

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