Pace values of Decimals is an important topic in the chapter “Decimals” in NCERT books for Class 6. The word decimal is taken from the Latin word “Decem”, meaning \(10.\). Decimal numbers are the standard form of representing integer numbers and non-integer numbers. The decimal numbers are one of the numbers that have the whole number and a fractional part split by the decimal point. The Decimal place value calculator tells us the place value of the decimal number. The digit after the decimal point represents the places of tenths, hundredths, thousandths etc.

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Decimals

The decimals are the supplement of the number system. The decimals can also be considered fractions only when the denominators are \({\text{10,100,1000}}\) etc. The numbers displayed in the decimal forms are called decimals.

Example: \({\text{17}}{\text{.235,0}}{\text{.149,125}}{\text{.005,2534}}{\text{.0}}\) etc. are the decimal numbers or decimals.

So, each of the decimal number or the decimal has two parts, which are given below:

1. Whole numbers
2. Decimal part

The digits in the number are split by a dot \(\left( . \right){\text{,}}\) called the decimal point.
In the given decimal number \(27.54,\) the number \(27\) is the whole number part, and the number \(54\) is the decimal part.

Decimal places: The number of digits taken in the decimal part of the decimal number is called the decimal places.

Examples: The number \(3.57\) has two digits after the decimal point, and the number \(85.325\) has three digits after the decimal points

Decimals: Properties

You can see a few of the properties of the decimal numbers under the operations of multiplication and division that are given below:

1. If you multiply any two of the decimal numbers in any order, you get the same product.
2. When you multiply any of the whole numbers with the decimal number in any order, you get the same product.
3. When you multiply the decimal fraction with the number \(1,\) then you get the product in the decimal fraction.
4. When you want to multiply the decimal fraction by the number \(0,\) you get the product as zero \(0.\)
5. If you divide any decimal number by \(1,\) the quotient is the decimal number.
6. If you divide the decimal number by the same number, the quotient is \(1.\)
7. When you divide the number \(0\) with any of the decimal number, you get the quotient as \(0.\)
8. You cannot divide any decimal number by the number \(0,\) as there is no reciprocal of \(0.\)

Decimals: Pace Values

You are aware that each of the place in the place value table has the value of ten times the value of the next place on its right side. For example, the value of the tens place is ten times more than the ones place. The value of the hundreds place is ten times more than the tens place etc.

In other words, the value of one place is one-tenth that of tens place, the value of tens place is one-tenth that of the hundreds place and so on.

Example: We will look at the place value of the number six in the following numbers:

Number	Place value
\(6543 \to \)	\(6000\)
\(5643 \to \)	\(600\)
\(5463 \to \)	\(60\)
\(5436 \to \)	\(6\)

You can observe that the digit six moves one place from left to right it’s value becomes one-tenth \(\frac{1}{{10}}\) of its previous value, when it moves two places from left to right, its value becomes one-hundredths \(\frac{1}{{100}}\) of its last value and so on.
Therefore, if we wish to move towards right beyond ones place, we will have to extend the place value table by introducing the places for tenths \(\frac{1}{{10,}}\) hundredths \(\frac{1}{{100,}}\) thousandths \(\frac{1}{{1000,}}\) and so on. In the following case, the given shape will be taken by the place value table:

Thousands	Hundreds	Tens	Ones	Tenths	Hundredths	Thousandths
\(1000\)	\(100\)	\(10\)	\(1\)	\(\frac{1}{{10}}\)	\(\frac{1}{{100}}\)	\(\frac{1}{{1000}}\)

Example: By using the above table if we write the number, \(257 + \frac{3}{{10}} + \frac{2}{{100}}\) then it would be:

Hundreds	Tens	Ones	Decimal point	Tenths	Hundredths
\(2\)	\(5\)	\(7\)		\(3\)	\(2\)

You can see the number in the above given table that will be written as \({\text{ 257}}{\text{.32}}\) and is the decimal or decimal number. You will be reading the number as “Two hundred fifty-seven point three two” or like “Two hundred fifty-seven and thirty-two hundredths”.

A decimal or a decimal number can have the whole number and a decimal part. The given table shows the whole number part and the decimal part of some decimal numbers:

Number	Whole number part	Decimal part
\(12.75\)	\(12\)	\(75\)
\(9.0437\)	\(9\)	\(0437\)
\(0.859\)	\(0\)	\(859\)
\(72.0\)	\(72\)	\(0\)
\(15\)	\(15\)	\(0\)
\(005\)	\(0\)	\(005\)
\(0.7\)	\(0\)	\(7\)

Remark: The decimals which have only one part, i.e., decimal part or the whole number part, those numbers are written using zero in the whole or the decimal parts.

When you want to read the decimal number, you have to use the following steps:

1. Read the whole number part
2. Read the decimal part as ‘point’.
3. Then you will read the numbers which are at the right side of the decimal point.
   a. Example: The number (17.25) will be read as seventeen point two five.
   b. OR
4. Read the whole number part.
5. Read the decimal point as ‘and’.
6. Read the number which is on the right side of the decimal point and then you read the name of the place of the last digit.
   a. Example: The number (8.527) is read as eight point and five hundred twenty-seven thousandths.

Decimals: Place Value Calculator

You can even use the calculator to check the decimal place value to display the place value for the decimal number. Then, the decimals number system is owned to express the whole numbers and the fractions together.

Now, you have to separate the whole number from the fraction by inserting a dot \(\left( . \right),\) known as the decimal point.

You can follow the given steps to use the decimal place value calculator:

1. First, you have to enter the decimal number in the required field.
2. Next, you have to click on the button “Solve” to get the place value.
3. Finally, the place value for a decimal number will appear in the output field.

Practice Exam Questions

Solved Examples – Place Value of Decimals

Q.1. Write the given decimal numbers \(20.5\) and \(4.2\) in the place value table.
Ans: Let us make a commonplace value table, assigning appropriate place value to the digits in the given numbers. We have,

Numbers	Ten \(10\)	Ones \(1\)	Tenths \(\frac{1}{{10}}\)
\(20.5\)	\(2\)	\(0\)	\(5\)
\(4.2\)	\(0\)	\(4\)	\(2\)

Q.2. Which is greater of \(48.23\) and \(39.35\)?
Ans: The given decimals have distinct whole decimal number parts, so compare the whole parts only.
In \(48.23,\) the whole number part is \(48.\)
In \(39.35,\) the whole number part is \(39.\)
\(\because 48 > 39\)
\(\because 48.23 > 39.35.\)

Q.3. Arrange the given decimals number in the ascending order: \({\text{5}}{\text{.64,2}}{\text{.54,3}}{\text{.05,0}}{\text{.259}}\) and \({\text{8}}{\text{.32}}{\text{.}}\)
Ans: The first step is to convert the given decimals into like decimals; we get
\({\text{5}}{\text{.640,2}}{\text{.540,3}}{\text{.050,0}}{\text{.259}}\) and \({\text{8}}{\text{.320}}{\text{.}}\)
Clearly, \({\text{0}}{\text{.259 < 2}}{\text{.540 < 3}}{\text{.050 < 5}}{\text{.640 < 8}}{\text{.320}}\)
Hence, given decimals in the ascending order are:
\({\text{0}}{\text{.259,2}}{\text{.54,3}}{\text{.05,5}}{\text{.64}}\) and \({\text{8}}{\text{.32}}{\text{.}}\)

Q.4. Find the product \({\text{0}}{\text{.008}} \times 0.74.\)
Ans: To find the product, we first multiply \(8\) by \(74.\)
We have, \({\text{8}} \times 74 = 592\)
Now,\({\text{0}}{\text{.008}}\) has \(3\) decimal places, and \({\text{0}}{\text{.74}}\) has two decimal places.
The sum of the decimal places \({\text{=3 + 2=5}}\)
So, the product must contain \(5\) places of decimals. Hence, \({\text{0}}{\text{.008}} \times {\text{0}}{\text{.74=0}}{\text{.00592}}\)

Q.5. Divide \(42.8\) by \(0.02.\)
Ans: We have,
\(\frac{{42.8}}{{0.02}} = \frac{{42.8 \times 100}}{{0.02 \times 100}} = \frac{{4280}}{2} = 2140\)
Hence, \(42.8 \div 0.02 = 2140\)

Q.6. Write the decimal place value for the given number: \({\text{87}}{\text{.543}}\)
Ans: The decimal place value for the given number is shown below in the table:

Tens	Ones	Decimal point	Tenths	Hundredths	Thousandths
\(8\)	\(7\)		\(5\)	\(4\)	\(3\)

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Summary

In this article, we have discussed that decimals are an extension of our number system. Decimals are fractions whose denominators are \({\text{10,100,1000}}{\text{.}}\) The decimal number has two parts, and they are the whole number part and the decimal part. The number of digits in the decimal part of a decimal number is known as the number of decimal places. The decimals which have the similar number of places are called as decimals. Otherwise, they are known as, unlike decimals. You can see the numbers, \({\text{0}}{\text{.1-0}}{\text{.10=0}}{\text{.100 }}\) etc, \({\text{0}}{\text{.5=0}}{\text{.50}}\) etc and so on. Annexing zero on the right side of the extreme right digit of the decimal part of a number does not alter the value of the number.

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Frequently Asked Questions (FAQs) – Place Value of Decimals

Frequently asked questions related to place value of decimals is listed as follows:

Q.1. How do you identify the value of the decimal?
Ans:After the decimal point, the first digit represents the tenths place, and after the tenths place, the next digit represents the hundredths place. The rest of the digits continue to fill in the place values until there are no digits left.

Q.2. How is the place value used to read decimals?
Ans: If you have a decimal number like \({\text{67}}{\text{.982}}\) the digit \(9\) represents the pace value of tenths, then the digit \(8\) will represent the hundredths place, and \(2\) illustrates the thousandths place.

Q.3. How do you work out missing decimals?
Ans: You have to see the given operation and then work accordingly.
Example: In the case of an addition, you have a number given \({\text{-1}}{\text{.083-3}}{\text{.82}}\)
So, you will arrange vertically and put zero in the empty box to equal the digits after the decimal point. Then add both given numbers to get the answer.

Q.4. How do we multiply decimals?
Ans: When you want to multiply the decimal numbers, you multiply them without a decimal point and next count the number of digits you have after the decimal point in each factor, and in the final product, you put the same number of digits after the decimal point.

Q.5. How do you find an area with decimals?
Ans: When you want to find the area with decimals, you have to multiply the decimal numbers by keeping in mind the digits after the decimal point.
Example:\({\text{2}}{\text{.51}} \times {\text{1}}{\text{.65 = 4}}{\text{.1415 }}\)

We hope this detailed article on the Place Values of Decimals helps you in your preparation. If you get stuck do let us know in the comments section below and we will get back to you at the earliest.