How to find Decimal Place Value?

We know that in mathematics, numbers are classified into different types, such as natural numbers, whole numbers, integers, rational numbers, etc. But what is a number system? A system of writing for representing numbers is referred to as a number system. There are different types of number systems, such as 

1. Decimal number system (Base – 10)
2. Binary Number System (Base- 2)
3. The Octal number system (Base- 8)
4. Hexadecimal number system (Base- 16)
   

Numbers are an integral part of our lives, right from counting the number of items in a list, to keeping things in order, measuring things, and much more. They are of different types such as even numbers, odd numbers, prime numbers, composite numbers, perfect numbers, consecutive numbers, etc. A number is a basic element of mathematics that is used to count, measure, label, etc. 

Based on the properties of numbers, they are classified into different types, and a decimal number is one of them, which is defined as a number consisting of a whole number and a fractional number separated by a decimal point. Let us consider an example to understand it better. 23.69 is a decimal number where 23 is a part of the whole number and .69 is the fractional part. With the help of the decimal place value charts, we can easily determine the correct place value of any digit of a given number. The decimal place value chart depicts the place values of the digits before and after the decimal point.

Decimal Value Place Chart

Hundred  thousands	Ten  thousands	Thousands	Hundreds	Tens	Ones	.	Tenths	Hundredths	Thousandths	Ten  thousandths
100,000	10,000	1000	100	10	1	.	1/10  (or) 0.1	1/100  (or) 0.01	1/1000  (or) 0.001	1/10,000  (or) 0.0001
Whole number part						Decimal point	Fractional part

From the decimal place value chart, we can observe that the part before the decimal point is the whole number part, and after the decimal point is the fractional part. We can also observe that the whole number part starts with ones, followed by tens, hundreds, and then thousands, and so on, while the fractional part starts with tenths, followed by hundredths, and then thousandths, and so on. For example, the place value of 7 is in the hundredth place of the number 45.371. If we exchange the position of 7 in the given number, then a new number will be formed and its place value will also be changed.

Thousands	Hundreds	Tens 4	Ones 5	. .	Tenths 3	Hundredths 7	Thousandths 1

The place value of 7 in the number 45.371 is 7 hundredths or 0.07

If interchange the positions of 7 and 5, then the new number will be 47.351.

Thousands	Hundreds	Tens 4	Ones 7	. .	Tenths 3	Hundredths 5	Thousandths 1

The place of 7 in the number 47.351 is 7 ones or 7.

Sample Problems 

Problem 1: Determine the place value of 3 and 7 in the number 346.479.

Solution:

By using the decimal place value chart, we can write the place values of all the numbers in 346.479.

Thousands	Hundreds 3	Tens 4	Ones 6	. .	Tenths 4	Hundredths 7	Thousandths 9

From the above table, we can write the place values of the digits in the given number.

Since 3 is in the hundreds place, the place value of 3 is 3 hundreds, or 300.

Number 7 is in the hundredths place, so the place of 7 is 7 hundredths or 0.07.

Problem 2: Determine the place values of all the digits in the number 2574.158.

Solution: 

By using the decimal place value chart, we can write the place values of all the numbers in 2574.158.

Thousands 2	Hundreds 5	Tens 7	Ones 4	. .	Tenths 1	Hundredths 5	Thousandths 8

From the above table, we can write the place values of the digits in the given number.

Number 2 is in the thousands place, so the place value of 2 is 2 thousands, or 2000.

Number 5 is in the hundreds place, so the place value of 5 is 5 hundreds, or 500.

Number 7 is in the tens place, so the place value of 7 is 7 tens, or 70.

Number 4 is in the ones place, so the place value of 4 is 4 ones, or 4.

Number 1 is in the tenths place, so the place value of 1 is 1 tenths, or 0.1.

Number 5 is in the hundredths place, so the place value of 5 is 5 hundredths, or 0.05.

Number 8 is in the thousandths place, so the place value of 8 is 8 thousandths, or 0.008.

Problem 3: Write the place values of numbers 2, 5, and 9 in the number 938.275.

Solution:

By using the decimal place value chart, we can write the place values of all the numbers in 938.275.

Thousands	Hundreds 9	Tens 3	Ones 8	. .	Tenths  2	Hundredths 7	Thousandths 5

Number 9 is in the hundreds place, so the place value of 9 is 9 hundreds, or 900.

Number 2 is in the tenths place, so the place value of 2 is 2 tenths, or 0.2.

Number 5 is in the thousandths place, so the place value of 5 is 5 thousandths, or 0.005.

Problem 4: Determine the place values of all the digits in the number 43.927.

Solution:

By using the decimal place value chart, we can write the place values of all the numbers in 43.927.

Thousands	Hundreds	Tens 4	Ones 3	. .	Tenths 9	Hundredths 2	Thousandths 7

From the above table, we can write the place values of the digits in the given number.

Number 4 is in the tens place, so the place value of 4 is 4 tens, or 40.

Number 3 is in the ones place, so the place value of 3 is 3 ones, or 3.

Number 9 is in the tenths place, so the place value of 9 is 9 tenths, or 0.9.

Number 2 is in the hundredths place, so the place value of 2 is 2 hundredths, or 0.02.

Number 7 is in the thousandths place, so the place value of 7 is 7 thousandths, or 0.007.

Problem 5: Determine the place values of the digits 1, 3, and 6 in the number 8302.7169.

Solution:

By using the decimal place value chart, we can write the place values of all the numbers in 8302.7169.

Thousands 8	Hundreds 3	Tens 0	Ones 2	. .	Tenths 7	Hundredths 1	Thousandths 6	Ten Thousandths 9

From the above table, we can write the place values of the digits in the given number.

Number 3 is in the hundreds place, so the place value of 3 is 3 hundreds, or 300.

Number 1 is in the hundredths place, so the place value of 1 is 1 hundredths, or 0.01.

Number 6 is in the thousandths place, so the place value of 6 is 6 thousandths, or 0.006.

Problem 6: Find all the place values of the digits in the number 51634.82.

Solution:

By using the decimal place value chart, we can write the place values of all the numbers in 8302.7169.

Ten thousands  5	Thousands 1	Hundreds 6	Tens 3	Ones 4	. .	Tenths 8	Hundredths 2	Thousandths

Number 5 is in the ten thousands place, so the place value of 5 is 5 ten thousands, or 50,000.

Number 1 is in the thousands place, so the place value of 1 is 1 thousands, or 1000.

Number 6 is in the hundreds place, so the place value of 6 is 6 hundreds, or 600.

Number 4 is in the tens place, so the place value of 3 is 3 tens, or 30.

Number 3 is in the ones place, so the place value of 3 is 4 ones, or 4.

Number 9 is in the tenths place, so the place value of 8 is 8 tenths, or 0.8.

Number 2 is in the hundredths place, so the place value of 2 is 2 hundredths, or 0.02.