Last modified on January 8th, 2022

chapter outline

 

Place Value

Place value, in mathematics, indicates the position of a digit in any number. Every digit has some value in the number, based on its position.

When we write a number in the general form, the position of each digit gets expanded. The position starts from the ones or units place. In any number, the order of the place values of the digits starts from right to left is-

ones/units (1s),

  • tens (10s),
  • hundreds (100s),
  • thousands (1,000s),
  • ten thousands (10,000s)…,

and it goes on.

For instance, let’s consider a number, 2645.

Here, 5 is at the units place.

4 is at the tens place.

6 represents the hundreds place.

2 represents the thousands place.

The figure below shows the how to find the place value from an expanded form of a number.

Figure 1 (heading: Place Value of a Number, filename: Place Value)

We might have a number with the same digits after one another. However, their place value determines their value in the number.

For example, in 4566, the 6 at the extreme right represents the units place.

But the next 6 represents the tens place.

Place Value and Face Value

The place value of a digit is the value of its position in a particular number, whereas the face value of the digit is its own value.

For example,

In 4659, the face value of 6 is 6, but its place value is hundreds.

In simple words

  • Place value signifies the position of a digit, and,
  • Face value signifies the worth of the same digit in a number.

Place Value Chart

Place value chart is the standard chart made universally to define the values of the digits in any number. It serves as the rule to ensure the digits to be aligned correctly.

There are 2 types of place value charts used universally based on the numeral system.

Indian Place Value Chart

The Indian place value chart is based on the Indian numeral system. The chart is given below :

Figure 2 (heading: Indian Place Value Chart, filename: Indian Place Value Chart)

[Sample link: https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/indian-place-value-chart-image-1-1622439984-1622449106.png ]

International Place Value Chart

The international place value chart is based on the international numeral system. The chart is given below :

Figure 3 (heading: International Place Value Chart, filename: International Place Value Chart)

[Sample link: https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/indian-place-value-chart-image-2-1613142016.png ]

[merge the 2 above images into 1 and give filename : Place Value Chart]

Let us solve an example to understand the above concept better.

Write the place value of 4 and 7 in 76429.

Solution:

As we know,
The 3rd position from the extreme right towards left is the hundreds place,
∴ The place value of 4 = hundreds
And,
The 5th position from the extreme right towards left is the ten thousands place
∴ The place value of 7 = ten thousands

Decimal Place Value Chart

The decimal place value chart helps us to locate the positions of the digits when a number has both whole numbers and decimals. The whole numbers part and the decimal part are separated by a ‘.’. this dot is called the decimal point.

Figure 4 (heading: Decimal Place Value Chart, filename: Decimal Place Value Chart)

[Sample link:     https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/decimal-place-value-2-1633606268.png  ]

For instance, let’s consider a number, 49.2468.

We will see the place values of the digits after the decimal point.

The place value of 2 = 1/10th (tenth or one-tenth)

The place value of 4 = 1/100th (hundredth or one-hundredth)

The place value of 6 = 1/1000th (thousandth or one-thousandth)

The place value of 8 = 1/10000th (ten thousandth or one-ten thousandth)

Let us solve an example to understand the above concept better.

What is the place value of the underlined digit- 84.1563?

Solution:

As we know,
The 2nd to the right of the decimal point is hundredth
∴The place value of 5 = 1/100th (hundredth)
And The place value of 3 = 1/1000th (thousandth)

Last modified on January 8th, 2022

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