Identify the value of digits in large numbers

Place value is a positional system in which a digit’s value depends on its position within groups of ones, thousands, millions, and billions: moving one place left multiplies its value by 10, while moving right divides it by 10. Learners identify a digit’s value, including the role of zero as a placeholder, and interpret whole numbers through billions in standard, word, and expanded forms, distinguishing face value from place value. Scientific notation and extensions to arbitrarily large or other-base numbers are beyond this scope.

Detailed Explanation: Identify the value of digits in large numbers

A digit’s place value tells how much it is worth because of its position in a number. Starting from the right, the places are:

\text{ones},\ \text{tens},\ \text{hundreds},\ \text{thousands},\ \text{ten-thousands},\ \text{hundred-thousands},\ \text{millions},\ldots

Each place to the left is worth $10$ times as much as the place before it.

Example

What is the value of the digit $6$ in

4,062,305,018?

Step 1: Use the commas to separate groups of three digits.

4\mid062\mid305\mid018

The groups are:

$4$ billion
$062$ million
$305$ thousand
$018$ ones

Step 2: Locate the digit $6$ .

The $6$ is in the millions group:

4\mid\boxed{062}\mid305\mid018

Within the millions group, $6$ is in the ten-millions place.

Step 3: Find the digit’s value.

A $6$ in the ten-millions place is worth

6\times 10,000,000=60,000,000.

So, the value of the digit $6$ is

\boxed{60,000,000}.

The digit itself, $6$ , is its face value. Its place value is $60,000,000$ . The zeros help hold the other digits in their correct places.

Learn by doing: Identify the value of digits in large numbers

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Place Value - Identify in Number

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