How to Identify the Value of a Digit on Numbers Up to a Billion

The value of a digit is the digit multiplied by the place it sits in: the 6 in 5,601,754 is in the hundred thousands place, so its value is 600,000. Below: how places are named up through the billions, a worked example, and practice questions.

Place is not the same as value

Every digit in a number sits in a place, and each place is worth ten times the one to its right: ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, and so on up through the billions.

The place is the name of the column. The value is what the digit is actually worth there: the digit multiplied by the place. In 4,700 the digit 7 is in the hundreds place, and its value is 7 × 100 = 700. Same digit, different place, different value: in 70 that 7 is worth 70, and in 7,000,000 it is worth seven million.

Worked example: 5,601,754

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Reading the table above from the left, the digit 5 sits in the millions place, so its value is 5,000,000. The 6 is in the hundred thousands place, worth 600,000. The 0 is in the ten thousands place and contributes nothing, but it holds that column open so every digit to its left keeps the right value. The 1 is worth 1,000, the 7 is worth 700, the second 5 is worth 50, and the 4 is worth 4.

Adding those values returns the number: 5,000,000 + 600,000 + 0 + 1,000 + 700 + 50 + 4 = 5,601,754. That sum is called the expanded form, and it is the fastest way to check you have read the places correctly.

Reading big numbers in periods

Commas split a number into periods of three digits. From the right: ones, thousands, millions, billions. Within each period the pattern repeats as hundreds, tens, ones, which is why 5,601,754 is read as “five million, six hundred one thousand, seven hundred fifty-four”.

Counting periods is quicker than counting digits. Two commas means the leading digit is in the millions; three commas means billions.

Common mistakes

• Giving the place instead of the value. “The 6 is in the hundred thousands” answers a different question from “the 6 is worth 600,000”.
• Skipping zeros when counting places. A zero holds its column. Dropping it shifts every digit to its left down one place and divides the value by ten.
• Counting places from the left. Place value is counted from the ones digit on the right.
• Confusing the two 5s. In 5,601,754 one is worth 5,000,000 and the other 50. Position, not the digit, decides.

Practice questions on the value of a digit

1. What is the value of the 8 in 3,842,000?
2. What is the value of the 9 in 91,405,267?
3. In 604,300, which digit has a value of 4,000?
4. Write 2,070,900 in expanded form.
5. The value of a digit in a number is 30,000,000. Which place is it in, and what is the digit?

Answers

1. 800,000. The 8 is in the hundred thousands place.
2. 90,000,000. The 9 is in the ten millions place.
3. The 4. It sits in the thousands place, so its value is 4 × 1,000.
4. 2,000,000 + 70,000 + 900.
5. The ten millions place, and the digit is 3.

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