Place Value Calculator (find the place and value of a digit)

Understanding the place value calculator — concept and principle

This calculator finds the place and the value of a digit in a number, lists every place where that digit appears, and shows the place of every digit, including decimals. Use it for primary-school maths, for reading large numbers aloud, and for checking expanded form.

How it is calculated

• Places to the left of the decimal point: ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, and so on.
• Places to the right: tenths (1/10), hundredths (1/100), thousandths (1/1,000), and so on.
• Value of a digit = digit × its place value.

The calculator searches from the left and reports the first occurrence of your digit, the number of times it appears, and the value of each occurrence. A zero holds a place but is worth 0.

The principle

Our number system is base 10 and positional: each place is worth ten times the place to its right. The same digit therefore means different amounts in different positions; a 7 can be 7, 70, 7,000 or 0.07. Writing a number as the sum of its digit values gives its expanded form. Places are grouped in threes (ones, thousands, millions, billions), which is why commas separate groups of three digits in English. Zero was the key invention that made this system work, because it marks an empty place.

Worked example

Default inputs: number 63,407,218.5, digit 7.

1. Reading from the left: 6 ten millions, 3 millions, 4 hundred thousands, 0 ten thousands, 7 thousands, 2 hundreds, 1 ten, 8 ones and 5 tenths.
2. The digit 7 is in the Thousands place.
3. Its value is 7 × 1,000 = 7,000.
4. 7 appears once; there are 8 digits before the point and 1 after it.
5. Expanded form: 60,000,000 + 3,000,000 + 400,000 + 0 + 7,000 + 200 + 10 + 8 + 0.5.

How to read the result

The place name tells you the size of the unit; the value tells you how much that digit contributes. If a digit appears more than once, each occurrence has a different value. Reading the number aloud by periods helps: sixty-three million, four hundred seven thousand, two hundred eighteen and five tenths.

Common mistakes

• Confusing the place (thousands) with the value (7,000).
• Calling the first place after the decimal point the "oneths"; it is the tenths.
• Ignoring zeros when counting places.
• Mixing up the order of tens and tenths.

Frequently asked questions

What is the difference between place and value?

The place is the position, such as hundreds; the value is the digit times that place, such as 300.

What place is the second digit after the decimal point?

The hundredths place, worth 1/100.

Why does a zero matter if it is worth nothing?

It holds the other digits in their places; without it 407 would become 47.

Sources: OpenStax, Elementary Algebra 2e (2020), §1.1 Introduction to Whole Numbers