Place Value to a Million

What you will learn

• Name every place from ones to millions.
• Read and write numbers up to a million, using zeros as place holders.
• Compare numbers and find the value of any digit.

Before you start: you should know tens and ones. See Counting and Place Value.

The idea

In our number system, the position of a digit tells you its value. Moving one place to the left makes a digit worth ten times as much. The digit $3$ is worth $3$ in the ones place, $30$ in the tens place and $300$ in the hundreds place.

The place value chart

A place value chart gives each place its own column. Seven columns take us from ones to millions.

The columns come in groups of three: ones, hundreds and tens form the ones group; then the thousands group; then millions. We separate groups with a comma, so $482{,}915$ is read “four hundred eighty-two thousand, nine hundred fifteen”.

Zero as a place holder

A zero in a column means “none of this place”. Without it the other digits would slide into the wrong places. $50{,}207$ has no thousands and no tens, so zeros hold those places.

Value of a digit and expanded form

To find what a digit is worth, multiply it by its place. In $482{,}915$ the $8$ is in the ten thousands place, so it is worth $80{,}000$. Writing a number as a sum of the values of its digits is called expanded form: $482{,}915 = 400{,}000 + 80{,}000 + 2000 + 900 + 10 + 5$.

Comparing large numbers

First count digits: the number with more digits is larger. If the digit counts match, compare from the left, one place at a time, and stop at the first place where they differ.

Worked examples

Example 1: Value of a digit

What is the $6$ worth in $963{,}240$?

1. Read the places from the right: ones $0$, tens $4$, hundreds $2$, thousands $3$, ten thousands $6$.
2. The $6$ is in the ten thousands place.
3. $6 \times 10{,}000 = 60{,}000$.

Answer: $60{,}000$.

Example 2: Writing from words

Write “seven hundred two thousand and thirty” in digits.

1. Seven hundred two thousand is $702{,}000$.
2. Thirty is $30$.
3. Put them together: $702{,}030$.

Answer: $702{,}030$.

Example 3: Which is bigger?

Compare $384{,}120$ and $384{,}210$.

1. Both have six digits.
2. The hundred thousands, ten thousands and thousands digits match: $3, 8, 4$.
3. The hundreds digits differ: $1$ and $2$. Two is bigger.

Answer: $384{,}210 > 384{,}120$.

Do not leave out zeros. $4{,}005$ and $45$ are very different numbers, and the zeros are what show it.

Why it matters

Populations, distances and prices all use large numbers. Reading them correctly is the first step before rounding, estimating and doing arithmetic with them, as in Rounding and Estimating.