Place value: units, tens, hundreds, thousands

Digit or number?

The two words are often confused, but they don't mean the same thing. A digit is one of the ten symbols that exist: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. A number is what you write by putting together one or more digits to represent a quantity.

Example: 7 is a digit AND a number (the number seven). But 47 is a number made up of two digits: the digit 4 and the digit 7. It's just like letters and words: a single letter often doesn't mean anything on its own, but combined with others, it forms a word with meaning.

Units, tens, hundreds, thousands

Our number system is a base-10 system: as soon as you reach 10 items in a group, you form a group of the next rank up.

• 10 units make 1 ten (10).
• 10 tens make 1 hundred (100).
• 10 hundreds make 1 thousand (1 000).
• 10 thousands make 1 ten thousand (10 000), and so on.

It's just like euros: 10 coins of €1 are worth one €10 note, 10 notes of €10 are worth one €100 note. Place value works on exactly the same principle of exchanging in groups of 10.

The place-value chart

To never make a mistake about a digit's position, we use a place-value chart: each column corresponds to a rank (units, tens, hundreds…), and you write a single digit per box, always starting from the right.

This column layout is the same one used for column operations: that's why you must always align the digits on the right before calculating.

Partitioning a number

Partitioning a number means writing it as a sum that shows the value of each digit. It's the most common place-value exercise, from age 6 (tens and units) up to age 9 or 10 (large numbers).

1. You identify each digit and its position, from left to right.
2. You multiply each digit by the value of its position (thousands, hundreds, tens, units).
3. You add it all up: that's the partition.

Another example with tens: 58 = 5 tens + 8 units = 50 + 8. And with hundreds: 346 = 3 hundreds + 4 tens + 6 units = 300 + 40 + 6.

The value of a digit depending on its position

This is THE key principle of all place value: the same digit is not worth the same amount depending on where it's written. Take the digit 5:

• In 52, the 5 is in the tens place → it's worth 50.
• In 528, the 5 is in the hundreds place → it's worth 500.
• In 5 280, the 5 is in the thousands place → it's worth 5 000.

It's the same digit, but its value is multiplied by 10 every time it shifts one position to the left. Understanding this also means understanding why multiplying by 10 means shifting every digit one place to the left (and adding a 0): 52 × 10 = 520.

Writing a number in words

A few useful rules for spelling numbers correctly:

• Compound numbers from 21 to 99 are written with a hyphen: twenty-one, forty-seven, ninety-eight.
• Hundred and thousand stay singular when they follow a number: three hundred, five thousand — never "three hundreds" or "five thousands" in this case.
• In British English, "and" is used before the tens/units part of a number: one hundred and forty-two, two thousand and five.

Mistakes to avoid

• Forgetting a 0 in a number that has an empty group (writing 47 instead of 407).
• Misaligning the digits when comparing numbers or setting out a calculation.
• Confusing the tens digit (a single digit) with the number of tens (which includes the hundreds and thousands).
• Thinking that "more digits always means a bigger or smaller number" without checking — 1 000 has 4 digits and is much bigger than 987, which has 3, but between two numbers of the same length, you have to compare digit by digit starting from the left.

Worked exercises