Place Value
Know exactly what each digit is worth
Understanding what each digit in a number truly represents — and why that matters for every calculation you do.
See It in Action
The Problem
What is the value of the digit 4 in the number 34,817?
Common Mistake
The 4 is in the thousands position, so its value is 4.
The position is correct (thousands), but the value isn't just "4" — a digit's value is the digit multiplied by its place. The student confused the digit with its value.
Correct Approach
The 4 is in the thousands position. So its value is 4 × 1,000 = 4,000. The digit 4 represents four thousands.
Answer: 4,000
Break the whole number apart: 30,000 + 4,000 + 800 + 10 + 7 = 34,817. The 4,000 slot is filled by our digit 4. ✓
The Core Concept
Every digit in a number has a position, and that position decides its value. In the number 3,472, the 3 isn't just "three" — it's three thousands (3,000). The 4 is four hundreds (400). The 7 is seven tens (70). And the 2 is two ones (2). The number is really 3,000 + 400 + 70 + 2.
This seems simple, but place value becomes trickier with larger numbers, decimals, and when zeros appear as placeholders. In 5,060, the zero in the tens place doesn't mean there are no tens sitting there like a blank — it's an active placeholder that keeps the 6 in the right column.
With decimals, place value works in reverse. In 0.347, the 3 is in the tenths place (3/10), the 4 is in the hundredths place (4/100), and the 7 is in the thousandths place (7/1000). Many students mix up 0.3 and 0.03 — but 0.3 is ten times bigger than 0.03.
Common Mistakes to Avoid
Confusing the digit with its value
The digit 4 and the value 4,000 are very different things. The digit is just the symbol; the value is what it's actually worth in that position.
Forgetting that zeros are placeholders
In 5,060, the zero in the tens place doesn't mean you skip tens — it means there are zero tens, keeping the 6 correctly in the hundreds place.
Getting decimal places wrong (0.3 vs 0.03)
0.3 means 3 tenths. 0.03 means 3 hundredths. They look similar but 0.3 is ten times bigger. The more places after the decimal point, the smaller the value.
Misreading large numbers
Always group digits in threes from the right: 1,234,567 reads as "one million, two hundred and thirty-four thousand, five hundred and sixty-seven." Don't try to read left-to-right without grouping.
Try It Yourself
In the number 206,054, write the value of the digit 6 AND the value of the digit 5.
Hint: Find each digit's position first. Count from the right: ones, tens, hundreds, thousands, ten-thousands, hundred-thousands.
Key Tips
Write out the place value columns (ones, tens, hundreds...) above each digit to avoid confusion.
For decimals, always read the number aloud: "zero point three" reminds you it's 3 tenths.
Zeros are never "nothing" — they're placeholders that keep every other digit in the right column.
Related Skills
Ready to practise Place Value?
Reading is the start. The Maths Gym has exercises designed around this skill — with instant feedback and progress tracking.