Numbers & the Number System • Topic 3 of 9

Place Value

Place value is the single most important idea in this chapter and the one CTET tests hardest. In our base-10 system the value of a digit depends on where it sits: reading right to left the columns are ones (10^0 = 1), tens (10^1 = 10), hundreds (10^2 = 100) and thousands (10^3 = 1000). Take 347: the 7 is in the ones place (7 x 1 = 7), the 4 in the tens (4 x 10 = 40), the 3 in the hundreds (3 x 100 = 300). This forces the distinction the exam loves. Face value is the digit by itself, regardless of position - in 3582 the face value of 8 is just 8. Place value is the face value multiplied by the column's worth - in 3582 the place value of 8 is 8 x 10 = 80. Zero earns its keep as a placeholder: it marks an empty column, which is the only thing separating 45, 405 and 450. The teaching arc is concrete-representational-abstract - bundles of ten straws and base-10 blocks before pictures before bare numerals - with trading games (ten ones for one ten, ten tens for one hundred) to drive home the ten-to-one structure.

✅ Solved examples

1. In the number 347, state the place value of the digit 4.
4 is in the tens place, so its place value is 4 x 10 = 40.
2. In 3582, give the face value and the place value of 8.
Face value of 8 is 8 (the digit itself). Place value is 8 x 10 = 80, since 8 sits in the tens place.
3. In 5347, what is the place value of 5?
5 is in the thousands place, so its place value is 5 x 1000 = 5000.
4. What does the 0 contribute in 405, and why does it matter?
The 0 sits in the tens place, meaning zero tens. It is a placeholder that keeps the 4 in the hundreds column - without it the number would collapse to 45.

✏️ Practice — try these, take hints as needed

1. In 729, what is the place value of 2?
2 is the middle digit.
Tens place.
20
2. In 6184, give the face value of 1.
Face value ignores position.
It is just the digit.
1
3. In 2860, what is the place value of 8?
8 is third from the right.
Hundreds column.
800
4. Which digit acts as a placeholder in 304?
It marks an empty column.
Tens place is empty.
0 (in the tens place)

📝 Topic test — 8 questions

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