Number System Fundamentals • Topic 1 of 7

Place Value and Face Value

Every digit in a number carries two values. Its face value is simply the digit itself, no matter where it sits. Its place value is the digit multiplied by the value of its position — ones, tens, hundreds, thousands, and so on. In 738492 the digit 3 lies in the ten-thousands place, so its place value is 3 × 10000 = 30000 while its face value is just 3. Each step to the left multiplies the place value by ten. SAT questions often ask for the difference between a digit's place and face value, or between the place values of the same digit in two positions.

✅ Solved examples

1. In 738492, by how much does the place value of 3 exceed its face value?
The 3 is in the ten-thousands place, so its place value is 30000 and its face value is 3. The difference is 30000 − 3 = 29997.
2. In 56757, find the difference between the place values of the two 5s.
The left 5 is in the ten-thousands place (50000); the right 5 is in the tens place (50). The difference is 50000 − 50 = 49950.
3. What is the place value of 7 in 473128?
Counting from the right, 7 occupies the ten-thousands place, so its place value is 7 × 10000 = 70000.
4. In 8888, the place value of the leftmost 8 is how many times that of the rightmost 8?
The leftmost 8 has place value 8000; the rightmost 8 has place value 8. So 8000 ÷ 8 = 1000 times.

✏️ Practice — try these, take hints as needed

1. In 902135, by how much does the place value of 9 exceed its face value?
Find which position the 9 occupies.
It is in the hundred-thousands place, so place value = 900000; face value = 9.
Subtract: 900000 − 9.
899991.
2. Find the difference between the place values of the two 3s in 3238.
Locate both 3s and their positions.
Left 3 is in the thousands place (3000); right 3 is in the tens place (30).
Subtract the smaller from the larger.
2970.
3. What is the place value of 6 in 640000?
Count the positions from the right.
6 sits in the lakh / hundred-thousands place.
Multiply 6 by 100000.
600000.
4. Find the sum of the place value and face value of 7 in 4712.
7 is in the hundreds place → place value 700.
Face value is always the digit itself → 7.
Add them.
707.
5. In 5847, what is the difference between the place value and face value of 8?
8 is in the hundreds place → 800.
Face value of 8 is 8.
800 − 8.
792.

📝 Topic test — 8 questions

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