Concept of Place Value

Place value can be defined as the value represented by a digit in a number based on its position in the number.

7289 = 7000 + 200 + 80 + 9

7 is at the thousands place, 2 at the hundreds place, 8 at the tens place, and 9 at the ones place. 

• 4 → It is in the thousands place.
  Place value = 4 × 1000 = 4000 

• 2 → It is in the hundreds place.
  Place value = 2 × 100 = 200 

• 6 → It is in the tens place.
  Place value = 6 × 10 = 60

• 8 → It is in the units (ones) place.
  Place value = 8 × 1 = 8

The place value after the decimal point represents the fractional part of the number

In 17.591, 

Before the decimal point (17)

• 17 → is the whole number part.

  • 7 → is in the units place → value = 7

  • 1 → is in the tens place → value = 10

After the decimal point (.591)

• 5 →  is in the tenths place → value = `5/10` $=0.5$

• 9 →  is in the hundredths place → value = `9/100` $=0.09$

• 1 → is in the thousandths place → value = `1/1000`$=\; 0.001.$

• Money: In ₹825.50, the digit 5 appears in both the tens and tenths places, showing the importance of position (₹50 vs ₹0.5).
• Measurements: A fruit weighs 1.250 kg: 1 kg + 2 tenths (200 g) + 5 hundredths (50 g).

• Each place to the left of the decimal grows ×10; each place to the right shrinks ÷10.

• Place value = digit × value of its place.

• After the decimal point: tenths (1/10), hundredths (1/100), thousandths (1/1000).

• Face value is always the digit itself (e.g., 5 in 45 = 5), but the place value depends on the digit’s position.