SSC CGL Preparation: Concepts and Practice

Learning outcome

Find a digit’s face and place values, compare numbers accurately and handle zeros and decimal signs correctly.

Concepts and reasons

A digit’s face value is the digit itself. Its place value depends on its position. Moving left from the units position gives tens, hundreds, thousands and so on. Moving right after the decimal point gives tenths (1/10), hundredths (1/100) and thousandths (1/1000).

Thus, a digit 6 in the hundreds position contributes 6 × 100 = 600; in the hundredths position it contributes 6/100 = 0.06. This is the base-ten system: each position has ten times the value of the position immediately to its right.

Leading zeros before the integer part do not change value: 0047 = 47. Such writing does not make 47 a four-digit number. But zeros inside a number can preserve essential positions: 407 and 47 differ.

To compare nonnegative (zero or positive) integers, ignore leading zeros, compare digit counts, then compare corresponding digits from the left. At the first unequal position, the larger digit determines the larger number. A difference of one hundred cannot be cancelled by the later tens and units, whose combined maximum is 99.

For decimals, compare integer parts first; then align decimal places, adding trailing zeros if needed. Trailing decimal zeros preserve value: 4.7 = 4.70. Zeros inserted elsewhere generally do not.

Every negative number is below zero. Among negative numbers, the one farther from zero is smaller.

Worked examples

Example 1. In 50507, both occurrences of 5 have face value 5. Their place values are 50000 and 500. Hence 50507 = 50000 + 500 + 7.

Example 2. Arrange -42, -7, 0 and 15. Negative numbers come first, and -42 lies farther below zero than -7. Therefore -42 < -7 < 0 < 15.

Example 3. Compare 6.08, 6.8 and 6.080. Write them as 6.080, 6.800 and 6.080. Therefore 6.08 = 6.080 < 6.8.

Common traps

More decimal digits do not necessarily mean a larger value. Face value and place value are not interchangeable. For negative numbers, do not copy the ordering of their positive magnitudes.

Practice questions

1. Find the face value and place value of 8 in 50806.
2. Is 0064 a four-digit number? Compare its value with 604.
3. Arrange -3.4, -3.04, 0, 3.004 and 3.04 in increasing order.

Answers and explanations

1. Face value = 8. The digit occupies the hundreds position, so place value = 8 × 100 = 800.
2. No: 0064 = 64, a two-digit number. Since 64 has fewer digits than 604, its value is smaller.
3. The order is -3.4 < -3.04 < 0 < 3.004 < 3.04. Compare aligned forms -3.400 and -3.040; for the positives, compare 3.004 and 3.040.