Compare Numbers 10⊡ and 140: Determining the Correct Inequality Sign

Question

There is an unknown digit behind the □ \Box

Determine the correct sign for the following expression:

10□?140 10\Box?140

Video Solution

Step-by-Step Solution

To solve this problem, we must determine which inequality sign fits the comparison 10□?14010\Box?140.

  • Step 1: Consider the expression 10□10\Box as 100+□100 + \Box, where □\Box is any digit from 0 to 9.
  • Step 2: Calculate the range of values for 10□10\Box:
    If □=0\Box = 0, then 10□=100+0=10010\Box = 100 + 0 = 100.
    If □=9\Box = 9, then 10□=100+9=10910\Box = 100 + 9 = 109.
  • Step 3: Compare all possible values of 10□10\Box (100 to 109) with 140.
  • Step 4: Since 109, the largest possible value, is less than 140, for any digit □\Box, 10□10\Box will always be less than 140.

Therefore, the correct inequality is 10□<14010\Box < 140. The proper sign for the expression is <.

Answer

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