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

There is an unknown digit behind the \Box

Determine the correct sign for the following expression:

10?140 10\Box?140

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1

Understand the problem

There is an unknown digit behind the \Box

Determine the correct sign for the following expression:

10?140 10\Box?140

2

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 1010\Box as 100+100 + \Box, where \Box is any digit from 0 to 9.
  • Step 2: Calculate the range of values for 1010\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 1010\Box (100 to 109) with 140.
  • Step 4: Since 109, the largest possible value, is less than 140, for any digit \Box, 1010\Box will always be less than 140.

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

3

Final Answer

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Which group contains numbers that are smaller in value than 87?

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