Question

complete the statement to explain why 3,■■7 will always be less than 7■■3. i know that 3,■■7 will always be less than 7■■3 because blank is always less than blank.

Explanation:

Step1: Analyze Place Value

In numbers like \( 3\underline{\quad}7 \) and \( 7\underline{\quad}3 \), the hundreds place (or the left - most non - zero digit place in a three - digit number) determines the magnitude when comparing. For \( 3\underline{\quad}7 \), the digit in the hundreds place is 3, and for \( 7\underline{\quad}3 \), the digit in the hundreds place is 7.

Step2: Compare Hundreds Place Digits

Since \( 3<7 \), regardless of the digit in the tens place (the middle digit), a number with 3 in the hundreds place will always be less than a number with 7 in the hundreds place. So \( 3\underline{\quad}7 \) (a three - digit number starting with 3) will always be less than \( 7\underline{\quad}3 \) (a three - digit number starting with 7) because the value of the hundreds place in \( 3\underline{\quad}7 \) (which is 3 hundreds or \( 3\times100 = 300\)) is less than the value of the hundreds place in \( 7\underline{\quad}3 \) (which is 7 hundreds or \( 7\times100=700\)).

Answer:

\( 3\underline{\quad}7 \) will always be less than \( 7\underline{\quad}3 \) because the digit in the hundreds place of \( 3\underline{\quad}7 \) (3) is less than the digit in the hundreds place of \( 7\underline{\quad}3 \) (7), and the hundreds place has a greater place value than the tens or ones place, so the number with 3 in the hundreds place is smaller.