Question

choose the symbol that correctly compares the two decimals below:
96.6 □ 95.4
□ =
□ >
□ <
choose the statement that describes the deciding factor in determining the comparison symbol chosen above.
□ the digit in the tenths place of 95.4 is less than the digit in the ones place of 96.6.
□ the digit in the ones place of 95.4 is less than the digit in the ones place of 96.6.
□ the digit in the tenths place of 95.4 is greater than the digit in the tenths place of 96.6.
□ the digit in the tenths place of 96.6 is greater than the digit in the tenths place of 95.4.

Explanation:

First Sub - Question (Comparing 96.6 and 95.4)

Step1: Compare the tens place

The tens place of 96.6 is 9 and the tens place of 95.4 is 9, so we move to the next place.

Step2: Compare the ones place

The ones place of 96.6 is 6 and the ones place of 95.4 is 5. Since \(6>5\), we know that \(96.6 > 95.4\).

• Option 1: Compares tenths place of 95.4 and ones place of 96.6, which is an incorrect comparison of different place values.
• Option 2: The ones place of 95.4 is 5 and the ones place of 96.6 is 6. Since \(5 < 6\), this statement correctly identifies that the digit in the ones place of 95.4 is less than the digit in the ones place of 96.6, which is the deciding factor for \(96.6>95.4\).
• Option 3: The tenths place of 95.4 is 4 and the tenths place of 96.6 is 6. \(4\) is not greater than \(6\), so this statement is false.
• Option 4: The tenths place of 96.6 is 6 and the tenths place of 95.4 is 4. While \(6 > 4\), the deciding factor for \(96.6>95.4\) is the ones place (since the tens place is the same), not the tenths place.

Answer:

\(>\)

Second Sub - Question (Deciding Factor)