Question

choose the symbol that correctly compares the two decimals below:
65.5 □ 64.6
□ =
□ >
□ <

choose the statement that describes the deciding factor in determining the comparison symbol chosen above.
□ the digit in each place value of 65.5 is identical to each place values digit in 64.6.
□ the digit in the ones place of 64.6 is less than the digit in the ones place of 65.5.
□ the digit in the tenths place of 64.6 is less than the digit in the ones place of 65.5.
□ the digit in the ones place of 65.5 is less than the digit in the ones place of 64.6.

Explanation:

First Sub - Question (Comparing 65.5 and 64.6)

Step1: Compare tens place

The tens place of 65.5 is 6, and the tens place of 64.6 is also 6.

Step2: Compare ones place

The ones place of 65.5 is 5, and the ones place of 64.6 is 4. Since \(5>4\), we can conclude that \(65.5 > 64.6\).

• Option 1: The digits in each place value are not identical (e.g., ones place: 5 vs 4, tenths place: 5 vs 6), so this is wrong.
• Option 2: The ones place of 64.6 is 4, and the ones place of 65.5 is 5. Since \(4 < 5\), this correctly explains why \(65.5>64.6\) (we compare from the highest place value, and when tens place is equal, ones place determines the comparison).
• Option 3: We compare place values of the same type (e.g., ones with ones, tenths with tenths), not tenths with ones, so this is wrong.
• Option 4: The ones place of 65.5 (5) is greater than the ones place of 64.6 (4), not less, so this is wrong.

Answer:

\(>\)

Second Sub - Question (Deciding Factor)