Question

1. order the decimals from greatest to least. 36.598 36.799 36.597 36.797

Explanation:

Step1: Compare the tenths place

The tenths digit of 36.598, 36.597 is 5; for 36.799, 36.797 it is 7. Since \(7 > 5\), numbers with tenths digit 7 are greater than those with 5. So we have two groups: \(\{36.799, 36.797\}\) (greater) and \(\{36.598, 36.597\}\) (lesser).

Step2: Compare within the 7 - tenths group

For 36.799 and 36.797, compare the thousandths place. \(9 > 7\), so \(36.799 > 36.797\).

Step3: Compare within the 5 - tenths group

For 36.598 and 36.597, compare the thousandths place. \(8 > 7\), so \(36.598 > 36.597\).

Step4: Combine the ordered groups

From greatest to least, we combine the ordered greater group and then the ordered lesser group: \(36.799 > 36.797 > 36.598 > 36.597\).

Answer:

\(36.799, 36.797, 36.598, 36.597\)