Explain the process to order the rational numbers from greatest to least. 2.8, 238, 2.125, 234

9514 1404 393

  238, 234, 2.8, 2.125

Step-by-step explanation:

1. Find the place value of the left-most digit of the number. The number with the largest place value is greatest.

2. If both numbers have digits with the same place value, the number with the largest leading digit is greatest.

3. If both numbers have largest leading digits with the same value, ignore that digit and repeat the comparison from the first step.

__

Application to the given list of numbers

The two numbers with hundreds-place digits are ...

  238, 234

Those both have 2 in the hundreds place, so we compare them ignoring the 2. That lets us compare ...

  38 and 34

Both of these numbers have 3 as a leading tens-place digit, so we compare them ignoring the 3. That lets us compare ...

  8 and 4

The ones-place digit 8 has a greater value than the ones-place digit 4, so ...

  238 > 234

__

The number 234 has a hundreds-place digit while the remaining numbers to compare have only a leading ones-place digit. Hence both of them are less than 234.

Their ones-place digits are the same (2), so we compare them using the tenths-place digits:

  0.8 and 0.125

The tenths-place digit 8 is greater than the tenths-place digit 1, so

  2.8 > 2.125.

The ordering of the four number is then ...

  238 > 234 > 2.8 > 2.125