Verified Answer :

  • To compare decimal numbers, normalize them by padding with trailing zeros so they have the same number of decimal places: \(5.5000, 5.9050, 5.9500, 5.5052\).
  • Group the numbers by their leading decimal digits (tenths place).
  • Within each group, compare digits from left to right (hundredths, then thousandths, etc.) to determine their order.
  • The final ordered sequence is \(\boxed{5.5, 5.5052, 5.905, 5.95}\).

Explanation

  1. Normalization of the Given Numbers

To order the numbers 5.5, 5.905, 5.95, and 5.5052 from least to greatest, we first need to normalize them so they have the same number of decimal places. This makes them easier to compare digit by digit.

The given numbers are:

  1. 5.5
  2. 5.905
  3. 5.95
  4. 5.5052

The greatest number of decimal places is four (in 5.5052). Therefore, we add trailing zeros to the other numbers so each has four decimal places:

  1. 5.5 = 5.5000
  2. 5.905 = 5.9050
  3. 5.95 = 5.9500
  4. 5.5052 = 5.5052
  1. Comparing Tenths Place

Now we compare the numbers using their decimal digits from left to right. All four numbers have a '5' in the units place, so we move to the tenths place.

Comparing the tenths place:

  • 5.5000 has a 5.
  • 5.5052 has a 5.
  • 5.9050 has a 9.
  • 5.9500 has a 9.

We can split these into two groups:
Group A (starts with 5.5): 5.5000 and 5.5052
Group B (starts with 5.9): 5.9050 and 5.9500

  1. Comparing Remaining Decimal Places

Now we compare the numbers within each group by looking at the subsequent decimal places.

In Group A (5.5000 vs 5.5052):

  • The hundredths place is 0 in both.
  • The thousandths place is 0 in 5.5000 and 5 in 5.5052.

Since 0 < 5, we conclude that 5.5000 < 5.5052.

In Group B (5.9050 vs 5.9500):

  • The hundredths place is 0 in 5.9050 and 5 in 5.9500.

Since 0 < 5, we conclude that 5.9050 < 5.9500.

  1. Final Ordering

Finally, we combine the ordered groups to determine the final order from least to greatest:
5.5000 < 5.5052 < 5.9050 < 5.9500.

Converting back to the original format, the ordered sequence is:
5.5, 5.5052, 5.905, 5.95.

Examples

Ordering decimal numbers is essential in many daily activities, such as shopping or scientific measurements. For example, if you are comparing the prices of various items per pound in a grocery store, or comparing the weight of different packages, you need to understand which values are smaller or larger. By normalizing the decimal places (like adding zeros to align the digits), you can quickly and accurately determine the order, helping you make smarter choices about which items to purchase or how to pack your bags effectively.

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