Order the decimals $-5.48, -5.483, -5.493$, and $-5.4083$ from greatest to least.

Question

01-11-2026
Mathematics

Answered

Order the decimals $-5.48, -5.483, -5.493$, and $-5.4083$ from greatest to least.

Verified Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-01T18:52:23-05:00

Standardize the decimal numbers to have the same number of decimal places: $-5.4800, -5.4830, -5.4930, -5.4083$.
Compare their absolute values: $5.4083 < 5.4800 < 5.4830 < 5.4930$.
Reverse the order for negative values: $-5.4083 > -5.4800 > -5.4830 > -5.4930$.
Final sorted list: $\boxed{-5.4083, -5.48, -5.483, -5.493}$.

Explanation

Analysis of the Given Numbers

We are given four negative decimal numbers: $-5.48$, $-5.483$, $-5.493$, and $-5.4083$. Our objective is to arrange these numbers from greatest to least. Recall that for negative numbers, the number with the smaller absolute value is actually greater (e.g., $-2 > -5$). Therefore, we can find the order by comparing the absolute values of these numbers and then reversing the result.

Standardizing Decimal Representation

To compare the numbers effectively, it is helpful to express them with the same number of decimal places by padding them with trailing zeros. The number with the most decimal places is $-5.4083$, which has four decimal places. Thus, we represent all numbers with four decimal places:

$-5.48 = -5.4800$
$-5.483 = -5.4830$
$-5.493 = -5.4930$
$-5.4083 = -5.4083$

Now, let's list their absolute values: $5.4800$, $5.4830$, $5.4930$, and $5.4083$.

Ordering the Numbers

Comparing the absolute values:

$5.4083$
$5.4800$
$5.4830$
$5.4930$

Ordering these from smallest to largest:
$5.4083 < 5.4800 < 5.4830 < 5.4930$.
Because we are dealing with negative numbers, the order is reversed:
$-5.4083 > -5.4800 > -5.4830 > -5.4930$.
Substituting the original numbers back, the order from greatest to least is:
$-5.4083, -5.48, -5.483, -5.493$.

Conclusion

The numbers in order from greatest to least are $-5.4083, -5.48, -5.483, -5.493$. Therefore, the ordered list is $\boxed{-5.4083, -5.48, -5.483, -5.493}$.

Examples

Understanding how to compare negative numbers is essential in real-life situations involving debt or temperature. For instance, if you have account balances of $\$-5.48, \$-5.483, \$-5.493,$ and $\$-5.4083$, knowing which balance is the 'greatest' tells you which account has the least amount of debt. Similarly, comparing sub-zero temperatures helps scientists track climate changes where, for example, a temperature of $-5.4083^\circ\text{C}$ is warmer than $-5.493^\circ\text{C}$. Accurate comparisons ensure that you can correctly interpret financial records or environmental data.