If d represents the hundredths digit and e represents the

If d represents the hundredths digit and e represents the thousandths digit in the decimal 0.4de, what is the value of this decimal rounded to the nearest tenth?

To answer the question we should know whether \(d\geq{5}\).

(1) d – e is equal to a positive perfect square --> easy to get two different result: \(0.4de=0.451\) (5-1=4=2^2), then 0.4de rounded to the nearest tenth will be \(0.5\) but if \(0.4de=0.421\) (2-1=1=1^2), then 0.4de rounded to the nearest nearest tenth will be \(0.4\). Not sufficient.

(2) \(\sqrt{d}>e^2\) --> also easy to get two different result: if \(\sqrt{d}=\sqrt{5}>1^2=e^2\) or \(\sqrt{d}=\sqrt{2}>1^2=e^2\). Not sufficient.

(1)+(2) 0.451 and 0.421 satisfy both statements and give different values of 0.4de when rounded to the nearest tenth: 0.5 and 0.4. Not sufficient.

Answer: E.

Rounding rules
Rounding is simplifying a number to a certain place value. To round the decimal drop the extra decimal places, and if the first dropped digit is 5 or greater, round up the last digit that you keep. If the first dropped digit is 4 or smaller, round down (keep the same) the last digit that you keep.

Example:
5.3485 rounded to the nearest tenth = 5.3, since the dropped 4 is less than 5.
5.3485 rounded to the nearest hundredth = 5.35, since the dropped 8 is greater than 5.
5.3485 rounded to the nearest thousandth = 5.349, since the dropped 5 is equal to 5.

Hope it helps.