For all real numbers x, let x denote the number obtained by rounding

Question

For all real numbers x, let  \overline{x}  denote the number obtained by rounding x to the nearest hundredth. If x = 21.9445, what is the value of  10x−10\overline{x}  ?

A. 0.005
B. 0.045
C, 0.095
D. 0.45
E. 0.95

https://gmatclub.com/forum/download/file.php?id=78081

Bunuel · Accepted Answer

There is a difference between the hundred th  digit and the hundred s  digit.

https://gmatclub.com/forum/download/file.php?id=68179

1234.567

1 - THOUSANDS 
  2 - HUNDRED  S 
  3 - TENS 
 4 - UNITS 
 . -  decimal point  
 5 - TENTHS 
  6 - HUNDRED  THS 
  7 - THOUSANDTHS

Hope it helps.

Bunuel · Answer

21.9445 rounded to the nearest hundredth is 21.94. Only the  first  dropped digit is considered when rounding — rounding is not cumulative.

Rounding means simplifying a number to a certain place value. To round a decimal, look at the  first  digit being dropped:

If it is 5 or greater, round up the last digit you keep. 
 If it is 4 or less, keep the last digit as is.

Examples:

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.

So, according to this, 21.944x rounded to the nearest tenth will be 21.94 regardless of the value of x.

Bunuel · Answer

Since  \overline{x}  denote the number obtained by rounding x to the nearest hundredth,  \overline{21.9445}=21.94 . Thus:

10x−10\overline{x}=

=10(x−\overline{x})=

=10(21.9445 - 21.94)=

=10(0.0045)=

=0.045

Answer: B.

dhruv1108 · Answer

Did anyone else find the language of this question problematic? Nearest 100th would naturally direct one to assuming something like 21.9445 -> 0 or 100. While in the question they mean rounding of the decimals.

SamCodes · Answer

Hello Bunuel,

While rounding the hundredth number do you not round off the thousandth number as well?
I rounded 21.9445 as 21.95, since I had rounded the thousandth number "4".

Thank you

Deepsimar · Answer

Hi. I converted 21.94 as in I took 22, can anyone help here? Why can't it be done?

Bunuel · Answer

Have you checked the discussion above? For example  this post ?

For all real numbers x, let x denote the number obtained by rounding

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For all real numbers x, let x denote the number obtained by rounding