n represent the hundredths digit in the number shown above.

Question

Consider a Number 3.1n5

n represent the hundredths digit in the number shown above. If the number is rounded to the nearest hundredth, which of the following could be the tenths digit in the rounded number?

A. 0
B. 2
C. 4
D. 5
E. 6

Bunuel · Accepted Answer

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.

For more check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.

P.S. Please read and follow: rules-for-posting-please-read-this-before-posting-133935.html

ConnectTheDots · Answer

3.1n5 - if rounded upto tenth digit, it can either be 3.1 or 3.2 . 
since 1 is not in choice, so 2 is the answer.

30 seconds. strip of the extra information : If the number is rounded to the nearest hundredth

gmatdaynnight · Answer

HI All,

I got this one in 53 seconds, please let me know in case there is any faster way to solve these kinds of questions.

In theis ques we are given the thousandth digit as 5, so the hundreth digit can take any value from 0-9. For the hundreth digit i considered 2 set of values (i) 0, 1, 2, 3 and (ii) 4, 5, 6, 7, 8, 9. Given that the thousandth digit is 5, the undreth digit has to go up by 1, and correspondingly, the tenth digit should also increase by 1 ( provided the hundreth digit is from the 2nd category. Since B was the only one amongst the feasable ans choise, i selected B .

KapTeacherEli · Answer

Very good summary!

Rounding can only do two things to a digit that remains in the number: leave a digit unchanged, or increase a digit by 1 (which can reset a 9 to a zero and increase the NEXT digit).

Since the tenths digit is currently a 1, almost everything else in the Q-stem is irrelevant. The tenths digit can never round to anything other than a 1 or a 2, and so (B) is the only possible answer.

felipelengert · Answer

In my opinion this question is wrong.. If you round the number to the nearst hundredth, the tenth digit will certainly be 1.
But this options is not available..

Am I right?

Bunuel · Answer

No. If n=9, then 3.1n5 rounded to the nearest hundredth would be 3.2.

felipelengert · Answer

Good point... tks Bunuel!

Theeldertwin · Answer

Hi Bunuel, shouldn't rounded to the nearest hundredth have 2 digits after decimal? Shouldn't the number be 3.1n or 3.1(n+1)? In both the cases the tenth digit should be 1 right?

Bunuel · Answer

Rounded to the nearest hundredth, 3.195 becomes 3.20. But 3.20 is the same value as 3.2, so the tenths digit is 2.

egmat · Answer

Hi Theeldertwin,

Your instinct is almost right, and you've spotted something real: rounding to the nearest hundredth  does  leave  two  digits after the decimal. So the result looks like 3.1 ? . The catch is the word  "could"  in the question - it's asking what the tenths digit  can possibly be  for  some  value of n, not what it always is.

Here's where your step 3.1(n+1) quietly breaks down. That formula is fine  as long as adding 1 to n stays a single digit . But n is a digit from  0  to  9 , so look at the one case where it doesn't:

- If  n = 9 , the number is  3.195 .
- The thousandths digit is  5 , so we round the hundredths  9  up.
- But  9 + 1 = 10  - it can't sit in one place. It  carries : the hundredths becomes  0  and the  1  rolls into the tenths.
- So  3.195  rounds to  3.20  - and now the tenths digit is  2 .

That single carry is the whole trick. For every other n ( 0  through  8 ) the tenths stays  1 , which isn't an answer choice. Only n =  9  produces a listed value, so  B (2)  is the answer.

Lock the idea in with a couple of quick ones: 
- Round  2.96  to the nearest tenth - does the units digit stay  2 , or does it become  3 ?
- Round  4.998  to the nearest hundredth - what happens to  both  digits in front?

Same mechanism each time: when the digit you're rounding up is a  9 , it resets to  0  and bumps the next digit left. That carry is exactly what your 3.1(n+1) shortcut was hiding.

Answer: B

Theeldertwin · Answer

Got it! Thanks for this!

n represent the hundredths digit in the number shown above.

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