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If digit h is the hudredths' digit in the decimal d=0.2h6, what is the value of d, rounded to the nearest tenth?

Given: \(d=0.2h6\).

(1) d < 1/4 --> 1/4 = 0.25 --> \(0.2h6<0.25\) --> \(h<5\) (\(0.2<d<0.25\))--> \(d\), rounded to the nearest tenth will be \(0.2\). Sufficient.

(2) h < 5 --> the same as above: \(d\), rounded to the nearest tenth will be \(0.2\). Sufficient.

Answer: D.

Note: 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.

Re: If digit h is the hundredths' digit in the decimal d=0.2h6, [#permalink]
24 Sep 2013, 17:37

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Re: hundreth digit [#permalink]
18 Mar 2014, 22:10

Hi Bunuel,

You mean to say that we completely ignore the 1000th digit ("6" in this question) and irrespective of it being more than 5, we will use the 100th digit and answer the question according to that. I thought we look at "6", so if we assume the 100th digit to be 4 (less than "5") it becomes 0.246, which first rounds off to 0.25 (because 6 is greater than 5) and then answer becomes is 0.3, rounding off 0.25->0.3. I think this was the wrong way (however, we were taught this in primary school). This is a learning for me. Please confirm.

Re: hundreth digit [#permalink]
19 Mar 2014, 01:49

2

This post received KUDOS

Expert's post

Eshan wrote:

Hi Bunuel,

You mean to say that we completely ignore the 1000th digit ("6" in this question) and irrespective of it being more than 5, we will use the 100th digit and answer the question according to that. I thought we look at "6", so if we assume the 100th digit to be 4 (less than "5") it becomes 0.246, which first rounds off to 0.25 (because 6 is greater than 5) and then answer becomes is 0.3, rounding off 0.25->0.3. I think this was the wrong way (however, we were taught this in primary school). This is a learning for me. Please confirm.

Looking forward to hearing from you.

Thanks and regards,

Eshan

Yes, when rounding to the nearest tenth, we only need to know the hundredth: when rounding we are interested in the first dropped digit. So, 0.246 rounded to the tenth is 0.2, not 0.3.

Re: hundreth digit [#permalink]
19 Mar 2014, 19:04

Bunuel wrote:

Eshan wrote:

Hi Bunuel,

You mean to say that we completely ignore the 1000th digit ("6" in this question) and irrespective of it being more than 5, we will use the 100th digit and answer the question according to that. I thought we look at "6", so if we assume the 100th digit to be 4 (less than "5") it becomes 0.246, which first rounds off to 0.25 (because 6 is greater than 5) and then answer becomes is 0.3, rounding off 0.25->0.3. I think this was the wrong way (however, we were taught this in primary school). This is a learning for me. Please confirm.

Looking forward to hearing from you.

Thanks and regards,

Eshan

Yes, when rounding to the nearest tenth, we only need to know the hundredth: when rounding we are interested in the first dropped digit. So, 0.246 rounded to the tenth is 0.2, not 0.3.

If digit h is the hundredths digit in the decimal n = 0.2h6, what is t [#permalink]
17 Apr 2015, 05:17

1

This post received KUDOS

#1 n< 1/4 implies that n < 0,25 which explicitly lets us round it down to 0,2 coz the hundredth digit in this case is 4 at max(which rounds down). SUFFICIENT #2 h<5. Lets look at our number: n = 0.2h6 rounds to n = 0.2(h+1). If h = 4 we get n = 0,25 which rounds up to 0,3, if h < 4 then the result is 0,2 INSUFFICIENT

A edit: #2 h<5. Since 6 is not the factor due to the fact that we are rounding to tenths, h being below 5 (0 1 2 3 or 4) lets us explicitly answer our question thus SUFFICIENT

Answer ends up being D.

Thanks for ur comemnt rich! Every day learning something new, huh.

Last edited by Zhenek on 17 Apr 2015, 11:11, edited 2 times in total.

Re: If digit h is the hundredths digit in the decimal n = 0.2h6, what is t [#permalink]
17 Apr 2015, 09:38

1

This post received KUDOS

Expert's post

Hi Zhenek,

When rounding a decimal to the 'nearest tenth", the thousandth's digit has NO EFFECT on the rounding. So in this question, the '6' is NOT a factor - only the H is. Knowing that, what would you do differently with Fact 2?

Re: If digit h is the hundredths digit in the decimal n = 0.2h6, what is t [#permalink]
17 Apr 2015, 14:51

Expert's post

Hi Zhenek,

Very good. While explicit "rounding" as a subject isn't something you'll be asked about too often on Test Day (likely just 1-2 times), the rules that govern it are not too complicated. As you 'lock in' more of these rarer categories, you'll see a nice increase in your Quant scores.

We need to find the value of n rounded to the nearest tenth i.e. we need to keep only one digit after the decimal.

Statement 1: n < 1/4

In decimal form, it means n < 0.25

If h were 5 or greater, n would become 0.256 or 0.266 or higher. All these values would be more than 0.25 so h must be less than 5 such as 0.246 or 0.236 etc. In all such cases, n would be rounded to 0.2

This statement alone is sufficient.

Statement 2: h < 5

This is even simpler. Since we have been given that h is less than 5, when we round n to the tenths digit, we will get 0.2

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