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How many digits will be there to the right of the decimal point in the

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Bunuel
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How many digits will be there to the right of the decimal point in the [#permalink] New post   24 Sep 2019, 22:02
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A
B
C
D
E

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65% (hard)

Question Stats:

49% (01:26) correct 51% (01:15) wrong based on 276 sessions
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Competition Mode Question



How many digits will be there to the right of the decimal point in the product of 95.75 and 0.02554 ?

A. 5
B. 6
C. 7
D. 8
E. None of these
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B
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Re: How many digits will be there to the right of the decimal point in the [#permalink] New post   24 Sep 2019, 22:13
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Quote:
How many digits will be there to the right of the decimal point in the product of 95.75 and 0.02554 ?

A. 5
B. 6
C. 7
D. 8
E. None of these

Total decimal places to the right = 7

However, 95.75 * 0.02554 would give the 7th demimal place as zero (because 5*4=20). Since we don't count the last number if its zero, then there would only be 6 decimal points to the right.

Hence, answer is option B
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Re: How many digits will be there to the right of the decimal point in the [#permalink] New post   Updated on: 24 Sep 2019, 22:54
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95.75 * 0.02554
= 95.75 * 25.54 * (1/1000)
= (383/4) * (1277/50) * (1/1000)
= (383*1277)/(200,000)
= (383*1277*5)/(1,000,000)

Estimate:
= (383*1277*5)/1,000,000
= (400*1250*5)/1,000,000
= 2,500,000/1,000,000
= 2.500000

So, it is about 6 decimal points

Answer is (B)

Posted from my mobile device

Originally posted by freedom128 on 24 Sep 2019, 22:31.
Last edited by freedom128 on 24 Sep 2019, 22:54, edited 1 time in total.
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KarishmaB
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Re: How many digits will be there to the right of the decimal point in the [#permalink] New post   26 Sep 2019, 06:16
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Bunuel wrote:

Competition Mode Question



How many digits will be there to the right of the decimal point in the product of 95.75 and 0.02554 ?

A. 5
B. 6
C. 7
D. 8
E. None of these


Note that we are multiplying 9575 with 2554 (and with total 7 decimal places).

2554 is divisible by 2 but not by 4.
9475 is not divisible by 2 but it is divisible by 5.
So when we multiply 9575 with 2554, we will end with one 0.
When we move 7 places back the 0 will be ignored and we will have 6 non zero digits after the decimal.

Answer (B)
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Re: How many digits will be there to the right of the decimal point in the [#permalink] New post   24 Sep 2019, 22:25
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95.75 * 0.02554 = 9.575 * 0.2554 = 2.445455
Digits to the right of the decimal point =445455
Hence there are 6 digits to the right of the decimal.

The answer is B.

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Re: How many digits will be there to the right of the decimal point in the [#permalink] New post   24 Sep 2019, 22:37
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How many digits will be there to the right of the decimal point in the product of 95.75 and 0.02554 ?

A. 5
B. 6
C. 7
D. 8
E. None of these

Both the two numbers have 2 and 5 digits respectively after decimal which after multiplication would result in 5 or greater number of digits.
0.75 can be written as 3/4 where 0.02554 not being a multiple of 4 results in 6 digits when divided by 4.

Answer (B).
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Re: How many digits will be there to the right of the decimal point in the [#permalink] New post   16 Aug 2023, 23:49
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KittyDoodles wrote:
KarishmaB wrote:
Bunuel wrote:

Competition Mode Question



How many digits will be there to the right of the decimal point in the product of 95.75 and 0.02554 ?

A. 5
B. 6
C. 7
D. 8
E. None of these


Note that we are multiplying 9575 with 2554 (and with total 7 decimal places).

2554 is divisible by 2 but not by 4.
9475 is not divisible by 2 but it is divisible by 5.
So when we multiply 9575 with 2554, we will end with one 0.
When we move 7 places back the 0 will be ignored and we will have 6 non zero digits after the decimal.

Answer (B)


Hi KarishmaB,

How can we validate whether the second last digit will be zero or not.

Thanks
Kitty



To make a 0, you need a 2 and a 5 as factors.

So e.g. 4637841 * 2 * 25 will have only one 0 at the end (called trailing zeroes) since we have only one pair of 2 and 5 available.

Similarly, 64746332 * 625 will end with exactly 2 trailing zeroes because 4 is a factor of 64746332 but 8 is not. Of course we have four 5s so 5s are more then enough but only two 2s hence we can make only two 10s ie only two trailing zeroes.

When we multiply 9575 with 2554, we get only one 2 from 2554 and two 5s from 9575 (which is divisible by 25).
Hence we get only one trailing zero.

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Re: How many digits will be there to the right of the decimal point in the [#permalink] New post   25 Sep 2019, 01:32
9575*2554 *1/10^7
the last digit of 9575*2554 will be 0
so digits on right of decimal point shall be 6
IMO B


How many digits will be there to the right of the decimal point in the product of 95.75 and 0.02554 ?

A. 5
B. 6
C. 7
D. 8
E. None of these
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Re: How many digits will be there to the right of the decimal point in the [#permalink] New post   26 Sep 2019, 04:56
Bunuel wrote:

Competition Mode Question



How many digits will be there to the right of the decimal point in the product of 95.75 and 0.02554 ?

A. 5
B. 6
C. 7
D. 8
E. None of these


Is there a quicker solution to this problem, besides the ones above? Bunuel, VeritasKarishma.
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Re: How many digits will be there to the right of the decimal point in the [#permalink] New post   26 Sep 2019, 05:22
95.75×0.02554=2.445445
Option B

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Re: How many digits will be there to the right of the decimal point in the [#permalink] New post   16 Aug 2023, 23:23
KarishmaB wrote:
Bunuel wrote:

Competition Mode Question



How many digits will be there to the right of the decimal point in the product of 95.75 and 0.02554 ?

A. 5
B. 6
C. 7
D. 8
E. None of these


Note that we are multiplying 9575 with 2554 (and with total 7 decimal places).

2554 is divisible by 2 but not by 4.
9475 is not divisible by 2 but it is divisible by 5.
So when we multiply 9575 with 2554, we will end with one 0.
When we move 7 places back the 0 will be ignored and we will have 6 non zero digits after the decimal.

Answer (B)


Hi KarishmaB,

How can we validate whether the second last digit will be zero or not.

Thanks
Kitty
GMAT Club Bot
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Re: How many digits will be there to the right of the decimal point in the [#permalink]
16 Aug 2023, 23:23
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