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Math Expert V
Joined: 02 Sep 2009
Posts: 59101
How many digits will be there to the right of the decimal point in the  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 49% (01:12) correct 51% (01:19) wrong based on 68 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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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.

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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.

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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

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Originally posted by chondro48 on 24 Sep 2019, 22:31.
Last edited by chondro48 on 24 Sep 2019, 22:54, edited 1 time in total.
Senior Manager  P
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Location: India
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Re: How many digits will be there to the right of the decimal point in the  [#permalink]

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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.

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Re: How many digits will be there to the right of the decimal point in the  [#permalink]

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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
Director  P
Joined: 24 Nov 2016
Posts: 778
Location: United States
Re: How many digits will be there to the right of the decimal point in the  [#permalink]

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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

Is there a quicker solution to this problem, besides the ones above? Bunuel, VeritasKarishma.
Senior Manager  G
Joined: 29 Jun 2019
Posts: 467
Re: How many digits will be there to the right of the decimal point in the  [#permalink]

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95.75×0.02554=2.445445
Option B

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Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9786
Location: Pune, India
Re: How many digits will be there to the right of the decimal point in the  [#permalink]

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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.

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Veritas Prep GMAT Instructor Re: How many digits will be there to the right of the decimal point in the   [#permalink] 26 Sep 2019, 06:16
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