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# What is the thousandths digit in the decimal equivalent of 53/5000?

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Re: What is the thousandths digit in the decimal equivalent of 53/5000? [#permalink]
53/5000=0.0106
therefore A
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Re: What is the thousandths digit in the decimal equivalent of 53/5000? [#permalink]
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Bunuel wrote:
What is the thousandths digit in the decimal equivalent of 53/5000?

A. 0
B. 1
C. 3
D. 5
E. 6

53/5000 = 53 /(5*10^3)
= (53/5) *10^-3
=10.6 * 10^-3
=.0106
Thousandths digit = 0
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Re: What is the thousandths digit in the decimal equivalent of 53/5000? [#permalink]
A

the value comes out to be0.0106

so the required digit=0
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Re: What is the thousandths digit in the decimal equivalent of 53/5000? [#permalink]
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Bunuel wrote:
What is the thousandths digit in the decimal equivalent of 53/5000?

A. 0
B. 1
C. 3
D. 5
E. 6

53/5000= (1/5) (53/1000) =0.2 * 0.053

Omitting decimal points before multiplication: 2 * 53 =106

thousandths digit = 0

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Re: What is the thousandths digit in the decimal equivalent of 53/5000? [#permalink]
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Bunuel wrote:
What is the thousandths digit in the decimal equivalent of 53/5000?

A. 0
B. 1
C. 3
D. 5
E. 6

$$\frac{53}{5000}$$

= $$\frac{53}{5}*1000$$

= $$\frac{10.60}{1000}$$

= $$0.0106$$

Thus, Answer will be (E) 6, however best method is shown by Mrosiji
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Re: What is the thousandths digit in the decimal equivalent of 53/5000? [#permalink]
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Bunuel wrote:
What is the thousandths digit in the decimal equivalent of 53/5000?

A. 0
B. 1
C. 3
D. 5
E. 6

We can manipulate the fraction to read:

106/10,000 = 0.0106, so the thousandths digit is 0.

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What is the thousandths digit in the decimal equivalent of 53/5000? [#permalink]
WRT to question ,
53/5,000 = 53 * 10^-3(power -negative 3) / 5
53/5 = 10.6 *10^-3(power -negative 3)
= 106*10^-3(power -negative 3)/10
= 106 * 10 to the power -^2
= 106 * 100
= 10600 , A answer <-
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Re: What is the thousandths digit in the decimal equivalent of 53/5000? [#permalink]
Mrosiji wrote:
53/5000 can be simplified this way --> (53 x 2) / (5,000 x 2) ----> now becomes 106/10,000.

106/10,000 = 0.0106

The hundredth digit is zero.

Ans A

I get seriously bogged down with calculations, and knowing that I could do it this way reduced a lot of the anxiety.

I think you meant to type 'the thousandths digit is zero'
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Re: What is the thousandths digit in the decimal equivalent of 53/5000? [#permalink]
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What is the thousandths digit in the decimal equivalent of 53/5000?

A. 0
B. 1
C. 3
D. 5
E. 6

53/5000= 53/5 x 10^-3= 10.6 x 10^-3= 0.0106

Where: [Ones] 0. 0[Tenths] 1[Hundredths] 0 [Thousandths] 6[Ten Thousandths]

I decided to start labeling each value as shown above while practising to prevent careless errors.
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Re: What is the thousandths digit in the decimal equivalent of 53/5000? [#permalink]
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Mrosiji wrote:
53/5000 can be simplified this way --> (53 x 2) / (5,000 x 2) ----> now becomes 106/10,000.

106/10,000 = 0.0106

The hundredth digit is zero.

Ans A

I get seriously bogged down with calculations, and knowing that I could do it this way reduced a lot of the anxiety.

Thank you so much!!!
best method ever!
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Re: What is the thousandths digit in the decimal equivalent of 53/5000? [#permalink]
What is the thousandths digit in the decimal equivalent of 53/5000?

What is the thousandths digit in the decimal equivalent of 106/10000?

$$106 * 10^{-4} = 0.0106$$

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Re: What is the thousandths digit in the decimal equivalent of 53/5000? [#permalink]
53/5000 --> 50+3/5000

We can write it as: 50/5000 + 3/5000
Now, 50/5000 --> 1/100 = 0.01
And, as we know 3/5 = 0.6; so, 3/5000 = 0.0006.

--> 0.01 + 0.0006= 0.0106.

So, the thousandths digit would be (A) i.e. 0.
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What is the thousandths digit in the decimal equivalent of 53/5000? [#permalink]
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Bunuel wrote:
What is the thousandths digit in the decimal equivalent of 53/5000?

A. 0
B. 1
C. 3
D. 5
E. 6

$$\frac{53}{5000}$$*$$\frac{2}{2}$$

$$=$$$$\frac{106}{10000}$$

$$=$$0.0106

So the thousand digit is 0

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Re: What is the thousandths digit in the decimal equivalent of 53/5000? [#permalink]
why is everyone doing this problem so ridiculously. Look, 53/5000 is very similar to 13/1000. divide 1000 by 13 and don't mess up your easy long division.. you will use up the full two minutes but it will guarantee you the correct answer.
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Re: What is the thousandths digit in the decimal equivalent of 53/5000? [#permalink]
Top Contributor
Abhishek009 wrote:
Bunuel wrote:
What is the thousandths digit in the decimal equivalent of 53/5000?

A. 0
B. 1
C. 3
D. 5
E. 6

$$\frac{53}{5000}$$

= $$\frac{53}{5}*1000$$

= $$\frac{10.60}{1000}$$

= $$0.0106$$

Thus, Answer will be (E) 6, however best method is shown by Mrosiji

Is not the right answer is $$A(0)$$?
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What is the thousandths digit in the decimal equivalent of 53/5000? [#permalink]
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Bunuel wrote:
What is the thousandths digit in the decimal equivalent of 53/5000?

A. 0
B. 1
C. 3
D. 5
E. 6

Key concept: It's very easy to convert a fraction to a decimal if that fraction has a power of 10 in its denominator.
For example, 6/10 = 0.6, 71/1000 = 0.071, and 9/10,000 = 0.0009

With the above concept in mind, let's take 53/5000 and create an equivalent fraction by multiplying top and bottom by 2 to get: 106/10,000
106/10,000 = 0.0106
So, we have:
0 in the tenths position
1 in the hundredths position
0 in the thousandths position
6 in the ten-thousandths position

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Re: What is the thousandths digit in the decimal equivalent of 53/5000? [#permalink]
Posting this in case it helps another individual with the same struggle I have on these problems;

1) Manipulate the fraction to something more malleable.

I took out a factor of 5 from the denominator to get it over 1,000, resulting in 53 / 1,000. This gives us a decimal of .053.

2) Get back to original proportion / decimal.

Since I increased the equation by decreasing the denominator by 5, I should decrease the proportion / decimal by the same value -> .053 / 5 = 0.0106