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In the biology lab of "Jefferson" High School there are 5.4*10^6 germs

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In the biology lab of "Jefferson" High School there are 5.4*10^6 germs  [#permalink]

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New post 14 Nov 2016, 04:34
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Re: In the biology lab of "Jefferson" High School there are 5.4*10^6 germs  [#permalink]

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New post 14 Nov 2016, 04:38
Bunuel wrote:
In the biology lab of "Jefferson" High School there are 5.4*10^6 germs, equally divided among 10,800 Petri dishes. How many germs live happily in a single dish?

A. 100
B. 200
C. 500
D. 1000
E. 5000


IMO C

5.4*10^6/ 10800==> 54*10^3/108==> 54000/108= 500
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Re: In the biology lab of "Jefferson" High School there are 5.4*10^6 germs  [#permalink]

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New post 14 Nov 2016, 15:19
Bunuel wrote:
In the biology lab of "Jefferson" High School there are 5.4*10^6 germs, equally divided among 10,800 Petri dishes. How many germs live happily in a single dish?

A. 100
B. 200
C. 500
D. 1000
E. 5000



IMO Solution = (5.4*10^6) / 10,800 = (54*10^5) / (54* 200) = 10^5 / 200 = 100 * 10^3 / 2*100 = 10^3 / 2 = 1,000 / 2 = 500. IMO 'C'.
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Re: In the biology lab of "Jefferson" High School there are 5.4*10^6 germs  [#permalink]

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New post 06 Nov 2019, 07:58

Official Explanation



The number of germs in a single dish equals the number of germs divided by the number of dishes. The top of the fraction is given in scientific notation. Changing the bottom to scientific notation will allow you to reduce some annoying 0's and work with more comfortable numbers.

Remember the rule: Maintain the balance between the digit term and the exponential term. If one goes up (↑) by a magnitude of 10, the other must go down (↓) by the same magnitude, and vice versa.

Germs: \(5.4×10^6=54×10^5\)

Dishes: \(10,800=108×10^2\)

Germs per dish: \(\frac{54×10^5}{108×10^2}\)

Note that 54108 can be reduced to \(\frac{1}{2}\). Thus, the calculation can be reduced to

\(\frac{1}{2}×\frac{10^5}{10^2}=\frac{1}{2}×10^{5−2}=\frac{1}{2}×10^3\)

\(=\frac{10^3}{2}=\frac{1,000}{2}=500\) germs per dish.

Answer: C
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Re: In the biology lab of "Jefferson" High School there are 5.4*10^6 germs  [#permalink]

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New post 09 Dec 2019, 17:54
Bunuel wrote:
In the biology lab of "Jefferson" High School there are 5.4*10^6 germs, equally divided among 10,800 Petri dishes. How many germs live happily in a single dish?

A. 100
B. 200
C. 500
D. 1000
E. 5000


5.4*1000000 = 5400000 / 10800 = 54000/108 = 500 (Note : 108*5=540 so only 2 zeros will be left)
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Re: In the biology lab of "Jefferson" High School there are 5.4*10^6 germs   [#permalink] 09 Dec 2019, 17:54
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