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04 Jul 2019, 15:11
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How many times is 6 % of 0.00005 greater than 2 % of 0.000025?
i have tried the following method but its time consuming any alternative method available?
a/b = [(6/100) * 5 * 10^(- 5)] / [(2/100) * 25 * 10^(- 6)]
a/b = [3 * 2 * 5 * 10^(- 5)] / [2 * 5 * 5 * 10^(- 6)] → you can simplify by 5
a/b = [3 * 2 * 10^(- 5)] / [2 * 5 * 10^(- 6)] → you can simplify by 2
a/b = [3 * 10^(- 5)] / [5 * 10^(- 6)]
a/b = (3/5) * 10^(- 5) / 10^(- 6)
a/b = (3/5) * 10^(- 5) * 10^(6)
a/b = (3/5) * 10^(- 5 + 6)
a/b = (3/5) * 10^(1)
a/b = (3/5) * 10
a/b = 30/5
a/b = 6 times
i have tried the following method but its time consuming any alternative method available?
a/b = [(6/100) * 5 * 10^(- 5)] / [(2/100) * 25 * 10^(- 6)]
a/b = [3 * 2 * 5 * 10^(- 5)] / [2 * 5 * 5 * 10^(- 6)] → you can simplify by 5
a/b = [3 * 2 * 10^(- 5)] / [2 * 5 * 10^(- 6)] → you can simplify by 2
a/b = [3 * 10^(- 5)] / [5 * 10^(- 6)]
a/b = (3/5) * 10^(- 5) / 10^(- 6)
a/b = (3/5) * 10^(- 5) * 10^(6)
a/b = (3/5) * 10^(- 5 + 6)
a/b = (3/5) * 10^(1)
a/b = (3/5) * 10
a/b = 30/5
a/b = 6 times
04 Jul 2019, 15:37
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silvertaurus
Firstly, you don’t need to express 6% and 2% as 6\100 and 2\100. Just use 6 and 2, because you have to simplify in the fraction.
Secondly, There are four zeroes after point in both 0.00005 and 0.000025. Just eliminate them. As above mentioned, you can do the same in the fraction anyway.
So, 6*0.5\2*0.25=3\0.5=6.
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Updated on: 05 Jul 2019, 17:59
Originally posted by TestPrepUnlimited on 04 Jul 2019, 15:52.
Last edited by TestPrepUnlimited on 05 Jul 2019, 17:59, edited 4 times in total.
Last edited by TestPrepUnlimited on 05 Jul 2019, 17:59, edited 4 times in total.
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You're correct. There is no need to do the prime factorization at the outset. That creates a LOT of extra writing. Instead convert to fraction or decimal, then cancel/simplify. For instance:
How many times is 6 % of 0.00005 greater than 2 % of 0.000025?
How many times is \(\frac{6}{100} \frac{5}{10^5}\) greater than \(\frac{2}{100} \frac{25}{10^6}\)?
Well, \(\frac{6}{100} \frac{5}{10^5} = \frac{30}{10^7}\),
and
\(\frac{2}{100} \frac{25}{10^6} = \frac{50}{10^8}\)
The question "how many times is A greater than B" can be translated to "A/B = what?"
So let's divide the two fractions:
\(\frac{30}{10^7}\) / \(\frac{50}{10^8}\)
=
\(\frac{30}{10^7} \frac{10^8}{50}\)
=
\(\frac{3}{5}\) * 10
=
6
Note that we can skip all the 10^7 10^8 steps by noting that, since we are dividing and both terms have the same number of 0s, we can just cancel them all out. That saves work and time. We included the exponent version to show why that works.
How many times is 6 % of 0.00005 greater than 2 % of 0.000025?
How many times is \(\frac{6}{100} \frac{5}{10^5}\) greater than \(\frac{2}{100} \frac{25}{10^6}\)?
Well, \(\frac{6}{100} \frac{5}{10^5} = \frac{30}{10^7}\),
and
\(\frac{2}{100} \frac{25}{10^6} = \frac{50}{10^8}\)
The question "how many times is A greater than B" can be translated to "A/B = what?"
So let's divide the two fractions:
\(\frac{30}{10^7}\) / \(\frac{50}{10^8}\)
=
\(\frac{30}{10^7} \frac{10^8}{50}\)
=
\(\frac{3}{5}\) * 10
=
6
Note that we can skip all the 10^7 10^8 steps by noting that, since we are dividing and both terms have the same number of 0s, we can just cancel them all out. That saves work and time. We included the exponent version to show why that works.
