How to find the percent? 4 is what percent of 10

Mathematics

1 answer:

Simora [160]3 years ago

3 0

Always use this formula to find a percentage:

% / 100 = Part / Whole replace the given values:

4 / 100 = Part / 10

Cross multiply:

4 x 10 = 100 x Part, or

40 = 100 x Part

Now, divide by 100 and get the answer:

Part = 40 / 100 = 0.4

Use again the same percentage formula:

% / 100 = Part / Whole replace the given values:

% / 100 = 4 / 10

Cross multiply:

% x 10 = 4 x 100

Divide by 10 and get the percentage:

% = 4 x 100 / 10 = 40%

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Notice that the series can be written as a combination of two geometric series, that can be found independently:

$\frac{3^{n-1}-1}{6^{n-1}} =\frac{3^{n-1}}{6^{n-1}} -\frac{1}{6^{n-1}} =(\frac{1}{2})^{n-1} -\frac{1}{6^{n-1}}$

The first one: $(\frac{1}{2})^{n-1}$ is a geometric sequence of first term ( $a_1$ ) "1" and common ratio (r) " $\frac{1}{2}$ ", so since the common ratio is smaller than one, we can find an answer for the infinite addition of its terms, given by: $Infinite\,Sum=\frac{a_1}{1-r} = \frac{1}{1-\frac{1}{2} } =\frac{1}{\frac{1}{2} } =2$

The second one: $\frac{1}{6^{n-1}}$ is a geometric sequence of first term "1", and common ratio (r) " $\frac{1}{6}$ ". Again, since the common ratio is smaller than one, we can find its infinite sum: