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A ratio is often converted to a fraction when it is expressed as a ratio to the whole. In the above example, the ratio of yellow cars to all the cars on the lot is 4:12 or 1:3. We can convert these ratios to a fraction, and say that 4 / 12 of the cars or 1 / 3 of the cars in the lot are yellow.
If the ratio consists of only two values, it can be represented as a fraction, in particular as a decimal fraction. For example, older televisions have a 4:3 aspect ratio , which means that the width is 4/3 of the height (this can also be expressed as 1.33:1 or just 1.33 rounded to two decimal places).
[1] [2] [3] The f-number is also known as the focal ratio, f-ratio, or f-stop, and it is key in determining the depth of field, diffraction, and exposure of a photograph. [4] The f-number is dimensionless and is usually expressed using a lower-case hooked f with the format f / N , where N is the f-number.
A pie chart showing the percentage by web browser visiting Wikimedia sites (April 2009 to 2012) In mathematics, a percentage (from Latin per centum 'by a hundred') is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign (%), [1] although the abbreviations pct., pct, and sometimes pc are also used. [2]
The golden ratio's negative −φ and reciprocal φ−1 are the two roots of the quadratic polynomial x2 + x − 1. The golden ratio is also an algebraic number and even an algebraic integer. It has minimal polynomial. This quadratic polynomial has two roots, and. The golden ratio is also closely related to the polynomial.
The convergents of the continued fraction for φ are ratios of successive Fibonacci numbers: φ n = F n+1 / F n is the n-th convergent, and the (n + 1)-st convergent can be found from the recurrence relation φ n+1 = 1 + 1 / φ n. [33] The matrix formed from successive convergents of any continued fraction has a determinant of +1 or −1.
30° and 60°. The values of sine and cosine of 30 and 60 degrees are derived by analysis of the equilateral triangle. In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained.
The same 1 / μ = 3 + √ 8 (the silver ratio squared) also is observed in the unfolded general continued fractions of both the natural logarithm of 2 and the n th root of 2 (which works for any integer n > 1) if calculated using 2 = 1 + 1.
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