Question

Convert \[\dfrac{7}{{12}}\] into a decimal.

Answer 1

Hint: In decimal form of a number the whole number is separated from the fractional part by a decimal point.

Complete step-by-step answer:
In the decimal form the whole number and the fractional part are separated by a decimal point. In our case the fraction is \[\dfrac{7}{{12}}\]. To express this in the decimal form divide \[7\] by \[12\]. When \[7\] is divided by \[12\] the quotient is \[0\]and the fractional part is \[\dfrac{7}{{12}}\]. Hence the whole number here is \[0\]and the fractional part is \[\dfrac{7}{{12}}\].
\[\therefore \] \[\dfrac{7}{{12}}\] \[ = \] \[0.583 = 0.58\]
In the above step we observe that the decimal form is recurring, i.e. the number \[3\] keeps on occurring after \[0.58\]. In this case we round off the number generally to two digits after the decimal point. Hence, rounding off \[0.583333\] to two digits after the decimal point we get
 \[\dfrac{7}{{12}}\] \[ = \] \[0.583 = 0.58\].

Additional information:
In some fractions if the denominator can be converted to \[100\], then convert the denominator to \[100\] by multiplying both the numerator and denominator with a suitable number instead of dividing the numerator with the denominator. This makes decimal conversion easier. For example for the fraction \[\dfrac{4}{{25}}\], the denominator \[25\] can easily be converted into \[100\] by multiplying it with \[4\]. Hence multiply both the numerator and the denominator by \[4\], and then convert it to a decimal:
\[\therefore \] \[\dfrac{4}{{25}}\] \[ = \] \[\dfrac{{4 \times 4}}{{25 \times 4}}\] \[ = \] \[\dfrac{{16}}{{100}}\] \[ = \] \[0.16\].

Note: Rounding off means to make the number simpler by preserving the significant figures and converting the numbers after the decimal point to a certain degree of accuracy. For example in the above sum the number \[0.583333\] was rounded off to two digits after the decimal point. For this observe the third digit after the decimal point that is \[3\], since \[3\] is less than \[5\] therefore the previous digit that is \[8\] remains the same, hence the rounded off number is \[0.58\]. If in case the number was greater than or equal to \[5\] then the previous digit would have been rounded off to the next higher integer.