How do you convert 1.8 as a fraction?

Question

How do you convert  1.8 as a fraction?

Savannah Anderson · Accepted Answer

I'd like to add the general way to convert finite decimal number into fractions: we know that, since we count in base #10#, dividing and multiplying by #10# shifts the beginning of the decimal digits, adding zeroes where necessary, so for example

#65*1\color(green)(0) = 65\color(green)(0)#, or

#48.26*10=482.5#, while

#65 div 10 = 6.5#, and

#48.26 div 10 = 4.826#.

Also, note that a power of ten is simply a one followed by as many zeroes as the exponent of the power, so for example

#10^\color(green)(3)=1\color(green)(000)#

Starting from this assumptions, it's easy to see that if you multiply (or divide) by a power of ten, you shift the beginning of the decimal digits right (or left) by a number of steps which is equal to the number of zeroes: working again with the examples above, we have

#65*1\color(green)(00) = 65\color(green)(00)#, or

#48.26*1000=48250#, while

#65 div 100 = 0.65#, and

#48.26 div 1000 = 0.04826#.

So, when you have a finite decimal number, you can alyaws see it as a whole number who has been divided by a proper power of ten. In your case, you can see #1.8# as #18#, with the beginning of the decimal digits shifted left by one. But for all we said above, shifting left by one means to divide by #10#, and so you have

#1.8=18/10 = 9/5#

Avery Alexander · Answer

undefined To convert 1.8 to a fraction, multiply both the numerator and denominator by 10 to remove the decimal. This gives $1.8 = \frac{18}{10}$. Simplify the fraction to its lowest terms, which is $ \frac{9}{5} $.