How do you write #4 1/3# as a decimal? Use bar notation if the decimal is a repeating decimal.

2 Answers
Dec 10, 2017

#4.bar(3)#

Explanation:

#4(1/3)= 13/3#

#13/3= 4.bar3#

Dec 10, 2017

#4.bar33#

Explanation:

There are a couple things you could do:

Example 1:
Change the mixed fraction to an improper fraction.

Multiply the denominator and whole number,

#3 xx 4 = 12#

Take that answer and add the numerator,

#12 + 1 = 13#

Now put that answer over the denominator,

#13/3#

Next step is to divide #3# into #13#.

#color(white)( (3)/color(black)(3)) color(white)( (color(black)(4.33)))/( ")" 13.00) ""#
#color(white)(xx)(12)/color(white)#
#color(white)(xxxii)1(0)-> #bring down 0 (it becomes 10)#color(white)#
#color(white)(xxxxi)9/ color(white)#
#color(white)(xxxxx)1 -> #It will continue to repeat##

Since #4.33# is a repeating decimal, you would write it with a bar.

#4.bar33#

Example 2:
Write #4 1/3# as an expression.

#4 + 1/3#

Divide #1/3# the same way as above,

#color(white)( (1)/color(black)(3)) color(white)( (color(black)(0.33)))/( ") 1.00 ""#

Now that you know #1/3# is #0.bar33#, add the whole number from the fraction,

#4 + 0.bar33 = 4.bar33#

A third way, and probably the easiest way, is to use a calculator. However, if you need to show work use the examples above.