How do you convert 4/15 to a decimal?

2 Answers
Feb 22, 2016

The decimal form of #4/15# is #0.2bar6#.

Explanation:

Divide the numerator by the denominator.

#4/15=#

#0.2666...=#

#0.2bar(6)#

In the United States, the repeating decimal is represented with a bar above the repeating decimal. The bar has a fancy name called a vinculum, which I've never heard anyone use. Different countries have different conventions. You can read about it at https://en.m.wikipedia.org/wiki/Repeating_decimal

Feb 9, 2018

Assuming you do not have a calculator and you need to solve this manually. The explanation takes longer than doing the maths.

#0.26bar6#

Explanation:

Using an example: note that the bar in #0.33bar(3)# means that the 3 repeats for ever

With some question you are left with no choice and have to do a division.

However, this question is one where you can use a #ul("sort of cheat method")# thus avoiding doing any long division. It's all about using what you already know.

Note that #2xx15=30#. We also now that #1/3=0.333... # where the 3's just keep on repeating for ever. Perhaps we can use this.

#ul("Lets have a play!")#

Multiply by 1 and you do not change the value. However, 1 comes in many forms.

#color(green)(4/15color(red)(xx1)color(white)("d")->color(white)("d")4/15 color(red)(xx2/2)=8/30)#

#8/30# is the same as #8xxubrace(1/3)xx1/10#
#color(white)("dddd.ddddddddddddd")uarr#
#color(white)("dddddddddddddddd")0.333bar3" we know this bit"#

#8xx0.333bar3xx1/10#

Just dealing with the #8xx0.333bar3# bit first

#0.333bar3#
#ul(color(white)("dddd")8 larr" Multiply")#
#color(white)("") 2.666......#

Now we deal with the #xx1/10# bit

#2.666...xx1/10=0.2666...#

Using the standard abbreviation we have:

#0.26bar6#