Question #e7107

2 Answers
Tazwar Sikder
Aug 14, 2017

#5.625#"

Explanation:

You already know #4 frac(1)(4)#" is the same as #4.25#", so you must know that #frac(1)(4)# is equal to #0.25#.

So let's find out what #frac(1)(8)# is in decimal form.

If you multiply #frac(1)(4)# by #frac(1)(2)#, you get #frac(1)(8)#:

#Rightarrow frac(1)(4) times frac(1)(2) = frac(1 times 1)(4 times 2) = frac(1)(8)#

Let's evaluate this again, but this time using decimals:

#Rightarrow frac(1)(4) times frac(1)(2) = 0.25 times 0.5#

#frac(1)(4)# is also half of #frac(1)(2)#, so let's write #0.25# as #frac(0.5)(2)#:

#Rightarrow frac(1)(4) times frac(1)(2) = frac(0.5)(2) times 0.5#

#Rightarrow frac(1)(4) times frac(1)(2) = frac(0.5 times 0.5)(2)#

#Rightarrow frac(1)(4) times frac(1)(2) = frac(frac(1)(2) times frac(1)(2))(2)#

#Rightarrow frac(1)(4) times frac(1)(2) = frac(frac(1)(4))(2)#

#Rightarrow frac(1)(4) times frac(1)(2) = frac(0.25)(2)#

Then, half of #25# is equal to #12.5#.

So half of #0.25# must be equal to #0.125#:

#Rightarrow frac(1)(4) times frac(1)(2) = 0.125#

#therefore frac(1)(8) = 0.125#

Now, let's evaluate #frac(5)(8)#:

#Rightarrow frac(5)(8) = frac(4)(8) + frac(1)(8)#

#Rightarrow frac(5)(8) = frac(1)(2) + frac(1)(8)#

#Rightarrow frac(5)(8) = 0.5 + 0.125#

#therefore frac(5)(8) = 0.625#

Finally, let's evaluate #5 + frac(5)(8)#:

#Rightarrow 5 + frac(5)(8) = 5 + 0.625#

#therefore 5 + frac(5)(8) = 5.625#

Therefore, #5 frac(5)(8)#" is expressed as #5.625#" in decimal form.

EZ as pi
Aug 14, 2017

#5 5/8= 5 625/1000 = 5.625#

Explanation:

A decimal is a way of writing fractions which have their denominators as powers of #10: 10, 10, 1000# and so on.

In the same way that you have learnt #1/4 = 0.25#, it is useful to know that #1/8 = 0.125" "#(This is just #1/4 div 2#)

Also:
#8xx125 = 1000" "# (*see below)
#4xx25=100#
#2xx5 = 10#

Make an equivalent fraction for #5/8#

#5/8 color(blue)(xx 125/125) = 625/1000" "[larrcolor(blue)(xx 125/125=xx1)]#

#:. 5 5/8=5 625/1000 = 5.625#

#rarr# do you also see that:

#16 xx 625 = 10,000#
#8xx125 = 1000#
#4xx25=100#
#2xx5 = 10#

Knowing these should help with the measurements on your ruler.
It will also help to memorise the eighths:

#1/8 = 0.125#
#3/8 = 0.375#
#5/8 = 0.625#
#7/8 = 0.875#

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