How do you simplify #9.594 div 0.06#?

Question

Julia Adams · Accepted Answer

undefined To simplify $9.594 \div 0.06$, divide 9.594 by 0.06. This results in 159.9. Therefore, $9.594 \div 0.06 = 159.9$.

Abigail Allen · Answer

#= 159.6#

The rule with dividing BY a decimal is simple ... DON'T!!

You can change any decimal into a whole number by multiplying by a power of #10#

Write the division as a fraction:

#9.594/0.06#

Multiply the numerator and the denominator by the same number

#9.594/color(blue)(0.06) color(red)(xx 100/100)" "larr [color(red)(100/100 =1)]#

This changes the denominator into a whole number:

#=959.4/color(blue)(6)" "larr# divide as usual

#6|ul(9" "^3 5" "^5 9." "^5 4)# #color(white)(xx)1color(white)(x.x)5color(white)(xxx)9. color(white)(x.)6" "larr# details below

#= 159.6#

#9 div 6 = 1 " carry " 3# #35 div 6 = 5 " carry " 5# #59 div 6 = 9 " carry " 5# #54div 6 = 9# , no remainder

Eva Abramson · Answer

A way to get round the decimal place in the initial division expression.

#159.9# Note that #9.594# is the same as #9594xx1/1000# Note that #0.06# is the same as #6xx1/100# So #9.594-:0.006# is the same as #[9594-:6]xx[1/1000-:1/100]# #(9594-:6)xx1/10# I will do the division first then multiply by the #1/10# at the very end #" "9594# #color(magenta)(1000)xx6->ul(6000) larr" subtract"# #" "3594# #color(magenta)(color(white)(1)500)xx6->ul(3000) larr" subtract"# #" "594# #color(magenta)(color(white)(10)90)xx6->ul(color(white)(0)540)larr" subtract"# #" "color(white)(0)54# #color(magenta)(color(white)(100)9)xx6->" "ul(54) larr" subtract"# #" "0# As we have 0 we may now stop the division #9594-:6 = color(magenta)(1599)# Now we multiply by the #1/10# giving: #159.9# ~~~~~~~~~~~~~~~~~~~~~~~~~~~ If the division had not finished with a 0 at that point then we would have gone into decimal values.