A nail is 0.1875 inches thick. What is its thickness as a fraction?

Answer 1

Thickness of the nail as a fraction is #3/16#

As the nail is #0.1875# inches thick, its thickness, written here in decimal, in terms of fraction can be written as
#1875/10000#

The prime factors of numerator and denominator are

#(3xx5xx5xx5xx5)/(2xx2xx2xx2xx5xx5xx5xx5)#
or #(3xxcancel5xxcancel5xxcancel5xxcancel5)/(2xx2xx2xx2xxcancel5xxcancel5xxcancel5xxcancel5)#
= #3/16#
Hence, its thickness as a fraction is #3/16#
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Answer 2

#3/16# of an inch

One way to find the fraction is as follows:

#2xx0.1875 = 0.375#
#color(white)()# * The resulting decimal also ends with #5#, so multiply that by #2# again:
#2xx0.375 = 0.75#
#color(white)()# * This still ends with #5#, so double again:
#2xx0.75 = 1.5#
#color(white)()# * Finally we get an integer by doubling again:
#2xx1.5 = 3#
#color(white)()# Looking back, notice that we have multiplied by #2^4 = 16#, so divide by #16# to get our fraction:
#0.1875 = 3/16#
#color(white)()# Footnote

If doubling had not eventually resulted in an integer, it would still make the problem simpler.

For example, if we were given #0.01875# instead of #0.1875# then we would arrive at #0.3# after doubling #4# times, then could write:
#0.01875 = 3/10*1/16 = 3/160#
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Answer 3

#0.1875= 3/16#

A decimal can be written as a fraction with a power of 10 in the denominator.

#0.1875 = 1875/10000" "larr# now we have to simplify.
Note that a number is divisible by 25 if the last 2 digits are #00" "25" "50" "75#
Also that a number is divisible by 125 if the last 3 digits are #125" "375" "625" "875#

However, let's simplify using 25.

#(1875div25)/(10000div25) = 75/400" "larr# and again
#(75div25)/(400div25) = 3/16#
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Answer 4

The thickness of the nail as a fraction is 3/16 inches.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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