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What is the value of #1.875# in fractional form?

Answer 1

Genesis Allen

#1.875 = 15/8#

Given:

#1.875#

Since the last digit is #5#, this is half of a shorter decimal number, so multiply it by #2# to find:

#1.875 = 1/2 * 3.75#

#3.75# also ends with a #5#, so is half of a shorter decimal:

#3.75 = 1/2 * 7.5#

#7.5# also ends with #5#, so is half of a shorter decimal:

#7.5 = 1/2 * 15#

Now that we've arrived at an integer, we can determine the simplest fraction:

#1.875 = 1/2 * 1/2 * 1/2 * 15 = 15/(2^3) = 15/8#

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Answer 2

Nathan Axel

#1.875 = 15/8#

Here's another way to find the fraction for a decimal representation if you have a calculator: use continued fractions.

Given:

#1.875#

Write down the whole number part #color(red)(1)#, subtract it and take the reciprocal to get approximately:

#1.14285714286#

Write down the whole number part #color(red)(1)#, subtract it and take the reciprocal to get approximately:

#6.99999999986#

We have obviously hit a rounding error and this value should be #7#, so write down #color(red)(7)# and stop.

What we have discovered is:

#1.875 = color(red)(1) + 1/(color(red)(1)+1/color(red)(7)) = 1+7/8 = 15/8#

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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.