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How do you evaluate the following expression using decimals?: # 4.136 - 8.2612 + 77/64 + 205/128#

Answer 1

#4.136-8.2612+77/64+205/128=-1.3205125#

Here #77/64# and #205/128# have only #2# as prime factors for denominators. In fact they are #2^6# and #2^7# and hence they can be converted into decimal form by multiplying numerator and denominator by #5^6=15625# and #5^7=78125#.

Hence #77/64=1.203125# and #205/128=1.6015625#.

Hence #4.136-8.2612+1.203125+1.6015625=-1.3205125#

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Answer 2

Aurora Arias

To evaluate the expression using decimals, first convert the fractions to decimals:

( \frac{77}{64} = 1.203125 )

( \frac{205}{128} = 1.6015625 )

Now, substitute these decimal values into the expression:

( 4.136 - 8.2612 + 1.203125 + 1.6015625 )

Now, perform the arithmetic:

( 4.136 - 8.2612 + 1.203125 + 1.6015625 = -3.1215125 + 2.8046875 )

Now, add the numbers:

( -3.1215125 + 2.8046875 = -0.316825 )

Therefore, the value of the expression is approximately -0.316825 when evaluated using decimals.

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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.