So there's this question and the answer is supposedly #6.47#. Can someone explain why? #x = 4.2 and y = 0.5# Both x and y have been rounded to 1 decimal place. #t = x + 1/y# Work out the upper bound for #t.# Give your answer to #2# decimal places.

1 Answer
EZ as pi
May 28, 2017

Use the upper bound for #x# and the lower bound for #y#.

The answer is #6.47# as required.

Explanation:

When a number has been rounded to #1# decimal place, it is the same as saying to the nearest #0.1#

To find the upper and lower bounds, use: #" "0.1div 2 = 0.05#

For #x:#

#4.2-0.05 <= x < 4.2 +0.05#
#" "4.15 <= x < color(red)(4.25)#

For #y:#

#0.5-0.05 <= y < 0.5+0.05#
#" "color(blue)(0.45) <= y < 0.55#

The calculation for #t# is:

#t = x+1/y#

Because you are dividing by #y#, the upper bound of the division will be found from using the lower bound of #y#
(Dividing by a smaller number will give a bigger answer)

#t = color(red)(4.25) +1/color(blue)(0.45)#

#t = 4.25+2.222222...#

#t = 6.4722222...#

Given to #2# decimal places the answer is #6.47# as given.

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