Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Dec 02, 2023

Find the lower and upper bounds of the mass of chemicals after a $7.3 \mathrm{~g}$ decrease from an initial $62 \mathrm{~g}$ , rounded to 2 significant figures.

STEP 1

Assumptions
1. The initial mass of the chemicals is 62g, rounded to 2 significant figures.
2. The mass of the chemicals decreased by 7.3g, rounded to 2 significant figures.
3. We need to find the lower and upper bounds of the final mass of the chemicals.

STEP 2

First, we need to find the lower and upper bounds of the initial mass of the chemicals. Since the initial mass is rounded to 2 significant figures, the lower bound is half a unit less than the given value and the upper bound is half a unit more.
$Lower\, bound\, of\, initial\, mass = 62 - 0.5$ $Upper\, bound\, of\, initial\, mass = 62 + 0.5$

STEP 3

Calculate the lower and upper bounds of the initial mass.
$Lower\, bound\, of\, initial\, mass = 62 - 0.5 = 61.5\, g$ $Upper\, bound\, of\, initial\, mass = 62 + 0.5 = 62.5\, g$

STEP 4

Next, we need to find the lower and upper bounds of the decrease in mass. Since the decrease in mass is rounded to 2 significant figures, the lower bound is half a unit less than the given value and the upper bound is half a unit more.
$Lower\, bound\, of\, decrease = 7.3 - 0.05$ $Upper\, bound\, of\, decrease = 7.3 + 0.05$

STEP 5

Calculate the lower and upper bounds of the decrease in mass.
$Lower\, bound\, of\, decrease = 7.3 - 0.05 = 7.25\, g$ $Upper\, bound\, of\, decrease = 7.3 + 0.05 = 7.35\, g$

STEP 6

Now, we can calculate the lower and upper bounds of the final mass of the chemicals by subtracting the upper and lower bounds of the decrease from the lower and upper bounds of the initial mass, respectively.
$Lower\, bound\, of\, final\, mass = Lower\, bound\, of\, initial\, mass - Upper\, bound\, of\, decrease$ $Upper\, bound\, of\, final\, mass = Upper\, bound\, of\, initial\, mass - Lower\, bound\, of\, decrease$

STEP 7

Plug in the values for the lower and upper bounds of the initial mass and the decrease to calculate the lower and upper bounds of the final mass.
$Lower\, bound\, of\, final\, mass = 61.5\, g - 7.35\, g$ $Upper\, bound\, of\, final\, mass = 62.5\, g - 7.25\, g$

STEP 8

Calculate the lower and upper bounds of the final mass.
$Lower\, bound\, of\, final\, mass = 61.5\, g - 7.35\, g = 54.15\, g$ $Upper\, bound\, of\, final\, mass = 62.5\, g - 7.25\, g = 55.25\, g$
The lower and upper bounds of the mass of the chemicals at the end of the experiment are 54.15g and 55.25g, respectively.

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