Question

practice problems:
perform the following calculations and report the answer to the correct number of significant figures
$6.70 + 11.9 + 251.875 - 89.552 =$
$2300/4.75 =$
$2.300/4.75 =$
$\frac{(100.0 - 85.457)}{(45.62 - 34)} =$
$\frac{(419.426 - 85.1)}{(2399.43)} =$
1.5 mathematical treatment of measurement results
in your own words, describe dimensional analysis.

Explanation:

First Set of Calculations (Step-by-Step Format)

Step1: Sum and subtract values

$6.70 + 11.9 + 251.875 - 89.552 = 180.923$

Step2: Round to 1 decimal place

(Least decimal places: 1, from 11.9)
$180.923
ightarrow 180.9$

Step3: Divide the two values

$2300/4.75 = 484.210...$

Step4: Round to 2 significant figures

(Least sig figs: 2, from 2300)
$484.210...
ightarrow 4800$

Step5: Divide the two values

$2.300/4.75 = 0.484210...$

Step6: Round to 3 significant figures

(Least sig figs: 3, from 4.75)
$0.484210...
ightarrow 0.484$

Step7: Calculate numerator and denominator

$\text{Numerator}: 100.0 - 85.457 = 14.543$
$\text{Denominator}: 45.62 - 34 = 11.62$

Step8: Divide and round to 2 sig figs

$\frac{14.543}{11.62} = 1.2515...
ightarrow 1.3$
(Least sig figs in subtraction: 2, from 34)

Step9: Calculate numerator

$419.426 - 85.1 = 334.326$

Step10: Divide and round to 3 sig figs

$\frac{334.326}{2399.43} = 0.1393...
ightarrow 0.139$
(Least decimal places: 1, from 85.1; result has 3 sig figs)

Dimensional analysis is a method used in science and math to check the consistency of equations, convert between units, and derive relationships by analyzing the fundamental physical dimensions (like mass, length, time) of all quantities involved. It relies on the rule that only quantities with identical dimensions can be added, subtracted, or equated to each other.

Answer:

$6.70 + 11.9 + 251.875 - 89.552 = 180.9$
$2300/4.75 = 4800$
$2.300/4.75 = 0.484$
$\frac{(100.0 -85.457)}{(45.62 -34)} = 1.3$
$\frac{(419.426 -85.1)}{(2399.43)} = 0.139$

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Dimensional Analysis Question (Answer-Explanation Format)