Two Nuggets Apart

Q. The two gold nuggets weigh 20.17 g and 20.15 g. How many grams heavier is the one than the other? expects 0.02 g

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The web of concepts

given read from the words equation asked

The equations it used

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Check an answer

Q. The two gold nuggets weigh 20.17 g $a = 20.17$ g and 20.15 g $b = 20.15$ g. How many grams heavier is the one than the other?

The playground

Inputs

heavier

a

20.17 g

lighter

b

20.15 g

Outputs

difference

d

The solution

Solved with Uncertainty

Given

$a = 20.17$ g
$b = 20.15$ g

Find $d$ .

Working

$a = 20.17$ g $= 0.02017$ kg
$b = 20.15$ g $= 0.02015$ kg
difference of measurements $d = a - b$
$d = 0.02017 - 0.02015$
$d = 0.02$ g
$d = 2 \times 10^{−5}$ kg $= 0.02$ g
$d \approx 0.02$ gto 1 significant figure

Conclusion

A difference keeps the decimal places of what went into it, not its figures: close numbers taken apart lose most of their significant figures.

The Ruby

1require_relative "../physics"23question :two_nuggets_apart do4  kind :numerical5  describes "The two gold nuggets weigh %{heavier} and %{lighter}. %{difference}?"6  given heavier: "20.17 g"7  given lighter: "20.15 g"8  asks difference: "How many grams heavier is the one than the other"9end

1require_relative "../questions/two_nuggets_apart"2require_relative "../science/units_and_measurement/uncertainty"34solve :two_nuggets_apart, using: Uncertainty do5  take heavier: :a, lighter: :b6  take difference: :d7  answer find_value(:difference, in: "g", figures: 1)89  conclusion "A difference keeps the decimal places of what went into it, not its figures: close " \10             "numbers taken apart lose most of their significant figures."11end

1require_relative "../solutions/two_nuggets_apart"23play_with :two_nuggets_apart do4  title "Two Nuggets Apart"5end

The laws

quantity	written	units	within	from
first measured	$a$	—	—	Uncertainty
error in first	$Δ a$	—	—	Uncertainty
relative error in first	$δ_{a}$	—	—	Uncertainty
second measured	$b$	—	—	Uncertainty
error in second	$Δ b$	—	—	Uncertainty
relative error in second	$δ_{b}$	—	—	Uncertainty
product	$p$	—	—	Uncertainty
error in product	$Δ p$	—	—	Uncertainty
relative error in product	$δ_{p}$	—	—	Uncertainty
total	$t$	—	—	Uncertainty
difference	$d$	—	—	Uncertainty
least count	$l_{c}$	m	—	Uncertainty
scale division	$d_{m}$	m	—	Uncertainty
divisions read past	$N_{d}$	—	—	Uncertainty

δ_{a} = \frac{Δ a}{a}

first error over first

δ_{b} = \frac{Δ b}{b}

second error over second

p = a \cdot b

product of measurements

δ_{p} = δ_{a} + δ_{b}

relative errors add

Δ p = δ_{p} \cdot p

error from relative error

t = a + b

sum of measurements

d = a - b

difference of measurements

l_{c} = \frac{d_{m}}{N_{d}}

division shared out