Question

absolute magnitudes of well - known stars
star name base - numeral form expanded form
sun 4.83
sirius (1 x 1) + (4 x 1/10) + (5 x 1/100)
arcturus - 0.31
vega (5 x 1/10) + (8 x 1/100)
spica - 3.55
barnards star (1 x 10) + (3 x 1) + (2 x 1/10) + (4 x 1/100)
proxima centauri (10 x 1) + (5 x 1) + (4 x 1/10) + (5 x 1/100)

Explanation:

Step1: Convert la forma expandida a la forma numeral base para Sirius

$(1\times1)+(4\times\frac{1}{10})+(5\times\frac{1}{100}) = 1 + 0.4+0.05=1.45$

Step2: Convert la forma expandida a la forma numeral base para Vega

$(5\times\frac{1}{10})+(8\times\frac{1}{100})=0.5 + 0.08 = 0.58$

Step3: Convert la forma expandida a la forma numeral base para Barnard's Star

$(1\times10)+(3\times1)+(2\times\frac{1}{10})+(4\times\frac{1}{100})=10 + 3+0.2 + 0.04=13.24$

Step4: Convert la forma expandida a la forma numeral base para Proxima Centauri

$(10\times1)+(5\times1)+(4\times\frac{1}{10})+(5\times\frac{1}{100})=10 + 5+0.4+0.05 = 15.45$

Step5: Escribir la forma expandida para el Sol

$4.83=(4\times1)+(8\times\frac{1}{10})+(3\times\frac{1}{100})$

Step6: Escribir la forma expandida para Arcturus

$- 0.31=-(0\times1 + 3\times\frac{1}{10}+1\times\frac{1}{100})$

Step7: Escribir la forma expandida para Spica

$-3.55=-(3\times1+5\times\frac{1}{10}+5\times\frac{1}{100})$

Answer:

Star Name	Base - Numeral Form	Expanded Form
Sirius	1.45	$(1\times1)+(4\times\frac{1}{10})+(5\times\frac{1}{100})$
Arcturus	- 0.31	$-(0\times1 + 3\times\frac{1}{10}+1\times\frac{1}{100})$
Vega	0.58	$(5\times\frac{1}{10})+(8\times\frac{1}{100})$
Spica	- 3.55	$-(3\times1+5\times\frac{1}{10}+5\times\frac{1}{100})$
Barnard's Star	13.24	$(1\times10)+(3\times1)+(2\times\frac{1}{10})+(4\times\frac{1}{100})$
Proxima Centauri	15.45	$(10\times1)+(5\times1)+(4\times\frac{1}{10})+(5\times\frac{1}{100})$