Wie rechnet man 16 / 625 = 0,256?

Question

Aufgabe:

                                     __16__

(⅖)²×(⅖)²=(⅖)²+²=(⅖)^4=625=0,256

Problem/Ansatz:

Wie hat man den Bruch 16

                                   ______

                                     625

in die Dezimalzahl 0,256 umgewandelt?

Comments

\( \frac{16}{625} \)=\( \frac{2^4}{5^4} \)=(\( \frac{2}{5} \))^4=(\( \frac{4}{10} \))^4=\( 0,4^{4} \)=\( 0,16^{2} \)=0,0256

Answer 1

\(\frac{2^4}{5^4}=\frac{2^4\cdot 2^4}{5^4\cdot 2^4}=\frac{16^2}{10000}=\frac{256}{10000}=0,0256\)

Answer 2

Hallo,

\(\big(\frac{2}{5}\big)^2\cdot \big(\frac{2}{5}\big)^2=\big(\frac{2}{5}\big)^4=\frac{16}{625}=\frac{256}{10000}=0,0256\)

Gruß, Silvia

Answer 3

16/625 = 2^4/5^4 = (2/5)^4 = 0,4^4 = 0,0256

4^4= 2^8 = 256

oder die dividierst es aus:

16:625 = 0,0256

160

-------

1600

1250

---------

3500

3125

-------

3750

3750

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Answer 4

\(\dfrac25=\dfrac{2*2}{5*2}=\dfrac{4}{10}=0,4\)

\(\left(\dfrac25\right)^4\\=\left(\dfrac{4}{10}\right)^4=\dfrac{4^4}{10^4}\\=   \dfrac{256}{10000}=0,0256\)