Задание 47

Докажите равенство:

\({\largeа)}\ 0{,}0(10)=0{,}(01);\phantom{\ 00000000}{\largeб)}\ 0{,}5(45)=0{,}(54);\phantom{\ 00000000}{\largeв)}\ 0{,}(77)=0{,}(7).\)

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Источник заимствования: Алгебра. Рабочая тетрадь. 7 класс. В 2 частях. Часть 1 / М.К. Потапов, А.В. Шевкин – Просвещение, 2018. – 23 c. ISBN 978-5-09-051661-7

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Решение:

\({\largeа)}\ 0{,}0(10)=0{,}(01),\)
\(\phantom{\largeа)}\ x=0{,}0(10),\)
\(\phantom{\largeа)}\ x=0{,}0101010{...},\)
\(\phantom{\largeа)}\ x=0{,}010101{...},\)
\(\phantom{\largeа)}\ x=0{,}(01)\)
\({\largeб)}\ 0{,}5(45)=0{,}(54),\)
\(\phantom{\largeб)}\ x=0{,}5(45),\)
\(\phantom{\largeб)}\ x=0{,}5454545{...},\)
\(\phantom{\largeб)}\ x=0{,}545454{...},\)
\(\phantom{\largeб)}\ x=0{,}(54)\)
\({\largeв)}\ 0{,}(77)=0{,}(7),\)
\(\phantom{\largeв)}\ x=0{,}(77),\)
\(\phantom{\largeв)}\ x=0{,}777777{...},\)
\(\phantom{\largeв)}\ x=0{,}(7)\)

Задание 46*Задание 48*