QuestionShow that equals 0.28 using long division.
Studdy Solution
STEP 1
Assumptions1. We are asked to prove that the fraction is equal to the decimal0.28. . We will use long division to convert the fraction into a decimal.
STEP 2
We will start by setting up the long division. The numerator (7) is the dividend and the denominator (25) is the divisor.
\require{enclose}
\begin{array}{r|l}
25 &7\end{array}
STEP 3
Since7 is less than25, we can't divide7 by25. So, we add a decimal point and a zero to the right of7, making it7.0.
\require{enclose}
\begin{array}{r|ll}
25 &7.0\end{array}
STEP 4
Now, we divide70 by25. The quotient is2 and the remainder is20.
\require{enclose}
\begin{array}{r|ll}
25 &7.0 \\
\multicolumn{2}{r}{2\enclose{longdiv}{70}} & \text{R}20\end{array}
STEP 5
We add another zero to the right of the decimal point and bring it down. Now, we have200.
\require{enclose}
\begin{array}{r|lll}
25 &7.00 \\
\multicolumn{2}{r}{2\enclose{longdiv}{70}} & \text{R}20 \\
\multicolumn{3}{r}{\enclose{longdiv}{200}}
\end{array}
STEP 6
Now, we divide200 by25. The quotient is8 and the remainder is0.
\require{enclose}
\begin{array}{r|lll}
25 &.00 \\
\multicolumn{2}{r}{2\enclose{longdiv}{70}} & \text{R}20 \\
\multicolumn{3}{r}{8\enclose{longdiv}{200}} & \text{R}0\end{array}
STEP 7
Since the remainder is0, we have finished the division. The quotient is0.28.
\require{enclose}
\begin{array}{r|lll}
25 &7.00 \\
\multicolumn{2}{r}{2\enclose{longdiv}{70}} & \text{R}20 \\
\multicolumn{3}{r}{\enclose{longdiv}{200}} & \text{R}0\end{array}Therefore, is equal to0.28.
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