Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
Let's prove algebraically that [tex]\(0.\dot{5} = \frac{5}{9}\)[/tex].
1. Assign the repeating decimal to a variable:
Let [tex]\( x = 0.\dot{5} \)[/tex]
2. Since [tex]\( 0.\dot{5} \)[/tex] is a repeating decimal, we know that:
[tex]\( x = 0.555555\ldots \)[/tex]
3. To eliminate the repeating part, multiply both sides of the equation by 10 to shift the decimal point one place to the right:
[tex]\( 10x = 5.555555\ldots \)[/tex]
4. Now, we have two equations:
[tex]\[ x = 0.555555\ldots \][/tex]
[tex]\[ 10x = 5.555555\ldots \][/tex]
5. Subtract the first equation from the second equation:
[tex]\[ 10x - x = 5.555555\ldots - 0.555555\ldots \][/tex]
6. Simplify both sides:
[tex]\[ 9x = 5 \][/tex]
7. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 9:
[tex]\[ x = \frac{5}{9} \][/tex]
Therefore, [tex]\( x = \frac{5}{9} \)[/tex].
1. Assign the repeating decimal to a variable:
Let [tex]\( x = 0.\dot{5} \)[/tex]
2. Since [tex]\( 0.\dot{5} \)[/tex] is a repeating decimal, we know that:
[tex]\( x = 0.555555\ldots \)[/tex]
3. To eliminate the repeating part, multiply both sides of the equation by 10 to shift the decimal point one place to the right:
[tex]\( 10x = 5.555555\ldots \)[/tex]
4. Now, we have two equations:
[tex]\[ x = 0.555555\ldots \][/tex]
[tex]\[ 10x = 5.555555\ldots \][/tex]
5. Subtract the first equation from the second equation:
[tex]\[ 10x - x = 5.555555\ldots - 0.555555\ldots \][/tex]
6. Simplify both sides:
[tex]\[ 9x = 5 \][/tex]
7. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 9:
[tex]\[ x = \frac{5}{9} \][/tex]
Therefore, [tex]\( x = \frac{5}{9} \)[/tex].
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.