Answer: Can I get brainliest and 5 stars? thank you.
a) [tex]\frac{65}{99}[/tex]
b) [tex]\frac{59}{90}[/tex]
c) [tex]\frac{13}{20}[/tex]
Step-by-step explanation:
a) [tex]0.65[/tex] I can't put line above it, but the line expresses that 6 and 5 and repeating infinitely. Let X equal the decimal number.
[tex]x=0.65[/tex]
First multiply by 1 followed by as many zeros as repeating numbers there are. In this case since 6 and 5 are the repeating numbers, we have to add 2 zeros which is basically multiplying by 100
0.65*100=65.65 (another 65 remains on the right because they're infinite.)
Now substract from the original number. Now we have a new equation that says: [tex]100x=65.65[/tex].
Substract equation 1 from equation 2.
[tex]100x=65.65\\-x=0.65[/tex]
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[tex]99x=65[/tex]
Solve just like any other equation. Divide by 99 to isolate x.
[tex]\frac{99x}{99}=\frac{65}{99}[/tex]
[tex]x=\frac{65}{99}[/tex] This is the fraction.
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b) [tex]0.65^-[/tex]This one is a little bit different because we only have 1 repeating number.
In this case we have to multiply by 10.
[tex]0.65^-*10=6.55^-[/tex]
Equation 1: [tex]x=0.65^-[/tex]
Equation 2: [tex]10x=6.55^-[/tex]
Substract.
[tex]10x=6.55^-\\-x=0.65^-[/tex]
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[tex]9x=5.9[/tex]
divide by 9 to isolate x
[tex]\frac{9x}{9}=\frac{5.9}{9}[/tex]
[tex]x=\frac{5.9}{9}[/tex]
To get rid of the decimal in the numerator, multiply both numerator and denominator by 10 so that we don't change the fraction.
[tex]x=(\frac{5.9*10}{9*10} )[/tex]
[tex]x=\frac{59}{90}[/tex] and this is your fraction.
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c) 0.65 this one has no repeating number. It's a finite decimal number.
I assume you already know that; [tex]a=\frac{a}{1}[/tex], so, we can do the same here to have a fraction.
[tex]0.65=\frac{0.65}{1}[/tex]
Now, in order to get rid of the decimal, multiply by 1 followed by as many zeros as decimal numbers are. In this case 2 zeros because there are 2 decimal numbers, so it's 100. Remember that if you do it in the numerator, you have to do it in the denominator as well to not change the fraction.
[tex]\frac{0.65*100}{1*100} =\frac{65}{100}[/tex]
Simplify if possible.
[tex]\frac{65/5}{100/5} =\frac{13}{20}[/tex] This is your fraction.
