Find the common fraction equivalent to 0.12

2 answers:

8 0

The answer is: " $\frac{4}{33}$ "  .
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Given: 0.1212121212..... repeating ; write that value as a fraction;
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In other words; we are given: "0.1212121212..... repeating infinitely" ;

→ that is to say; "0.12 ... ; {the "12" decimal portion repeats infinitely} ;
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→ We write this value, as a fraction, as: "12/99" ;
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→Explanation:
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Note: "0.99999999...... repeating infinitely; = "1" .
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→Since:

Let us say that we have:

"x = 0.999999 ; repeating infinitely;

In order words, let us say we have: "x = 0.9.... ; the "9" decimal repeats infinitely;
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Then "10x" ; (that is: "10" multlipled by "x"; or "10*x" or "10x" ); is equal to:

"10" * (0.999999.....) = 9.99999999...... (the "9" decimal repeats infinitely);

in other words: 10x = 9.99999999....

Divide each side by "10" ;

to get "x = 0.9999999....." ; the decimal "9" repeats indefinitely...." ;

But if you have: "10x = 10" ; divide each side of the equation by "10" ;
you get: "x = 1" .
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Also, if "x = 0.9999...(repeating infinitely);

then: 10x = 9.99999.
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10x = 9.999999999999999......
−   x = 0.999999999999999.......
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9x = 9.00000000000000000000.....

→ 9x = 9 ;

Divide each side of the equation; to get;

9x /9 = 9/ 9 ; to get: x = 1 ; and we have: x = 0.9999.... ; so
x= 0.99999.... = 1 ;
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So, if the numbers "12" is repeating, we divie "12" by "99" ;
that is; we divide "12" by "two 9's" ; since "12" is a "TWO-digit number"; a "two-digit number" is being repeated infinitely.
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So; 0.12121212.....(the "12" is the decimal that repeats infinitely);

= 12/99 ; which can be simplified;

Divide each side (both the numerator AND the denominator); by "3" ;
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" 12/99 " = "(12÷3) / (99÷3) = 4/33 " .
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The answer is: $\frac{4}{33}$   .
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LuckyWell [14K]3 years ago

6 0

Answer is 4/33 hope this helps

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It took sandy two hours to jog 13 miles. She ran 7 1/2 miles in one hour. How far did she run during the second hour

Zarrin [17]

Sandy ran 5 ½ during the second hour.

Total amount Sandy used to jog for 2 hours = 13 miles
Amount Sandy used to run in the 1st hour = 7 ½

<h2>Further Explanation</h2>

Therefore the amount Sandy used to run in the 2nd hour = Total amount Sandy used to jog for 2 hours – Amount Sandy used to run in the 1st hour

= 13 – 7 ½ (and can be expressed as 7 + ½)

= 13 – (7 + ½)

= 13 – 7 – ½

= 6 – ½ (otherwise expressed as 6/1 – 1/2)

= (6 x 2) – (1 x 1) / 2

= (12) – (1) / 2

= 12 – 1 / 2

= 11/2

= 5 ½

Hence, Sandy ran 5 ½ miles during the second hour.

Based on the above expression, it is observed that there is an element of fractions in the math problem. Also, BODMAS was clearly used to derive the solution to the given question.

Recall, 13 – (7 + ½). The mathematical signs, (–) and (+) were multiplied; one of mathematics rule states that – x + = –; thus 13 – 7 – ½

Notably, fractions deal with denominators and numerators; and in these questions, with the help of BODMAS, they (6/1 – 1/2) were used to factor each other out to derive the final answer 5 ½.

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