For example, 0.123123123. . . is a repeating decimal; the “123” will repeat endlessly. Any repeating decimal is equal to a rational number. For example, 0.123123. . . is equal to 123/999, or 41/333.
∴ Fraction form of the decimal 0.123123....... is 41333.
Explanation: The simplest exact fraction for the decimal number 0.123 is 1231000 .
Solution: 0.123 as a fraction is 123/1000.
So this number is a non-terminating repeating decimal because the bar shows it has endless repeats of the same three digits. [Write this on the card.] Show me on your whiteboard: is 0.123 rational or irrational? [Rational.]
Therefore, 0.123 bar can be expressed in the form of p/q as 41/333.
43.123456789 is a rational number of the form p/q and q is of the form 2m × 5n and the prime factors of q will be either 2 or 5 or both, 43.
Divide the repeating digits by the difference between the power of 10 used to multiply the decimal and 1. Therefore, the fraction form of 0.1212 is 433.
- 0.111111... = 1 and: 10x - x = 9x So, we can write 9x = 1. Hence, x = 1/9 is your fraction.
Solution: 0.124 as a fraction is 31/250.
0.2222… is equal to the fraction with 2 in its numerator (since that's the single number after the decimal point that's repeating over and over again) and 9 in its denominator. In other words, 0.2222… = 2/9.
Repeated decimals can be converted into fractions by shifting the decimal to the right and subtracting the decimals. To do this, multiply the number by 10 to the second power, then subtract. For example, 0.363636 repeating is 4/11 and 0.7141414 repeating is 707/990.
So we can see that our original decimal of 0.333333... is equal to the fraction 1/3.
Answer: 0.33333 as a fraction is 1/3.
Let us proceed to evaluate 0.33333 as a fraction.
0.33333333333… =1/3.
Answer and Explanation: 0.00137174211 expressed in fraction form is 137 , 174 , 211 100 , 000 , 000 , 000 . It may seem intimidating to convert a long decimal to a fraction, but we can use a simple process.
First, we can recognize that 0.16666666666 is approximately equal to 1/6.
∴ Fraction form of the decimal 0.12121212....... is 433.
Answer: the first two are terminating decimals. The 0.1212 … and the 0.123123 … are repeating decimals. There is no universally accepted notation for a repeating decimal.
Explanation: we can show 0.121212 as 0. (12) It means that 12 after the point repeat again and again. It implies that this number is not rational.
Any repeating decimal is equal to a rational number. For example, 0.123123. . . is equal to 123/999, or 41/333.
As, we observe that 0.12012001200012... is a non terminating, non repeating number, it's an irrational number. Hence, the given statement is incorrect, which is option (b). Note: We can't solve this question without knowing the difference between rational and irrational numbers.
Jeremy says that 5.676677666777... is a rational number because it is a decimal that goes on forever with a pattern. Is he correct? Why or why not? Yes, because the decimal is repeating.