43.123456789 is a terminating decimal. It is rational because decimal expansion is terminating. Therefore, it can be expressed in p/q form where factors of q are of the form 2n.
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.
43.123456789 43.123456789 is terminating So, it would be a rational number In a terminating expansion of 𝑝/𝑞, q is of the form 2n 5m So, prime factors of q will be 2 or 5 or both only.
(i) 43.123456789 has a terminating decimal expansion. This implies it is a rational number of the form pq and q is of the form 2m×5n 2 m × 5 n , where p and q are non-negative integers. The prime factors of the denominator of the given rational number are 2 and 5 .
For example, take the number 0.33333... Even though this is often simplified as 0.33, the pattern of 3's after the decimal point repeat infinitely. This means that the number can be converted into the fraction 1/3, and is a rational number.
(d) 0.4014001400014... is a non-terminating and non-recurring decimal and therefore is an irrational number.
Jeremy says that 5.676677666777... is a rational number because it is a decimal that goes on forever with a pattern.
In fact any decimal number which ends after a limited number of places beyond decimal point, or in which digits repeat endlessly after decimal place, are rational number. Here in 3.33333............ , 3 gets repeated endlessly i.e. till infinity and hence is a rational number.
The digit 3 is obtained endlessly as new trailing zeros are added and the division algorithm continued. The decimal 0.3333… is called a recurring decimal.
Just divide the numerator by the denominator . If you end up with a remainder of 0 , then you have a terminating decimal. Otherwise, the remainders will begin to repeat after some point, and you have a repeating decimal.
All the non terminating non repeating numbers are irrational numbers. We know that a non terminating number is a decimal number that goes on endlessly with an infinite number of digits. Thus, we observe that 0.12012001200012... is a non terminating number.
(i) Clearly , the given number 23.123456789 is a terminationg decimal. So, it is rational and the prime factors of its denominatior are 2 or 5 or both.
Show that 0.1234 is rational. A rational number is any number that can be expressed as the ratio of two integers. All terminating and repeating decimals can be expressed in this way so they are irrational numbers.
Ans: The number 0.101100101010 is a terminating decimal number, and the terminating decimals are considered as rational numbers, so this number is not an irrational number.
3, 9 Classify the following numbers as rational or irrational: (v) 1.101001000100001 1.10100100010000 It is a non-terminating , non-repeating decimal therefore, it is a irrational number.
D) 3.141141114 is an irrational number because it has not terminating non repeating decimal expansion.
If the number is in decimal form then it is rational if the same digit or block of digits repeats. For example 0.33333... is rational as is 23.456565656... and 34.123123123... and 23.40000... If the digits do not repeat then the number is irrational.
The decimal 0.3333 is a rational number. It can be written as the fraction 3333/10,000. A rational number is defined as any number that can be written as a ratio, or fraction, of two integers. Since both 3,333 and 10,0000 are integers, or whole numbers, you know the decimal 0.3333 is a rational number.
Repeating Decimals vs Terminating Decimals
Repeating decimals are those in which the digits repeat in a pattern. On the other hand, terminating decimals are those that have an end. For example, while 0.4444.....is a repeating decimal, 0.4 is a terminating decimal.
The number "pi" or π (3.14159...) is a common example of an irrational number since it has an infinite number of digits after the decimal point. ... If a number can be expressed as a ratio of two integers, it is rational.
Here, the given number is expressed in the form of p/q and has recurring decimal. Hence, -0.6666….. is a rational number.
>>2 - √(3) is an irrational number.
A repeating decimal is a decimal that does not terminate but keeps repeating the same pattern. 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.
As another example, √2 = 1.414213…. is irrational because we can't write that as a fraction of integers. The decimal expansion of √2 has no patterns whatsoever. In particular, it is not a repeating decimal.
0.66666 is a rational number with repeating decimals.