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It is not irrational
The number 1237/1250 is actually a rational number, not an irrational number. This is because it can be expressed as a fraction where both the numerator (1237) and the denominator (1250) are integers.
For the decimal expansion of a rational number to terminate, the denominator after simplification must be in the form of ( 2^n \times 5^m ), where ( n ) and ( m ) are non-negative integers. This is because the decimal system is based on the number 10, which is ( 2 \times 5 ).
In the case of 1237/1250, the denominator is already in the form of ( 2^n \times 5^m ) because ( 1250 = 2^1 \times 5^3 ). Therefore, the decimal expansion of 1237/1250 will terminate.
To find out after how many places it will terminate, we can simply perform the division:
1237÷1250=0.9896
The decimal expansion terminates after 4 decimal places. So, the decimal expansion of the rational number 1237/1250 terminates after 4 decimal places. It’s important to note that all rational numbers have decimal expansions that either terminate or repeat. Since 1237/1250 terminates, it confirms that it’s a rational number.
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