the decimal expansion of 147/120 will be terminate after how many decimal
3 decimal
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To determine whether the decimal expansion of 147/120 terminates or repeats, we can simply simplify the fraction and check the prime factors of the denominator.
Step 1: Simplify the fraction 147/120. Both 147 and 120 are divisible by 3, so we can divide them both by 3.
147 ÷ 3 = 49
120 ÷ 3 = 40
Therefore, 147/120 simplifies to 49/40.
Step 2: Check the prime factors of the denominator (40). The prime factors of 40 are 2 and 5.
Step 3: Since the prime factors of the denominator are only 2 and 5, the decimal expansion of the fraction will be terminating.
To determine the exact number of decimal places, we need to find the power of 10 that can cancel out the prime factors of 5. In this case, the highest power of 5 in the prime factorization of 40 is just 1 (5^1 = 5).
Therefore, the decimal expansion of 147/120 will terminate after 1 decimal place.