Rational Numbers in Different Forms Practice
Math 8 Q1 (Pre-Algebra) / The Number System
Which of the following rational numbers can be expressed as a repeating decimal: 78, 512, 1725, or 3140?(1 point)
To determine which of the given numbers can be expressed as a repeating decimal, we need to analyze their factors and check if they have a terminating or repeating decimal representation.
Let's analyze each number:
1. 78: This number can be written as 78/1. When we divide 78 by 1, we get a terminating decimal representation of 78.
2. 512: This number can be written as 512/1. When we divide 512 by 1, we get a terminating decimal representation of 512.
3. 1725: This number can be written as 1725/1. When we divide 1725 by 1, we get a terminating decimal representation of 1725.
4. 3140: This number can be written as 3140/1. When we divide 3140 by 1, we get a terminating decimal representation of 3140.
Based on our analysis, none of the given numbers can be expressed as a repeating decimal.
To determine which of the given rational numbers can be expressed as a repeating decimal, we need to check if the number can be written in the form of a fraction with a denominator that results in a repeating decimal.
Let's go through each number one by one:
1. 78:
To check if 78 can be expressed as a repeating decimal, we need to convert it into a fraction: 78/1. Since the denominator is not divisible by any prime factors other than 2 or 5, the fraction will not produce a repeating decimal.
2. 512:
Converting 512 into a fraction gives us 512/1. Similar to the previous case, the denominator only has prime factors of 2, and therefore, it will not result in a repeating decimal.
3. 1725:
Expressing 1725 as a fraction gives us 1725/1. The denominator 1 does not contain any prime factors other than 2 and 5, so it will not give a repeating decimal.
4. 3140:
Writing 3140 as a fraction gives us 3140/1. Just like the previous cases, the denominator 1 does not have any prime factors other than 2 and 5, which means it will not result in a repeating decimal.
Based on our analysis, none of the given numbers can be expressed as a repeating decimal.