Convert -0.625 to a simplified fraction.
Understand the Problem
The question asks to convert the decimal -0.625 into a simplified fraction. This involves expressing the decimal as a fraction with a power of 10 in the denominator, and then simplifying the fraction to its lowest terms.
Answer
$-\frac{5}{8}$
Answer for screen readers
$ -\frac{5}{8} $
Steps to Solve
- Write the decimal as a fraction
Express the decimal -0.625 as a fraction by placing the digits after the decimal point over the appropriate power of 10. Here, 0.625 has three digits after the decimal, so we write it as a fraction with $10^3 = 1000$ in the denominator:
$$ -0.625 = -\frac{625}{1000} $$
- Simplify the fraction
Simplify the fraction $-\frac{625}{1000}$ by finding the greatest common divisor (GCD) of the numerator (625) and the denominator (1000) and dividing both by it. We can recognize that both 625 and 1000 are divisible by 25. Dividing both by 25 gives:
$$ -\frac{625 \div 25}{1000 \div 25} = -\frac{25}{40} $$
Now, we can see that both 25 and 40 are divisible by 5. Dividing both by 5 gives:
$$ -\frac{25 \div 5}{40 \div 5} = -\frac{5}{8} $$
Since 5 and 8 have no common factors other than 1, the fraction $-\frac{5}{8}$ is in its simplest form.
$ -\frac{5}{8} $
More Information
The decimal -0.625 is equivalent to the simplified fraction $ -\frac{5}{8} $. Decimal to fraction conversion is a fundamental concept in mathematics, useful in various applications.
Tips
A common mistake is not simplifying the fraction completely. For example, stopping at $-\frac{25}{40}$ instead of simplifying further to $-\frac{5}{8}$. Another common error is making a mistake in determining the sign of the fraction; since the initial decimal is negative, the resulting simplified fraction should also be negative.
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