To express 0.125 as a fraction, we need to understand the concept of decimal place value. In decimal notation, each digit represents a different power of 10, with the first digit to the right of the decimal point representing tenths, the second digit representing hundredths, the third digit representing thousandths, and so on.
Express 0.125 as a fraction
So, 0.125 can be expressed as follows:
0.125 = 1/10 + 2/100 + 5/1000
To simplify this expression and obtain a single fraction, we need to find a common denominator for the three fractions. The smallest common denominator is 1000, since it is divisible by 10, 100, and 1000. We can then rewrite the three fractions with this denominator:
0.125 = 1/10 * 100/1000 + 2/100 * 10/10 + 5/1000
Simplifying each fraction, we get:
0.125 = 100/1000 + 20/1000 + 5/1000
Combining the fractions, we get:
0.125 = (100 + 20 + 5) / 1000
Simplifying the numerator, we get:
0.125 = 125 / 1000
Finally, we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 125. Dividing both by 125, we get:
0.125 = 1/8
Therefore, 0.125 can be expressed as the fraction 1/8.
In conclusion, to express a decimal as a fraction, we need to understand the concept of decimal place value and find a common denominator for the fractions. We then simplify the expression by combining the fractions and simplifying the numerator and denominator. By following these steps, we can easily express any decimal as a fraction.