Learn how to convert 0.015625 to a fraction by following these decimal to fraction conversion steps. Understand the concept of fractions, how to simplify them, and find the fractional equivalent of 0.015625.
Understanding 0.015625 as a Fraction
What is a Fraction?
Fractions are a fundamental concept in mathematics that represent a part of a whole. They consist of two numbers: a numerator and a denominator, separated by a slash (/) or a horizontal line. The numerator represents the number of equal parts we have, while the denominator represents the total number of equal parts in the whole.
Converting Decimal to Fraction
Converting a decimal to a fraction can be done by understanding the place value of the digits after the decimal point. In the case of 0.015625, the number is already in decimal form. To convert it to a fraction, we need to determine the place value of each digit.
The digit 0 is in the thousandths place, the digit 1 is in the ten-thousandths place, and the digit 5 is in the hundred-thousandths place. We can express these place values as powers of 10: 0.015625 = (0 * 10^-3) + (1 * 10^-4) + (5 * 10^-5).
To simplify the process, we can rewrite 0.015625 with the denominator as a power of 10, which is 10^5. This gives us 0.015625 = 15625/1000000.
Simplifying Fractions
Simplifying fractions involves reducing them to their simplest form by dividing both the numerator and denominator by their greatest common divisor (GCD). In the case of 15625/1000000, the GCD is 625. By dividing both the numerator and denominator by 625, we get 15625/1000000 = 25/160.
Writing 0.015625 as a Fraction
To write 0.015625 as a fraction, we have already determined that it is equivalent to 25/160. Therefore, 0.015625 can be expressed as the fraction 25/160.
Fractional Equivalent of 0.015625
The fractional equivalent of 0.015625 is 25/160. This means that 0.015625 represents 25 parts out of a total of 160 equal parts.
Decimal to Fraction Conversion Steps
To convert a decimal to a fraction, follow these steps:
- Determine the place value of each digit after the decimal point.
- Write the decimal as a sum of fractions, with each digit’s place value expressed as a power of 10.
- Simplify the fraction by dividing the numerator and denominator by their greatest common divisor.
- Write the simplified fraction as the fractional equivalent of the decimal.
By following these steps, you can convert any decimal to its fractional representation.
