Question

Write each decimal as a fraction in simplest form. Show your work!

1. 0.008
2. -0.6
3. -2.05
4. 3.75

Answer 1

To write decimals as fractions, identify the place value of the last digit to form the fraction and then simplify. For example, 0.008 becomes 1/125, -0.6 becomes -3/5, -2.05 becomes -41/20, and 3.75 becomes 15/4 after simplification.

Step-by-step explanation:

Writing each decimal as a fraction in simplest form is a matter of identifying the place value of the last digit and then reducing the fraction to its simplest form. Here's how you can convert the given decimals:

1. 0.008 - Since the last digit is in the thousandths place, you write this as 8/1000. Simplifying, you divide both numerator and denominator by the greatest common divisor, which is 8, yielding 1/125.
2. -0.6 - With the last digit in the tenths place, this is -6/10. After simplifying by dividing numerator and denominator by 2, we get -3/5.
3. -2.05 - The last digit is in the hundredths place, so this is -205/100. Simplifying by dividing both by 5, we get -41/20.
4. 3.75 - Here, the last digit is in the hundredths place, giving us 375/100. Dividing both the numerator and denominator by 25, we obtain 15/4.

Through this process, we convert decimals to fractions and simplify them to their simplest form using the basic principles of fractions and division.