Fractions and decimals are two ways of writing the exact same amount. Once you can move between them, you can pick whichever form is easiest for the problem in front of you.
The number of decimal places tells you exactly what denominator to use: 1 place means tenths (over 10), 2 places means hundredths (over 100). Write the digits (without the point) as the numerator, then simplify.
0.6 has 1 decimal place, so it's 6 tenths: 6/10. Both 6 and 10 can be divided by their greatest common factor, 2, giving the simplified fraction 3/5.
0.75 has 2 decimal places, so it's 75 hundredths: 75/100. The greatest common factor of 75 and 100 is 25, giving 3/4.
Writing the fraction is only half the job — always check whether it can be simplified. A fraction is fully simplified when the numerator and denominator share no common factor besides 1.
There are two ways to turn a fraction into a decimal. Use whichever one fits the problem:
If the denominator is a factor of 10, 100, or 1000, multiply the top and bottom by the same number to reach a power of 10 — then write it straight as a decimal.
This always works, for any fraction — a fraction bar just means division. Use long division, adding a decimal point and zeros to the numerator as needed.
Method 1 — 4 is a factor of 100, so multiply top and bottom by 25:
Method 2 — 8 isn't a factor of 10, 100, or 1000, so divide instead. Since 1 doesn't divide evenly by 8, add a decimal point and zeros to keep going: 1 becomes 1.000.
Try dividing 1 by 3: 1.000 ÷ 3 = 0.333, and it keeps going forever — 0.3333... This is called a repeating decimal. We won't practice those here, but it's good to know they exist!
Work through each conversion in two stages.
Here's the fraction.