- Fractions, decimals, & percentages FAQ
- Rewriting decimals as fractions: 2.75
- Write decimals as fractions
- Rewriting decimals as fractions challenge
- Worked example: Converting a fraction (7/8) to a decimal
- Fraction to decimal: 11/25
- Fraction to decimal with rounding
- Converting fractions to decimals
Frequently asked questions about fractions, decimals, and percentages
What's the difference between a terminating and repeating decimal?
A terminating decimal is one that ends. For example, we can write as the decimal , which has just two decimal places. A repeating decimal, on the other hand, goes on forever. For example, we can write as the decimal , where the keeps repeating. Sometimes we use an overline to show which digits are repeating. So we could write as .
Every simplified rational fraction where the denominator has factors other than and will be a repeating decimal. Sometimes, the repeating part is longer than one digit. For example, we can write as the decimal or .
We can compare terminating and repeating decimals in a similar way as we compare two terminating decimals. We start from the largest place value, then compare each place value from left to right until we find one where the numbers differ.
For example, let's compare and . The two decimals both have ones and tenths. However, has hundredths, and has hundredths. So .
Try it yourself with our Converting fractions to decimals exercise.
How do we calculate percent increase and decrease?
To find the percent increase or decrease, we need two numbers: the original number and the new number. We divide the difference between the two by the original number. We'll get our value in decimal or fraction form, and we can rewrite it as a percent from there.
For example, if we start with and increase to , we'd find:
That was a positive change, so we had a increase.
On the other hand, if we start with and decrease to , we'd find:
That was a negative change, so we had a decrease.
Try it yourself with our Percent problems exercise.
How can writing percent expressions in different ways be helpful?
Writing equivalent forms of percent expressions can let us choose the form that makes the context clearest or that is easiest for us to calculate.
Suppose we wanted to find the price of a sewing machine after an discount. If the sewing machine originally cost dollars, we could represent the price after the discount like this:
Writing it that way makes it clear that we're taking away a percentage. If we wanted to make it faster to calculate, we might write the same amount like this:
Then we only have one operation to calculate, but the subtraction is less obvious.
Other times, we use a different form to help us use mental math. For example, suppose that there were of rain last year, but this year, it rained as much. We could write that as , but some people find it easier to calculate . They both mean the same thing, so use the one that works best for you!
Try it yourself with our Equivalent expressions with percent problems exercise.
Want to join the conversation?
- who created math?(10 votes)
- Can a repeated decimal go on forever?(4 votes)
- why is this important(2 votes)
- What if I don't understand how to do it?(2 votes)
- ask someone else you know. i would recommend your school teacher or a classmate, or your parents/guardians.(3 votes)
- what i dont understand is how thay got there answer and why did thay do what thay did to get there answer. pleas help :[(3 votes)
- How can we compare terminating and repeating decimals?(2 votes)