Two fractions are given. For each one, write its decimal equivalent and determine if the decimal is terminating or non-terminating.
a. 9/20
b. 4/15
I really have no idea how to do this. Please help! I'm not asking for the answer, just how to get it.
Am I right? 9/20 is a terminating number and 4/15 isn't?
just do the long division
9/20 means 9 divided by 20
Think back, back, to the fourth grade, when they introduced decimals, and just do the math.
Or, google long division with decimals for many examples and videos.
Oh okay. I think I get it. I googled terminating and non-termanating decimals and it's basically if numbers go on after the decimal. Thank you!
correct
To find the decimal equivalent of a fraction, you need to divide the numerator by the denominator. Let's start with the first fraction, 9/20.
To do this division, you can use long division or a calculator. Since dividing 9 by 20 might not give an exact decimal, we will use long division to find a decimal approximation.
1. Write 9 as the dividend and 20 as the divisor.
2. Perform long division by dividing 20 into 9. The quotient is the whole number part of the decimal, and the remainder helps us determine the fractional part.
The long division steps would look like this:
0.45
__________
20 | 9.00
-0
------
90
- 80
------
10
- 0
----
0
In this case, the division terminates, meaning it ends with a remainder of 0. The decimal equivalent of 9/20 is 0.45, and it is a terminating decimal.
Now let's move on to the second fraction, 4/15.
Using the same approach, perform long division by dividing 15 into 4:
0.26...
__________
15 | 4.00
-0
------
40
- 30
------
10
0
----
00
In this case, the division does not terminate, and we see the same remainder of 10 repeating indefinitely. The decimal equivalent of 4/15 is 0.26..., and it is a non-terminating decimal.
So, to determine if a decimal is terminating or non-terminating, you need to check if the division terminates (ends with a remainder of 0) or if it repeats indefinitely.