Question

A repeating decimal + A fraction is

Answer 1

1. Step-by-step explanation:

How to transform a repeating decimal into a fraction?

To convert a decimal into a fraction we would usuallly write it over 100 and if it can be simplified any further we would. On the other hand repeating decimals are a bit different.

Let‘s see how to convert them:

$0.333333$

Imagine this decimal goes on and on forever and I want to convert it into a

fraction:

1. First step is to multiply by a factor of 10 then misusing it by a factor of one which would give you a whole number.

So let’s say: $0.33333 * 10 - 0.333333 * 1$

- It’s because the digits match up to subtract to a whole number so if I find the value is would be 3/9 since 10 - 1 is equal to 9 and 3.3333 - 0.33333 would be 3 but I can simplify this to 1/3.

$0.33333 = 1/3$

Now let’s use this knowledge to calculat a value:

$0.482482482 + 1/2$

Let’s convert this repeating decimal into a fraction:

$0.482482482 * 1000 - 0.482482482 * 1 = 482/999$

I have multiplied it by 1000 because that’s when we minus it gives me a whole number: 482.

Okay know let’s add them together:

$482/999+1/2$

$482*2/999*2+1*999/2*999=$

$964/1998+999/1998$

$1963/1998$

So the answer to 1/2 + the repeating decimal(0.482482) is 1963/1998

If you would like to learn further:

Watch: Converting Repeating Decimal to Fraction on Khan Academy

Note: I can’t paste the link because it says it contains swear words!