Question

Express 0.32 as a fraction in simplest form.

(The two gets a bar line over it- bar line over the 2 means its a repeating decimal)

Please answer this equation in full steps!

Answer 1

To express 0.32 as a fraction in simplest form, we can use the formula for converting repeating decimals to fractions. In this case, the fraction is 32/99.

Step-by-step explanation:

To express 0.32 as a fraction in simplest form, we need to convert the decimal to a fraction. Since the decimal is a repeating decimal with a bar line over the 2, it means that the 2 repeats indefinitely. To convert a repeating decimal to a fraction, we can use the formula:

x = 0.32 (repeating) = n / (10m - 1)

Where n is the number without the repeating part, and m is the number of repeating digits. In this case, n = 32 and m = 2. Plugging these values into the formula, we get:

x = 32 / (102 - 1) = 32 / 99

Therefore, the fraction in simplest form is 32/99.

Answer 2

In order to change a decimal into a fraction, you have to put it over 1. So, it'll be .32/1.

Next, for each number behind the decimal you're going to add a zero to the multiple of 10. Since there are 2 numbers behind this decimal, you'll be multiplying the number by 100. So, you'll multiply:

100 x 0.32= 32 and 100 x 1= 100

Your new fraction is 32/100. You'll start simplifying now.

What can go into both numbers evenly? 4 is the highest for this problem.

We will now divide 32 by 4 and divide 100 by 4.

32 ÷ 4 = 8

100 ÷ 4 = 25. This will give you a new fraction of 8/25. We'll look to see if any numbers can go evenly into each other...and in this problem, nothing further can.

Therefore, your simplified fraction of 0.32 is 8/25.