When decimals and fractions meet

Hi all! Hope your weekend was great! Today, we learned how to convert fractions to decimals and decimals to fractions. We also went over how to set up algorithms for operactions with decimals.

To convert fractions to decimals, you divide the numerator by the denominator. So, the fraction a/b would be a divided by b. Here’s an example of how to write a fraction as a decimal:

fractions to decimals

To solve for this decimal, you would have to add a decimal point and a zero in the tenths place because 10 does not go into 3. Then, you would divide as if it were 30 divided by 10. Carry the decimal point under the division sign up to the answer.

The decimal may not always come out nicely like that. If the numbers after the decimal point form a repetition of a pattern of numbers, then you can stop divided and add a line over the repeating portion of the decimal. Here’s what that would look like.

repeating decimal

The answers for both of these examples are rational numbers. A rational number is a fraction of two integers that is either a terminating decimal or a repeating decimal. An irrational number would be a decimal that does not end but has no repetition of any patterns. Ex. 0.12657893462…..

There are two ways to convert a decimal to a fraction. If the decimal is a terminating decimal, you would just put all the numbers after the decimal point over the appropriate number. If the decimal is written in tenths, it would go over 10. If it were written in hundredths, it would go over  100, and so on. Then reduce to find the final answer.

terminating fraction

This decimal is written in tenths, so 8 would be written over 10. 8/10 reduces down to 4/5 by dividing 2.

If the decimal is a repeating decimal, then you will have a slightly more complicated process to go through to convert it to a decmial. First, the decimal would represent the variable x. So, if the decimal is .3333…, x would equal .3333…. Then, look at one set of the repeating group. In this case it would be 3. Since that group has only 1 number in the pattern, you would multiply x by 10. So, you would have 10x=3.3333… To get the fration, you would subtract the 10x and x then solve for x. Here’s what that would look like:

10x=3.333…-   x=0.333…=9x=3.00

x= 3/9= 1/3

Solving algorithms for decimals are not that tricky once you know how to set them up. I’ll show you an example for each operation.

Addition:

addition

For addition, you have to make sure that the decimal point in each number is lined up. To solve, just add and carry like normal. The answer for this problem is 5.23.

Subtraction:

b

Set up the algorithm for subtracting decimals just like addition. Solve like normal. The answer to this problem is 2.35.

Multiplication:

c

To multiply decimals, the place that the decimals are in does not matter. Just multiply like normal, then count the total number of numbers that are after a decimal point in the algorithm. Place that many places in the decimal in the final answer. The answer to this problem is 11.088.

Divison:

0.1 ÷ 0.8 would look like:

a

To divide, the number that is outside the brackets cannot be a decimal. So, you move the decimal point to the right until it is a whole number. Move the decimal under the bracket the same amout of spaces. Place the decimal point in the answer above the number under the brackets. Divide like normal.

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