In the previous lesson on decimals, you learned that the first digit to the right of a decimal point is the tenths.
0.8 is the same as 8/10. That's because:
0.1 = 1/10
The second digit to the right of a decimal point is the hundredths.
0.02 is the same as 2/100. That's because:
0.01 = 1/100
So what's 0.09 as a fraction?
Yes, it's 9/100!
Every decimal can be written as a fraction, and every fraction can be written as a decimal.
So, how can we turn fractions into decimals and back?
To turn a fraction into a decimal, just divide the numerator by the denominator using long division.
Let's try it with this fraction:
We divide the numerator by the denominator using long division:
How many 5's can fit into 3?
None, because 5 is a bigger number than 3.
So we write zero on top, and add a decimal point after the zero.
We also add a zero after 3 in the dividend. It now looks like we're dividing 30 by 5.
Now think: how many 5's fit into a 30?
That's right, 6.
So, we write 6 on top. Make sure to write it after the decimal point.
We write the product of 5 and 6 below the 30.
Then we subtract this product from the number in the dividend, 30.
We have no remainder.
This means...
3/5 as a decimal is 0.6
Nice work.
Let's try another example:
Convert 4/8 to a decimal
First, write 4 divided by 8 in long division form.
Next, ask yourself how many 8's can fit into 4.
The answer is 0.
We write that on top. Then write a decimal after it.
Write a zero after 4 to extend the dividend. We now look at it as 40.
Now, figure out how many 8's fit into 40.
That's right, 5.
Write your answer on top, after the decimal point.
We write the product of 8 and 5 under 40.
Then we subtract 40 from 40. We get 0. That means there's no remainder.
So, 4/8 written as a decimal is 0.5
A mixed number is made up of a whole number and a fraction part.
Let's learn to convert mixed numbers to decimals with an example.
In this mixed number, 2 is the whole number part and 6/8 is the fraction.
When converting mixed numbers, we set aside the whole number and focus on the fraction first.
We set aside 2, and convert 6/8 to a decimal first.
How? 🤔
We divide 6 by 8.
6 divided by 8 equals 0. So we write that at the top.
Then we add a decimal point after it.
We also add a zero after 6. It now looks like we're dividing 60 by 8.
How many 8's can fit in 60?
Yes, 7.
We multiply 8 x 7, and we get 56. This is how much we've divided away from the dividend so far. Let's subtract that from the dividend:
60 - 56 = 4.
It looks like we still have a remainder. We need to keep dividing.
So we extend our dividend by adding a zero at the end. Then we bring down this zero down beside 4. That gives us 40.
How many 8's can fit in 40?
Correct, 5.
Now, we have no remainder.
What decimal did we get as the quotient, or answer?
That's right, 0.75.
Now, we add this decimal with the whole number that we set aside earlier.
2 + 0.75 = 2.75
So, 2 and 6/8 is 2.75 in decimal form.
Great job learning how to convert fractions and mixed numbers to decimals.
Now, practice what you just learned to help you remember for longer.