Every fraction can be written as a decimal, and every decimal can be written as a fraction.
Decimals and fractions are related because they both show parts of a whole.
For example, the decimal 0.5 is equal to the fraction 1/2.
0.5 is equal to "5 tenths". If we express that as a fraction, it would be 5/10.
If we simplify 5/10, we get 1/2.
To simplify a fraction, we divide both numerator and denominator by the greatest factor that is common to both.
Using this knowledge, we can now compare decimals and fractions!
Which of these is larger?
0.6 ____ 2/4
We can't compare them right away because they're not in the same form. ❎
On the left side is a decimal and on the right side is a fraction.
So we have to convert, or turn, the fraction into a decimal first.
In this case, the fraction we want to convert is 2/4.
So we divide the numerator, 2, by the denominator, 4.
Then we solve the division problem.
2/4 in decimal form is 0.5. 🎉
Now, we can compare the two decimals.
0.6 _____ 0.5
0.6 > 0.5
We now know that 2/4 is equal to 0.5.
So we can replace 0.5 in the inequality with 2/4:
0.6 > 2/4 ✅
Great work. 👏
Compare 0.65 and 3/4
First, convert 3/4 to a decimal.
We divide 3 by 4.
Then we solve to find the answer.
We see that...
3/4 in decimal form is 0.75
Now we can compare that with our other decimal.
0.65 _____ 0.75
Which symbol will make this statement true?
Let's compare the tenths place values.
We know that 6 is less than 7.
That means...
0.65 < 0.75
This means that...
0.65 < 3/4 ✅
Great job.
Compare 3.65 to 3 and 3/5
The first step is to convert the mixed number 3 and 3/5 into a decimal.
When converting mixed numbers, we set aside the whole number first. Then we convert the fraction.
In this case, we set aside the whole number 3 and convert 3/5.
To convert the fraction, we start by dividing 3 by 5.
We solve to get the answer.
3/5 converted to a decimal is 0.6.
Let's add the decimal back to our whole number:
3 + 0.6 = 3.6
Now, we know that 3 and 3/5 is 3.6 in decimal form.
Let's go back to our original comparison statement.
Compare 3.65 and 3 and 3/5
Using the converted fraction, we can now re-write it like this.
3.65 _____ 3.6
We can add a 0 after the last digit of 3.6 to make it easier to compare the numbers. This does not change the value of the number.
3.65 _____ 3.60
Compare the tenths place first.
We see that they're the same, so we go to the hundredths place.
The first one has 5 hundredths, and the other one has 0 hundredths.
5 hundredths is greater than 0 hundredths.
This means that ...
3.65 > 3.60
Now we now know that...
3.65 > 33/5 ✅
Excellent work. 👏
Now, complete the practice.