In this exercise, we are given a mixed number and a decimal.
- 5 311 ? - 5.2
To compare these numbers, we should make sure they are written in the same form. Let's then rewrite the mixed number as a decimal. Before we do that, we should rewrite it as a fraction. Let's also ignore the negative sign for just a moment.
We found that 5 311 is equal to 58 11 when it is written as a fraction. This means that we actually want to find the quotient 58÷ 11. We find the quotient by dividing the numerator of the fraction by its denominator. Let's do it!
We can see that the pattern starts to repeat itself after a few steps. This means that the decimal is a repeating decimal. We can write it using bar notation. Remember, the bar goes over the decimal part that repeats itself.
5.272727 ... = 5.27
We found that 5811 written as a decimal is 5.27. Since we previously found that 5 311 is equal to 5811, we can say that 5 311 written as a decimal is 5.27.
5 311=58/11 ⇓ 5 311=5.27
Therefore, - 5 311 is equal to - 5.27. Now that both numbers are written as decimals, we can graph them on a number line. Then we will compare which one is greater than the other. When doing so, note that the bar over 2 in - 5.2 means that the 2s repeat infinitely.
- 5.2 = - 5.222222...
Let's go!
On the number line, we can see that - 5.27 is to the left of - 5.2. This means that - 5.27 is less than - 5.2. Because - 5.27 is equal to - 5 311, - 5 311 is also less than - 5.2.
- 5.27 < - 5.2 ⇔ - 5 311 < - 5.2
