Exercise 34 Page 240

We want to order the following numbers from least to greatest. 2/9, 21 %, 0.21, 11/50 The numbers are in different forms. Let's write them as decimals since decimals are usually easier to compare.

Writing as Decimals

We have three numbers that we want to write as decimals — 29, 21 %, and 1150. Let's start with 29. We can write it as a decimal by dividing the numerator by the denominator.

The fraction 29 written as a decimal is 0.222..., or 0.2. Let's keep it in the first form because it will be easier to compare it with the other numbers. Let's also use 0.211... instead of 0.21 for that number. Next, we want to write 21 % as a decimal. To write a percent as a decimal, we remove the percent sign and move the decimal point two places to the left.

We see that 21 % = 0.21. Let's now rewrite 1150 as a decimal by multiplying the numerator and the denominator by 2. This will make the denominator a power of ten, so writing it as a decimal will be simpler.

We have that 1150 = 0.22.

Comparing the Numbers

Now let's compare the numbers. 0.222..., 0.21, 0.211..., 0.22 ⇓ 0.21 < 0.211... < 0.22 < 0.222... Finally, let's return our numbers to their original forms to give our answer. 21 % , 0.21 , 11/50 , 2/9