**Scales based on other powers of 10 besides 100 (percent) and murder rates per 100,000.**

**Fractions, decimals and percents.**

**Changing repeating decimals to fractions in lowest terms.**

**Approximating and simplifying square roots.**

**Rounding decimals.**

Let's consider 3/7. If you type 3/7 into the calculator, you'll get 0.428571429. If we wanted to write the fraction with a bar over the repeating part, the answer would be

______

.428571

Usually, fractions like this are written as decimals rounded to the nearest tenth, hundredth or thousandth. Let's do all three versions here.

3/7 rounded to the nearest tenth.

Step 1: Erase everything after the first digit, which gives us .4

Step 2: Because the left most digit we erased is a 2, we leave the .4 alone.

**3/7 ~= .4 rounded to the nearest tenth.**

3/7 rounded to the nearest hundredth.

Step 1: Erase everything after the second digit, which gives us .42

Step 2: Because the left most digit we erased is an 8, we change .42 to .43, rounding up.

**3/7 ~= .43 rounded to the nearest hundredth.**

3/7 rounded to the nearest thousandth.

Step 1: Erase everything after the third digit, which gives us .428

Step 2: Because the left most digit we erased is a 5, we increase .428 to .429.

**3/7 ~= .429 rounded to the nearest thousandth.**

**Rounding error.**

If we multiply 7 × 3/7, we get 3 exactly. If we multiply 7 by a rounded version of 3/7, we won't get exactly 3. If we rounded the approximation off, when we multiply we will be below the target. If we round the approximation up, we will be above the target.

7 × .4 = 2.8, so we are 0.2 below 3.

7 × .43 = 3.01, so we are 0.01 above 3.

7 × .429 = 3.003, so we are 0.003 above 3.