# 2.3.3 More Practice Rounding

## Activity: Rounding Your Answer

Round the answer to the last calculation 3.26865671641791 to:

(a) The thousandths place holder.

### Discussion

Find the digit in the thousandths place holder. Then look at the first digit that you will cut off. If it is 0, 1, 2, 3, or 4, then leave the number as it is; if it is 5, 6, 7, 8, or 9, then round up the final digit of your answer by 1. (You can ignore all the later digits that you are cutting off, because they are to the right of the decimal point.)

### Answer

(a) Count 3 decimal places (this is the thousandths place) and look at the next digit.

The first digit to be cut off is 6, which falls in to the “5 or more” category, so you will round up the final digit of your answer, meaning you will increase it by 1. The answer, rounded to 3 d.p., is 3.269.

(b) 2 decimal points.

### Answer

(b) Count 2 decimal places (this is the hundredths) and look at the next digit.

The first digit to be cut off is 8, (which is again “5 or more”), so round up the final digit of your answer by adding 1. The answer, rounded to 2 d.p., is 3.27.

Here are a couple more examples to give you practice at rounding.

## Activity: More Rounding

Carry out the following calculations and write down the full calculator answer. Round the answer to 1 d.p. first. Then, round the calculator answer to 2 d.p.

(a)

### Discussion

There are lots of numbers here, so take your time entering them into the calculator. Watch the screen to make sure that you are entering them correctly, and correct any mistakes as you go along.

### Answer

(a)

To round the answer to 1 d.p., look at the first digit that you will cut off.

It is 1, so leave the previous digit as it is. The answer, rounded to 1 d.p., is 5.9.

To round the answer to 2 d.p., look at the first digit that you will cut off.

It is 7, so round the last digit of the answer up by adding 1. The answer, rounded to 2 d.p., is 5.92.

(b)

### Answer

(b)

Notice that the full calculation does not fit in the black window, so the final digits are missing. However, the full answer appears below in the white window.

To round the answer to 1 d.p., look at the first digit that you will cut off.

It is 7, so round the previous digit of the answer up by adding 1. The answer, rounded to 1 d.p., is 194467.7.

To round the answer to 2 d.p., look at the first digit that you will cut off.

It is 5, so we round up. The answer, rounded to 2 d.p., is 194467.68.

## Activity: Rounding Brainstretcher—An Interesting Observation!

You may have noticed that the full answer to part (a) in the previous activity has a repeating pattern of the digits 756. Why does the final digit break this pattern? Why do you think it is 7, not 6?

### Discussion

Think about rounding to 14 d.p.

### Answer

When the calculator rounds the answer to 14 d.p., the first digit that it cuts off (following the pattern) is 7. This is “5 or more,” so the final digit in the answer is rounded up from 6 to 7.

To recap:

- To enter a decimal, use the button on the calculator or the period key on your keyboard.

The calculator will give answers to 14 decimal places. This is usually much too precise, so round your answer, either as the question asks, or, for a practical calculation, to a sensible number of figures. For example, if working with money, rounding the nearest (cent) hundredth is reasonable.

2.3.2 Calculator Exploration: Decimals and Rounding