Writing a decimal correct to a number of decimal places

The rules for rounding are as follows. To illustrate, we use an example.

Example 1

Round 10.125 89 correct to two decimal places.

• Look at the rounding digit, in this case 2.
• Look at the next digit to the right of the rounding digit, in this case 5.
• If this next digit is 0, 1, 2, 3 or 4, leave the rounding digit alone.
• If this next digit is 5, 6, 7, 8 or 9, increase the rounding digit by 1.
• In this case, the next digit is 5 so the rounding digit increases from 2 to 3.
• Now discard all the digits after the rounding digit.

Thus, we write 10.125 89 as 10.13 correct to two decimals places.

Example 2

The process is the same with recurring decimals.

Write 45.7456 correct to:

1. one decimal place
2. two decimal places
3. three decimal places

Solution

1. 45.7456 = 45.7 correct to one decimal place
   (The rounding digit is 7 and the digit to the right is 4.)
2. 45.7456 = 45.75 correct to two decimal places
   (The rounding digit is 4 and the digit to the right is 5.)
3. 45.7456 = 45.746 correct to three decimal places
   (The rounding digit is 5 and the digit to the right is 6.)

The process is the same with terminating decimals.

Example 3

Write \(0.\dot{4}\dot{6}\) correct to:

1. one decimal place
2. two decimal places
3. three decimal places

Solution

1. \(0.\dot{4}\dot{6}=0.4646\ldots=0.5\) correct to one decimal place
   (The rounding digit is 4 and the digit to the right is 6.)
2. \(0.\dot{4}\dot{6}=0.4646\ldots=0.46\) correct to two decimal places
   (The rounding digit is 6 and the digit to the right is 4.)
3. \(0.\dot{4}\dot{6}=0.4646\ldots=0.465\) correct to three decimal places
   (The rounding digit is 4 and the digit to the right is 6.)