Rounding, Estimation and Bounds

Number

Decimal places are counted rightwards from the decimal point
Apply the same rule: inspect the first digit beyond the place being kept
- 6.7183 to two decimal places is 6.72

An answer must show exactly as many decimal places as were asked for, including a final zero
- 0.4961 to two decimal places is 0.50, not 0.5
This differs from place-value rounding, where zeros before the decimal point are structural rather than decorative
Where rounding up cascades through a 9, carry it as with ordinary addition
- 3.897 to two decimal places is 3.90, because 89 becomes 90

Worked example

Rounding where the digits carry

Round 0.4961 to two decimal places.

Solution:

The second decimal place holds 9, and the digit to its right is 6
Since 6 is at least 5, the 9 rounds up, which carries into the tenths column
49 hundredths becomes 50 hundredths
The answer is 0.50, written with the final zero because two decimal places were requested