IB Maths AI 1.6 Notes

Rounding

Handling numbers involves working accurately with rounded values, recognising the limits of measured data, and checking whether answers are sensible. This includes rounding, upper and lower bounds, percentage error and estimation.

Rounding makes a number simpler while keeping it close to the original value. You may round to the nearest whole number, a given number of decimal places, or a given number of significant figures.

• To round to a given decimal place, look at the digit immediately after the place you want to keep. If it is $5$ or more, round up. If it is less than $5$, leave the digit unchanged.
• To round to a given number of significant figures, start counting from the first non-zero digit. Keep the required number of digits, then use the next digit to decide whether to round up.

For example, $3456.78$ rounded to the nearest whole number is $3457$. Rounded to $2$ decimal places, it stays as $3456.78$. Rounded to $1$ significant figure, it becomes $3000$.

Round $5.6789$ to the nearest whole number, to $2$ decimal places, and to $1$ significant figure.

• To the nearest whole number, $5.6789$ rounds to $6$.
• To $2$ decimal places, look at the third decimal digit. Since it is $8$, round up to get $5.68$.
• To $1$ significant figure, keep the $5$ and look at the next digit, which is $6$, so round up to $6$.