21
Rounding numbers
Textbook: pp. 117–118
GoalKnow the rule for rounding numbers to a given place and find the rounding error.
New words
rounding · yaxlitlashrounding down · kami bilan yaxlitlashrounding up · ortig‘i bilan yaxlitlashdropped digit · tushirib qoldiriladigan raqam
Explanation
Approximate values are often obtained by rounding numbers. To round to a given place, the following digits are dropped. The rule: if the first dropped digit is less than 5, the last kept digit stays the same (rounding down); if the first dropped digit is 5 or more, the last kept digit is increased by one (rounding up). An approximate equality is written with the ≈ sign. This rule makes the absolute error of the rounding as small as possible. In whole numbers, the dropped places are replaced by zeros.
Worked examples
Round 7.3482 to hundredths: the first dropped digit is 8 ≥ 5, so 7.35. The error is |7.3482 - 7.35| = 0.0018. To tenths: 7.3 (the dropped digit 4 < 5).
Round 14 600 to thousands: the first dropped digit is 6 ≥ 5, so 15 000. Round 28 450 to thousands: the digit is 4 < 5, so 28 000.
Class activity
“Rounding relay”: pupils round a given number in turn to tenths, hundredths and units, writing the error at each step.
Practice
1
Round 5.764 to tenths.
5.8
2
Round 0.0346 to hundredths.
0.03
3
Round 73 512 to thousands.
74 000
4
Why do we round up when the dropped digit is 5?
By convention: 5 is the midpoint, and the rule of rounding up gives everyone the same answer.