59
Approximate value and rounding
Textbook: Part 2, lesson 59, pp. 90–93
GoalApproximate values; lower and upper approximations; the rule for rounding numbers.
New words
approximate value · taqribiy qiymatrounding · yaxlitlashapproximately equal (≈) · taxminan teng (≈)place · xona
Explanation
If a < x < b, then a is the lower approximation of x and b is its upper approximation. Replacing a number with the nearest whole number is called rounding to the whole; the ≈ sign is used. To round a number to a given place, the digits after that place are replaced by 0 if they are before the point and dropped if they are after the point. If the first dropped digit is 5, 6, 7, 8 or 9, add 1 to the previous digit; if it is 0, 1, 2, 3 or 4, the previous digit stays. For example, 3.5 ≈ 4, 2.337 ≈ 2.34, 461 ≈ 460.
Worked examples
Round 27.463 to tenths: the first dropped digit is 6 → 27.4 + 0.1 = 27.5. So 27.463 ≈ 27.5.
Round 62 738 to hundreds: 62 7|38, the first dropped digit is 3 → 62 700. 3 508 612 ≈ 3 509 000 (to thousands).
Class activity
“Rough measuring”: measure the length of a table with a ruler, then round it to whole centimetres and to tenths. Which is more exact?
Practice
1
Round 6.47 to tenths.
6.5
2
Round 12.349 to hundredths.
12.35
3
Round 8.5 to the nearest whole number.
9
4
Why is 3.5 rounded to 4?
3.5 is equally far from both wholes; by agreement it is rounded up.