Rounding Numbers

Rounding Numbers

Scientists have a convention for rounding numbers to the appropriate number of significant figures. In the age of calculators that mindlessly present many digits more than are significant, knowing how to round numbers “to the nearest tenth” or “to the nearest millionth” is essential.

Imagine that we have a set of numbers that we need to round to the nearest integer (i.e. the nearest whole number, without any digits to the right of the decimal point).

(1) If the first digit to the right of the decimal point is smaller than 5, drop all digits to the right of the decimal point and leave the first digit to the left of the decimal point unchanged. For example:

137.4

137.3

137.2 are rounded to 137

137.1

137.0

(2) If the first digit to the right of the decimal point is larger than 5, drop all digits to the right of the decimal point and add 1 to the first digit to the left of the decimal point (i.e., round up). For example:

137.6

137.7

137.8 are rounded to 138

137.9

(3) If the first digit to the right of the decimal point is 5 and the digit to the left is an even number, then drop all digits right of the decimal point and leave the first digit to the left of the decimal point unchanged. For example:

130.5 is rounded to 130

132.2 is rounded to 132

134.4 is rounded to 134

136.5 is rounded to 136

138.5 is rounded to 138

(4) If the first digit to the right of the decimal point is 5 and the digit to its left if an odd number, then drop all digits to the right of the decimal point and add 1 to the first digit to the left of the decimal point (i.e., round up). For example:

131.5 is rounded up to 132

133.5 is rounded up to 134

135.5 is rounded up to 136

137.5 is rounded up to 138

139.5 is rounded up to 140

This minimizes the cumulative effect of “rounding errors.”

Practice in Rounding:

a) 1234.567 rounded to the nearest hundredths place is _____________

b) 1234.997 rounded to the nearest hundredths place is _____________

c) 1234.567 rounded to the nearest tenths place is _________________

d) 1234.957 rounded to the nearest tenths place is _________________

e) 1234.857 rounded to the nearest tenths place is _________________

f) 1234.567 rounded to the nearest integer is _____________________

g) 1234.567 rounded to the nearest tens place is ___________________

Answers:

a) 1234.57

b) 1235.00

c) 1234.6

d) 1235.0

e) 1234.8

f) 1234

g) 1230

For more information you can go to:

http://mathworld.wolfram.com/Rounding.html