Comparing, Ordering and Rounding Decimals   Comparing Decimals At the beginning of this course, we we encountered the number line, a graphical device that helps us visualize the relationships between two numbers.  Just as we can place whole numbers on the number line, we can also place decimals on the number line.  If two numbers are on a number line, then the number to the right is the larger one.   We see that that          0.5 < 2        and     0.3 < 0.5 To compare two decimals without placing them on a number line, follow the following method: Start from left to right and compare corresponding digits.  If the digits are the same, move to the right. If the digits are different then the larger number is the one with the larger digit. Example Fill in the blank with a "<", ">", or an "=" sign   3.1714        3.169 Solution We see that the ones digits, 3 and 3, are the same, the tenths digit, 1 and 1 are the same, but the hundredths digits, 7 and 6, are different with 7 > 6.  Hence the inequality is ">" 3.1714  >  3.169 0.0005        0.0023 Solution We see that the ones digits, the tenths digits, and the hundredths digits are all 0.  The left hand side has 0 for the thousandths digit while the right hand side has 2 for its thousandths digit.  Hence the inequality is "<" 0.0005  <  0.0023 Exercises Fill in the blank with a "<", ">", or an "=" sign   34.916        34.924        18.126        18.1260        123.437          123.337        Example Place the following decimals from in order from smallest to largest         2.753    2.75    2.357    3    2.7 Solution We first add zeros to the ends of the shorter decimals to make comparison easier         2.753    2.750    2.357    3.000    2.700 Now we see that the smallest is 2.357, since its tenths digit, 5, is smaller than 5.  Next is 2.700, since its hundredths digit, 0, is smaller than 5.  Next comes 2.750 since its thousandths digit, 0, is smaller than 3.   Example Place the following decimals from in order from smallest to largest         49.1        49.16        49.31        27    49.01 Rounding Decimals to a Specified Decimal Place It is often necessary to round a decimal to the nearest tenth, hundredth, thousandth, etc.  When dealing with money we usually round to the nearest hundredth so that we can read the number in dollars and cents.  The rules of rounding decimals are the same as the rules for rounding whole numbers.  We look at the digit to the right and determine if it is 5 or greater.  If it is greater than 4, round up.  Otherwise round down. Example Round 32.537 to the nearest hundredth.   Solution The digit to the right of the hundredth place is "7".  Since 7 is greater than 4, we round up.  Change the 3 to a 4.  We write         32.54   Example Round 27.8149 to the nearest tenth.   Solution The digit to the right of the tenth place is "1".  Since 1 is not greater than 4, we round down.  Keep the 8 the same.  We write         27.8 Exercise Round the following numbers as indicated. 651.955 to the nearest tenth        49.942 to the nearest hundredth      Back to the Decimals page Back to the Math 187A page Back to the Math Department page e-mail Questions and Suggestions