How To Order Decimals From Least To Greatest Tutorials Review

Let’s say your homework asks you to order the decimals 12. 45, 12. 457, and 11. 47. The whole number 11 is smaller than 12, so 11. 47 is automatically going to be the smallest (least) number.

Let’s go back to our old example. Since we already figured out that 11. 47 is the smallest decimal, we’re left with 12. 45 and 12. 457 to sort. Draw a table with 6 columns and 2 rows to fit both numbers. If you were asked to order a list of decimals like 0. 3, 0. 4, 0. 01, 0. 02, and 0. 5, your chart would need to have 5 rows and 4 columns (including one column for the decimal point).

Let’s take a look at the two decimals in our table. The number 12. 45 only has 4 digits, so you’d add a 0 to the thousandths place (making it 12. 450). This makes it a lot easier to compare with 12. 457, right?

In our chart, both 12. 45 and 12. 457 have a 4 in the tenths column. So, we’d move onto the hundredths column and make a new comparison. Let’s say you’re asked to compare 0. 1 and 0. 01. The decimal 0. 1 has a 1 in the tenths column while 0. 01 only has a 0. Therefore, 0. 1 is the bigger number.

Let’s take another glance at our table—both 12. 45 and 12. 457 have a 5 in the hundredths place, so you’d shift over to the thousandths column for another comparison. Pretend you were asked to compare the decimals 4. 04 and 4. 02. The number 4. 04 has a 4 in the hundredths place while 4. 02 only has a 2, which makes 4. 04 the bigger decimal.

Let’s take a final look at our table. The decimal 12. 45 has a 0 in the thousandths place while 12. 457 has a 7. With this in mind, 12. 457 is a bigger decimal than 12. 45.

If your assignment asks you to order the decimals 14. 36, 13. 458, and 14. 369, you could write them like: 14. 3613. 45814. 369

14. 3613. 45814. 369

In our example, the number 13 is smaller than 14, so you’d automatically mark 13. 458 as the smallest number.

Take 14. 36 and 14. 369, for instance—both decimals have a 3 in the tenths place and a 6 in the hundredths place. In the thousandths place, however, 14. 36 has a 0 while 14. 369 has a 9.

In our example, 14. 369 falls to the right of 14. 36— that makes 14. 369 the larger number.

For our example problem, the final list would be: 13. 458, 14. 36, 14. 369. You can also use the less than sign to show their relationship: 13. 458 < 14. 36 < 14,369.

Let’s take a look at the decimal 12. 38. For this number, the digits 1 and 2 are whole numbers, while 3 and 8 are fractional numbers. In Europe, people use a decimal comma instead of a decimal point. [11] X Research source

In the number 51 the 5 digit is in the tens place. It has a value of 5 tens. In the number 50,001, the digit 5 is in the ten-thousands place—this gives it a value 5 ten-thousands, or 50,000. The smallest place value for whole numbers is the ones place. Ten sets of 1 move the 1 into the tens place, while 10 sets of 10 move the number into the hundreds place. See the pattern? This pattern continues for the higher place values.

For example, in the number 1. 5, the digit 5 is in the tenths place. It has the value of 5 tenths, or 510{\displaystyle {\frac {5}{10}}}. In the number 1. 0005, however, the digit 5 has a value of 5 ten-thousandths, or 510,000{\displaystyle {\frac {5}{10,000}}}. The tenths place is the largest place value for fractional numbers. Ten hundredths make one-tenth, 10 thousandths make 1 hundredth, and 10 ten-thousandths create 1 thousandth. When comparing fractional numbers, it helps to convert decimals into fractions:110>1100{\displaystyle {\frac {1}{10}}>{\frac {1}{100}}}. To convert a fraction into a decimal, simply divide the numerator by the denominator. [13] X Research source