Learning About Decimals: Elementary Decimals

Using Decimals

Many students first encounter decimals when they're using the metric system. In this system, fractions, like tenths of a centimeter or hundredths of a kilogram, are represented using decimals. Parts of whole metric units can also be written with fractions, but the decimal system allows us to record and compare even the tiniest differences in measurements more efficiently than fractions do.

Decimal Place Values

The decimal system divides units into extremely tiny pieces, like tenths, hundredths and even thousandths. The first place to the right of the decimal point is the tenths place, the second place is the hundredths place and the third place is the thousandths place. Here are the fractional equivalents for these decimal place values:

1/10 = 0.1

1/100 = 0.01

1/1,000 = 0.001

If you measure your pencil eraser and find that it is 1/10 of a centimeter thick, you can write this amount as 0.1 cm. A grain of sand might be about 1/100 of a centimeter, or 0.01 cm. An object that's 1/1,000 of a centimeter, or 0.001 cm, might be too small to be seen with the naked eye.

Comparing Decimals

After you've learned to measure and record amounts using the decimal system, you'll be asked to compare decimals. If there are whole numbers to the left of the decimal point, compare these first. If one is larger than the other, then you don't need to look at the digits to the right of the decimal point. For instance, 23.999 is less than 24.0, since 24 > 23. The numbers to the right of the decimal point always represent fractions of one, and no fractional amount could make 23 larger than 24.

If the numbers to the left of the decimal point are the same, look at the numbers in the tenths places of the two decimals. Whichever decimal has the larger number in this place is greater. For instance, 0.6 > 0.324. You can verify this by writing each of the decimals as a fraction and comparing them. The fraction 6/10 = 600/1,000, and 600/1,000 > 324/1,000.

For decimals with the same numbers in the tenths place, you'll need to compare the digits in the hundredths place. For instance, 0.324 < 0.334 because 2 < 3. Once again, you can prove this by converting the decimals to fractions: 324/1,000 < 334/1,000.

Finally, if the two decimals have the same digits in both the tenths and hundredths places, compare the digits in the thousandths places. For example, the decimal 0.325 > 0.324 because 5 > 4.