Decimals: Comparing, Ordering, Rounding, Multiplying, Dividing, Adding and Subtracting

Decimals are numbers that include a period called a decimal point. The digits to the right of the decimal point are a value less than one. This handy guide will help students learn how to read decimals, compare and order decimals, as well as round them, and the standard order of operations.

Decimals represent numbers that include a part of a whole. With decimals, the part that is less than 1 is always separated into 10, or a power of 10, parts. For example, one (1), one tenth (0.1), and one hundredth (0.01). When writing a decimal, put the decimal point between the ones column and the tenths column. The place values to the left of the decimal are the hundreds, tens, and ones. The place values to the right of the decimal are the tenths, hundredths, and thousandths. To read decimals, read the whole number. Say the word ""point." Read the number after the decimal point. Say the decimal place of the last digit to the right. 333.2 is read "three hundred thirty three point two". To read 98.7 aloud , you would say "ninety-eight point seven".

To compare and order decimals, the rules are similar to working with whole numbers. Put the numbers in order from greatest to least. Align the numbers along the decimal point. Work from left to right, comparing each place value. If all the digits are the same, move to the next place. Compare digits in each place. Now, put the numbers in order from greatest to least.

To round decimals, follow the same rules as those for rounding whole numbers. To round, first underline the place to round to and look at the digit one place to the right. For example, to round 4.386 to the nearest tenth, you would underline the 3. If the digit is less than 5, the digit you are rounding to stays the same. If the digit you are rounding to is greater than or equal to 5, add 1 to the place value. 4.386 is 4.4 rounded to the nearest tenth.

To add decimals, align the decimal points. If the numbers do not have the same number of decimal places, write an equivalent decimal. Adding zeros to the right of the last decimal does not change the value of the number. For example, to add 14.98 + 13.830, add an extra 0 to 14.98 and align the decimal points.

To subtract decimals, follow the same rules.

To multiply decimals, ignore the decimal point, and multiply as whole numbers. Count the number of decimal places in both factors. Place the decimal point that many places from the right in the product. For example
0.46
X 0.9
________

0.414

To divide decimals, move the decimal point in the divisor to the right enough places to make it a whole number. Move the decimal point in the dividend the same number of places to the right. Add zeros if necessary. Divide like whole numbers. Place the decimal point in the quotient directly above it in the dividend. For example, in 4/0.002, move the decimal point three places to the right after the 2 and do the same for the 4. Now divide as necessary, and your answer will be 2000.