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Solving problems with rational numbers in decimal form

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Rational Numbers in Decimal Form

A rational number written in decimal form is either terminating or repeating. Learn to add and subtract decimals by lining up the decimal point, multiply and divide decimals using place-value rules, and solve word problems by identifying which operation the wording calls for.

Rational numbers written as decimals

Every rational number can be written as a decimal — either a terminating decimal that ends, like 0.75, or a repeating decimal that has a pattern that goes on forever, like 0.333... Real-world quantities such as money, distance, and measurements are usually given in decimal form, which is why solving word problems with decimals is such a common skill — the same numbers can also be compared and ordered once they are written this way.

Solving a word problem with decimals Word problem: a runner covers 3.25 miles on Monday and 2.4 miles on Tuesday. Total distance: line up the decimal points, then add: 3.25 + 2.40 = 5.65 miles. A runner covers 3.25 miles Monday, 2.4 miles Tuesday. Total distance? 3.25 + 2.40 5.65 line up the decimal points
Adding decimals: line up the decimal points, then add each column just like whole numbers.

To add or subtract decimals, line up the decimal points first, filling in any missing places with zeros so every number has the same number of digits after the point. Then add or subtract column by column, exactly as with whole numbers, keeping the decimal point in the same place in the answer.

To multiply decimals, multiply as if the decimal points weren't there, then count the total decimal places in both numbers and place the point that many digits from the right in the answer. To divide decimals, move the decimal point in the divisor to make it a whole number, moving the decimal point in the dividend the same number of places, then divide as usual.

The hardest part of a decimal word problem is often deciding which operation to use. Words like "total" or "altogether" signal addition; "left over" or "difference" signal subtraction; "each" or "per" often signal multiplication or division. Once the operation is clear, the calculation follows the same rules as above.

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