Summary: Operations on Decimals

Key Concepts

• Add or subtract decimals.
  1. Write the numbers vertically so the decimal points line up.
  2. Use zeros as place holders, as needed.
  3. Add or subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.
• Multiply decimal numbers.
  1. Determine the sign of the product.
  2. Write the numbers in vertical format, lining up the numbers on the right.
  3. Multiply the numbers as if they were whole numbers, temporarily ignoring the decimal points.
  4. Place the decimal point. The number of decimal places in the product is the sum of the number of decimal places in the factors. If needed, use zeros as placeholders.
  5. Write the product with the appropriate sign.
• Multiply a decimal by a power of [latex]10[/latex].
  1. Move the decimal point to the right the same number of places as the number of zeros in the power of [latex]10[/latex].
  2. Write zeros at the end of the number as placeholders if needed.
• Divide a decimal by a whole number.
  1. Write as long division, placing the decimal point in the quotient above the decimal point in the dividend.
  2. Divide as usual.
• Divide decimal numbers.
  1. Determine the sign of the quotient.
  2. Make the divisor a whole number by moving the decimal point all the way to the right. Move the decimal point in the dividend the same number of places to the right, writing zeros as needed.
  3. Divide. Place the decimal point in the quotient above the decimal point in the dividend.
  4. Write the quotient with the appropriate sign.
• Strategy for Applications
  1. Identify what you are asked to find.
  2. Write a phrase that gives the information to find it.
  3. Translate the phrase to an expression.
  4. Simplify the expression.
  5. Answer the question with a complete sentence.

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