1.7 Decimals  (Page 6/10)

Converting a decimal to a percent makes sense if we remember the definition of percent and keep place value in mind.

To convert a decimal to a percent, remember that percent means per hundred. If we change the decimal to a fraction whose denominator is 100, it is easy to change that fraction to a percent.

Recognize the pattern? To convert a decimal to a percent, we move the decimal point two places to the right and then add the percent sign .

Convert each decimal to a percent: ⓐ 0.51 ⓑ 1.25 ⓒ 0.093.

Solution

ⓐ
Move the decimal point two places to the right.	$\mathrm{51\%}$

ⓑ
Move the decimal point two places to the right.	$\mathrm{125\%}$

ⓒ
Move the decimal point two places to the right.	$\mathrm{9.3\%}$

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Key concepts

• Name a Decimal
  1. Name the number to the left of the decimal point.
  2. Write ”and” for the decimal point.
  3. Name the “number” part to the right of the decimal point as if it were a whole number.
  4. Name the decimal place of the last digit.
• Write a Decimal
  1. Look for the word ‘and’—it locates the decimal point. Place a decimal point under the word ‘and.’ Translate the words before ‘and’ into the whole number and place it to the left of the decimal point. If there is no “and,” write a “0” with a decimal point to its right.
  2. Mark the number of decimal places needed to the right of the decimal point by noting the place value indicated by the last word.
  3. Translate the words after ‘and’ into the number to the right of the decimal point. Write the number in the spaces—putting the final digit in the last place.
  4. Fill in zeros for place holders as needed.
• Round a Decimal
  1. Locate the given place value and mark it with an arrow.
  2. Underline the digit to the right of the place value.
  3. Is this digit greater than or equal to 5? Yes—add 1 to the digit in the given place value. No—do not change the digit in the given place value.
  4. Rewrite the number, deleting all digits to the right of the rounding digit.
• Add or Subtract Decimals
  1. Write the numbers so the decimal points line up vertically.
  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 Decimals
  1. Determine the sign of the product.
  2. Write in vertical format, lining up the numbers on the right. Multiply the numbers as if they were whole numbers, temporarily ignoring the decimal points.
  3. Place the decimal point. The number of decimal places in the product is the sum of the decimal places in the factors.
  4. Write the product with the appropriate sign.
• Multiply a Decimal by a Power of Ten
  1. Move the decimal point to the right the same number of places as the number of zeros in the power of 10.
  2. Add zeros at the end of the number as needed.
• Divide Decimals
  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 - adding 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.
• Convert a Decimal to a Proper Fraction
  1. Determine the place value of the final digit.
  2. Write the fraction: numerator—the ‘numbers’ to the right of the decimal point; denominator—the place value corresponding to the final digit.
• Convert a Fraction to a Decimal Divide the numerator of the fraction by the denominator.