6.10: Summary of Key Concepts
- Page ID
- 53018
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Summary of Key Concepts
Decimal Point
A decimal point is a point that separates the units digit from the tenths digit.
Decimal or Decimal Fraction
A decimal fraction is a fraction whose denominator is a power of ten.
Converting a Decimal to a Fraction
Decimals can be converted to fractions by saying the decimal number in words, then writing what was said.
Rounding Decimals
Decimals are rounded in much the same way whole numbers are rounded.
Addition and Subtraction of Decimals
To add or subtract decimals,
Align the numbers vertically so that the decimal points line up under each other and the corresponding decimal positions are in the same column.
Add or subtract the numbers as if they were whole numbers.
Place a decimal point in the resulting sum directly under the other decimal points.
Multiplication of Decimals
To multiply two decimals,
Multiply the numbers as if they were whole numbers.
Find the sum of the number of decimal places in the factors.
The number of decimal places in the product is the number found in step 2.
Multiplying Decimals by Powers of 10
To multiply a decimal by a power of 10, move the decimal point to the right as many places as there are zeros in the power of ten. Add zeros if necessary.
Division of a Decimal by a Decimal
To divide a decimal by a nonzero decimal,
Convert the divisor to a whole number by moving the decimal point until it appears to the right of the divisor's last digit.
Move the decimal point of the dividend to the right the same number of digits it was moved in the divisor.
Proceed to divide.
Locate the decimal in the answer by bringing it straight up from the dividend.
Dividing Decimals by Powers of 10
To divide a decimal by a power of 10, move the decimal point to the left as many places as there are zeros in the power of ten. Add zeros if necessary.
Terminating Divisions
A terminating division is a division in which the quotient terminates after several divisions. Terminating divisions are also called exact divisions.
Nonterminating Divisions
A nonterminating division is a division that, regardless of how far it is carried out, always has a remainder. Nonterminating divisions are also called nonexact divisions.
Converting Fractions to Decimals
A fraction can be converted to a decimal by dividing the numerator by the denominator.