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Decimals—Explanation 1/31/11—mm-fd
Decimals—Explanation
Decimal numbers include a whole number part (which is sometimes zero), a decimal point, and a decimal fraction.
The value of the combined whole number and decimal fraction is determined by the placement of the decimal point. Whole numbers are written to the left of the point and decimal fractions to the right. The diagram below illustrates the values of the places occupied by each digit.
—Ten millions —Millions —Hundred thousands —Ten thousands —Thousands —Hundreds —Tens —Units ∙^
Decimal point
—Tenths —Hundredths —Thousandths —Ten thousandths —Hundred thousandths —Millionths —Ten millions 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 Whole Number Decimal Fraction
Reading decimal numbers
- Read the whole number.
- Read the decimal point as “and.”
- Read the decimal fraction; use the place value of the last digit (farthest to the right).
Examples: 0.86 eighty-six hundredths 3.659 three and six hundred fifty-nine thousandths 182.0012 one hundred eighty-two and twelve ten thousandths
Ordering decimal fractions
- Place the numbers in a vertical column with the decimal points in a vertical line.
- Add zeroes on the right in the decimal fractions to make columns even.
- The largest number in a column to the right of the decimal point has the greatest value.
- If two numbers in a column are of equal value, examine the next column to the right and so on.
- The smallest number in the column to the right of the decimal point has the least value. If two numbers in the first column are of equal value, examine the second column to the right and so on.
Decimals—Explanation 1/31/11—mm-fd
Example: Of the following decimal fractions (0.623, 0.841, 0.0096, 0.432) which has the greatest value? The least value?
0.841 has the greatest value; 0.0096 has the least value.
Ordering mixed decimals In mixed numbers, the values of both the whole number part and the decimal fraction are considered.
Example: Which decimal number (0.4, 0.25, 1.2, 1.002) has the greatest value? The least value?
1.2 has the greatest value; 0.25 has the least value.
Note: Any whole number is understood to end in a decimal: 768=.
Addition and Subtraction of Decimals
- Write the numerals in a vertical column with the decimal points in a straight line.
- Add zeroes as needed to complete the column.
- Add or subtract each column as indicated by the symbol.
- Place the decimal point in the sum or difference directly below the decimal points in the column.
- Place a zero to the left of the decimal point if there is no whole number.
Examples: Add: 14.8 + 6.29 + 3.
Subtract: 5.163 – 4.
Decimals—Explanation 1/31/11—mm-fd
Example: 80.96 ÷ 352 Example: 3.339 ÷ 1.
. 352 80. 70 4 105 6 105 6
∧ ∧
Dividing by 10 or a power of 10 (100, 1000, 10,000, 100,000)
- To get the answer, move the decimal point in the dividend to the left the same number of places as there are zeroes in the divisor.
- Zeroes may be added as needed.
Example: 358.0 ÷ 100 = 3.
Dividing by 0.1 (0.01, 0.001, 0.0001, 0.00001)
- To get the answer, move the decimal point in the dividend to the right as many places as there are digits to the right of the decimal point in the divisor.
- Zeroes may be added as needed.
Example: 46.31 ÷ 0.001 = 46,
Conversion
Converting a decimal fraction to a proper fraction
- The numerator is the same as the digits to the right of the decimal point.
- The denominator is determined by the place value of the digit the farthest to the right in the decimal fraction.
- Reduce to lowest terms.
Example: 0.
Converting a proper fraction to a decimal fraction
- Divide the numerator by the denominator.
- Extend the decimal the desired number of places (often three).
- Place a zero to the left of the decimal point in a decimal fraction.
Example: 4/5 5
