
A decimal is a number that can be written as a fraction whose denominator is 1, 10, 100, 1000, and so on. For example: Decimal Notation = Fraction Notation In a whole number, the decimal point is located to the right of the digit in the ones place. For example: (252 = 252 .). The place value of a digit is determined by where it is in relation to the decimal point. The digits to the left of the decimal point are whole numbers; they have place values of 1, 10, 100, 1000, 10,000 and so on. The digits to the right of the decimal point are fractional parts; they have place values of and so on. Note: each place is as large as the place to its immediate left. In the place value chart, the numbers to the left of the decimal point end in ‘s’ and represent the whole number part of the decimal while the numbers to the right of the decimal point end in ‘ths’ and represent the fractional part of the decimal. To write the word name for a Decimal: If there is no number other than ‘0’ to the left of the decimal point, omit steps one and two.
Example: 253.5674 is two hundred fiftythree and five thousand six hundred seventyfour ten thousandths. To add or subtract decimals, line up all the decimal points in a vertical column. Example 1. add: 10.5 + 3 +.072 + 195.0035 Example 2. Subtract: 123.7450 – 2.00034 To multiply two decimals:
Examples: 1. 2.7 x 4 = 10.8 Notice that there is ‘1’ decimal place in the product. 2. 3.456 x .5 = 1.7280 In this product, there are ‘4’ decimal places. 1.7280 can also be written as 1.728. 3. .45 x .12 Notice that 45 x 12 = 540, but there should be 4 decimal places in the product. Therefore, add a zero to the left of the ‘5’. .45 x .12 = .0540 = .054 To divide two decimal numbers:
Examples: Multiplication and Division by powers of Ten: A power of ten is a number that can be written as a product of tens; 10, 100, 1000, 10000…..are powers of ten. In exponential form, these are A power of ten can be recognized by looking for the number ten written with an exponent or a single ‘1’ followed by zeros. To multiply a number by a power of ten, move the decimal point to the right. To divide a number by a power of ten, move the decimal point to the left. The number of places to move is shown by the number of zeros in the power of ten. If the exponent of ten is negative, move the decimal point to the left as in division. Examples: 