Decimals


 * Link to Decimal Information -** **http://www.aaamath.com**

** Addition of Decimals **
 * Decimals are fractional numbers. The decimal 0.3 is the same as the fraction 3/10. The number 0.78 is a decimal that represents 78/100.**
 * Adding Decimals is just like adding other numbers.**
 * Always line up the decimal points when adding decimals.**
 * Remember to put the decimal point in the proper place in your answer.**

**Adding Decimals**
 * How to add Decimals that have different numbers of decimal places**
 * **Write one number below the other so that the bottom decimal point is directly below and lined up with the top decimal point.**
 * **Add each column starting at the right side.**

code 3.2756 + 11.48 = 14.7556 code
 * Example: Add 3.2756 + 11.48 **

**Tenths as Decimals - I** The fraction 7/10 could be written as the decimal 0.7. The period or decimal point indicates that this is a decimal. The decimal 0.7 could be pronounced as SEVEN TENTHS or as ZERO POINT SEVEN. If a decimal is less than 1, place a zero before the decimal point. Write 0.7 not .7**
 * Decimals are a method of writing fractional numbers without writing a fraction having a numerator and denominator.

**Tenths as Decimals-II** The fraction 7/10 could be written as the decimal 0.7 The period or decimal point indicates that this is a decimal. The decimal 0.7 could be pronounced as SEVEN TENTHS or as ZERO POINT SEVEN. There are other decimals such as hundredths or thousandths. They all are based on the number ten just like our number system. A decimal may be greater than one. The decimal 3.7 would be pronounced as THREE AND SEVEN TENTHS.**
 * Decimals are a method of writing fractional numbers without writing a fraction having a numerator and denominator.

**Place Values of Decimals** The first digit after the decimal point is called the tenths place value. There are six tenths in the number O.6495. The second digit tells you how many hundredths there are in the number. The number O.6495 has four hundredths. The third digit is the thousandths place. The fourth digit is the ten-thousandths place which is five in this example. Therefore, there are six tenths, four hundredths, nine thousandths, and five ten-thousandths in the number 0.6495.**
 * Decimal numbers, such as O.6495, have four digits after the decimal point. Each digit is a different place value.

**Subtracting Decimals** code 11.48 __3.2756__  8.2044
 * How to subtract decimals that have different numbers of decimal places**
 * **Write the number that is being subtracted from. Write the number that is being subtracted below the the first number so that the decimal point of the bottom number is directly below and lined up with the top decimal point.**
 * **Add zeros to the right side of the decimal with fewer decimal places so that each decimal has the same number of decimal places.**
 * **Subtract the bottom number from the top number.**
 * Example: Subtract 11.48 - 3.2756**

code

**Multiplying thousandths by tenths** How to multiply a three digit decimal by a one digit decimal number (for example 0.529 * 0.7): > code 0.529 0.7__ code > code 6 0.529 x _0.7__ 3  code > code 26 0.529  _0.7__    03 code > code 26 0.529  _0.7__ 0.3703 code **Convert Scientific Notation to Decimal Numbers** The number 6.5x10-7 written in decimal format would be 0.00000065 because the decimal point was moved 7 places to the left to form the decimal 0.00000065.**
 * Place one decimal above the other so that they are lined up on the right side. Draw a line under the bottom number. Temporarily disregard the decimal points and multiply the numbers like multiplying a three digit number by a one digit number.
 * Multiply the two numbers on the right side. (9 * 7 = 63). This number is larger than 10 so place a six above the center column and place three below the line in the right column.
 * Multiply the digit in the top center column (2) by the digit in the center of the right column (7). The answer (2*7=14) is added to the 6 above the center column to give an answer of 20. The units place value (0) of 20 is placed below the line and the tens place value (2) of the 20 is placed above the five.
 * The five of the top number is multiplied by the seven of the multiplier (5*7=35). The two that was previously carried is added and 37 is placed below the line. At the start we disregarded the decimal places. We must now count up the decimal places and move the decimal place to its proper location. We have three decimal places in 0.529 and one in the decimal 0.7 so we move the decimal four places to the left to give the final answer of 0.3703.
 * Scientific notation is used to express very large or very small numbers. A number in scientific notation is written as the product of a number (integer or decimal) and a power of 10. The number has one digit to the left of the decimal point. The power of ten indicates how many places the decimal point was moved.