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Division of Decimals by Decimals The procedure for the division of decimals is very similar to the division of whole numbers. Make the divisor into a whole number by multiplying both it and the dividend by the same number (such as 10, 100, 1000 etc.). An easy way to do this is to move the decimal point to the right end of the divisor and move the decimal point of the dividend the same number of places. How to divide a four digit decimal number by a two digit decimal number (e.g 0.4131 ÷ 0.17). Place the divisor before the division bracket and place the dividend (0.4131) under it. 0.17)0.4131 Multiply both the divisor and dividend by 100 so that the divisor is not a decimal but a whole number. In other words move the decimal point two places to the right in both the divisor and dividend 17)41.31 Proceed with the division as you normally would except put the decimal point in the answer or quotient exactly above where it occurs in the dividend. For example: 2.43 17)41.31 Exponents and Square Roots An exponent is a number that tells how many times the base number is used as a factor. For example, 34 indicates that the base number 3 is used as a factor 4 times. To determine the value of 34, multiply 3*3*3*3 which would give the result 81. If a negative number is raised to an even power, the result will be positive. (-2)4 = -2 * -2 * -2 * -2 = 16 If a negative number is raised to an odd power, the result will be negative. (-2)5 = -2 * -2 * -2 * -2 * -2 = -32 The negative number must be enclosed by parentheses to have the exponent apply to the negative term. Note that (-2)4 = -2 * -2 * -2 * -2 = 16 and -24 = -(2 * 2 * 2 * 2) = -16 Exponents are written as a superscript number (e.g. 34) or preceded by the caret (^) symbol (e.g. 3^4). Some facts about exponents: Zero raised to any power is zero (e.g. 05 = 0) One raised to any power is one (e.g. 15 = 1) Any number raised to the zero power is one (e.g. 70 = 1) Any number raised to the first power is that number (e.g. 71 = 7) To “unsquare” a number means to find a number that, when multiplied by itself, gives you the original number. Unsquaring a number is also called finding the square root (symbol √ ). Example: √9 is 3, because 32 (or 3 * 3) = 9. Multiplication of Two and Three Digit Numbers Example: 529 * 67 Step 1: Place one number above the other so that the hundreds', tens' and ones' places are lined up. Draw a line under the bottom number. Step 2: Multiply the two numbers in the ones' places. (9 * 7 = 63). This number is larger than 9 so place a 6 above the tens' place column and place 3 below the line in the ones' place column. 6 529 67 3 Step 3: Multiply the digit in the top tens' place column (2) by the digit in the lower ones' place column (7). The answer (2*7=14) is added to the 6 above the top tens' place column to give an answer of 20. The 0 of 20 is placed below the line and the 2 of the 20 is placed above the hundreds' place column. 26 529 67 03 Step 4: The hundreds' place of the top number (5) is multiplied by the ones' place of the multiplier (5*7=35). The two that was previously carried to the hundreds' place is added and the 37 is placed below the line. 26 529 67 3703 Step 5: After 529 has been multiplied by 7 as shown above, 529 is multiplied by the tens' place of the multiplier which is 6. The number is moved one place to the left because we are multiplying by a tens' place number. The result would be 3174: 15 529 67 3703 3174 Step 6: A line is drawn under the lower product (3174) and the products are added together to get the final answer of 35443. 15 529 67 3703 3174 35443