Adding and Subtracting with Decimals Before you can add or subtract numbers with decimals, all the decimal points must be lined up. (It will help if you use zeros to fill in places so that the numbers you are working with all have the same number of decimal places.) Examples: Add the following: 23 + 2.6 +.11 first rewrite the numbers filling decimal places 23.00 + 2.60 +.11 = 23.00 all the decimal points must be lined up 2.60 +.11 25.71 3.6 +.71 = 3.60 +.71 = 3.60 +.71 4.31 Subtract the following: 456.03-22 = 456.03-22.00 = 456.03-22.00 434.03 12.3 -.99 = 12.30 -.99 = 12.30 -.99 11.31
Multiplying with Decimals Step 1: Step 2: Step 3: Step 4: Ignore the decimal point and multiply as usual. Count the number of digits to the right of the decimal point in the first number. Count the number of digits to the right of the decimal point in the second number. Add the number of digits. This will be the number of decimal places in your answer. Examples:.21 2.21 2.21 2 x.6 1 x 6 0 x.06 2.126 3 1.26 2.0126 4 3 decimal places 2 decimal places 4 decimal places
DECIMAL RULES YOU MUST MEMORIZE ADDITION AND SUBTRACTION Line up decimals. Annex(put in) zeros to make numbers end at the same place. Add or subtract numbers. Bring decimal straight down. MULTIPLICATION Multiply the numbers as if there are no decimals in the problem. Do not line them up. Count the digits to the right of the decimal. Make sure the same amount of digits is to the right of the decimal in the product. Remember to underline digits in problem, then underline digits to the right in product. EXAMPLE: 45.09 x 5.7 ` 45.09 x 5.7 31563 22545X 257.013 --start at right --move 3 places left DIVISION If the decimal is in the dividend, it goes straight up, If the decimal is in the divisor you must move it over to the right, then move the decimal in the dividend over the same number of times you moved it in the divisor. Rewrite the problem and divide as usual. Notes about remainders: If the dividend is a whole number and you get a remainder, put a decimal point and zero next to the last number in the dividend. The decimal goes up and the zero goes down to meet the remainder. Continue to divide. If you still get a remainder put another zero and continue until you get no remainder or you see a repeating decimal. If the directions tell you to round to a certain place value, you can stop one place after the rounding place so you can round the answer.
DECIMALS PLACE VALUE CHART ONES TENTHS HUNDREDTHS THOUSANDTHS TEN THOUSANDTHS HUNDRED THOUSANDTHS Reading Decimals: First, read the whole number and say and for the decimal point. Next, read the number to the right of the decimal. Last, say the place value of the last digit. Writing Decimals: The last word you read or hear is the place value of the last digit. Underline the last word. Decimals are parts of a whole. Example: We use a period (.) for a decimal point. We read the decimal point as the word and.. 10ths 100ths 1000ths tenths hundredths thousandths Write in words: 6.003 six and three thousandths 41.23 forty-one and twenty-three hundredths
Rounding Whole Numbers and Decimals Find the place, look next door, 5 or greater, add 1 more. Everything to the left stays the same. Everything to the right becomes zero. The zeros after the decimal can be dropped! Round to the nearest ten 47.87 ~ 50.00 (drop zeros after decimal) 50.00 = 50 Round to the nearest tenth 47.87 ~ 47.90 47.90 = 47.9 Round to the nearest hundred 736.986 ~ 700.000 700.000 = 700 Round to the nearest hundredth 736.986 ~ 736.990 736.99 NOTE: If there is a 9 in the place you are rounding it really becomes 10 so you put a 0 in the place and add 1 to the number to the left. You are regrouping. Example: Round the nearest tenth: 25.96 26.0 When you add 1 to the nine it becomes 10 so the 9 changes to a zero and the 5 became a 6 because you added 1 to it.
Estimating Sums and Differences (+ and ) Round to the nearest whole number or front digits, then add or subtract. Remember to drop zeros after decimal. Note: Round to the same place. 123.99 100 or 124 Rounding to the lower place value gives you a closer +305.43 + 300 +305 estimate, but rounding to a higher place is easier to do 400 429 mentally. Estimating Products (X) Round to the leading digits, Multiply the leading digits and tack on the zeros. Any zeros after a decimal may be dropped. 2345 2000 635.67 600.00 600 X 59 X 60 X34.75 X30.00 X30 120,000 drop 18,000 zeros! Estimating Quotients ( ) Round the divisor first, then change the dividend so it is compatible with the divisor. This means the divisor will go into the dividend evenly with no remainder. 23,456 43 Round 43 to 40 24,000 40 = 600 Then change the 23 so it is compatible with 4. Change it from 23 to because 24 can be divided by 4 evenly.
Comparing and Ordering Decimals Be sure to understand the directions are you comparing from greatest to least or least to greatest? Compare the digits in the highest place value (left side). Make sure you compare the digits in the same place value. Line up the decimals and fill in zeros to make numbers end at the same place value. Remember: Whole numbers are always bigger than decimals. Tenths are always bigger than hundredths and thousandths.