Decimals

1. Decimals By: Sandy Denson

2. Table of Contents • Place Value 2,3 • Writing Decimals as Fractions 4,5 • Writing Fractions as Decimals 6,7 • Comparing Decimals 8 • Adding and Subtracting Decimals 9 • Multiplying Decimals by Decimals 10 • Multiplying Decimals by 10, 100, 1000 11 • Dividing Decimals 12

3. Place Value Chart 1 2 3 . 4 5 6 Hundreds Ones Tenths Thousandths Tens Decimal Point Hundredths 123.456 One hundred twenty-three and four hundred fifty-six thousandths

4. Remember: . Tenths Hundredths Thousandths Hundreds Tens Ones 3 5 7 . 6 4 2 When writing or saying numbers with decimal parts, we must say “ths” at the end of the ten, hundred, and thousand that is on the right side of the decimal point. Three hundred fifty-seven and six hundred forty-two thousandths

5. Writing Decimals as Fractions When we read the decimal number, we automatically know what the denominator of our fraction is going to be. Our numerator of the fraction is going to be the number we say. For example 0.5, we say this as five tenths. Therefore when we write our fraction it will have a denominator of 10 and a numerator of 5. 5/10

6. Writing Decimals as Fractions 0.4 4/10 0.6 6/10 0.05 5/100 0.21 21/100 0.007 7/1000 0.675 675/1000

7. Writing Fractions as Decimals By reading the fraction out loud, it lets us know what place value we are going to write our decimal number to. For example: 23/100 We read this fraction as twenty-three hundredths. We know that hundredths has two decimal places. Therefore, we must have two places to the right of the decimal. 0.23

8. Writing Fractions as Decimals 5/10 0.5 9/10 0.9 12/100 0.12 7/100 0.07 139/1000 0.139 3/1000 0.003

9. Comparing Decimals = 12.345 13.675 < When comparing decimals, the first thing to do is to compare the whole numbers first. Whatever side is larder, will be the larger number. Therefore in this problem, we would say that 12.345 is less than 13.675.

10. Adding and Subtracting Decimals The most important thing to remember when adding or subtracting decimals is to keep the decimal points all lined up vertically. In order to do this, we must write the problem vertically and not horizontally. In order to keep the decimals lined up, you can add zeros to the numbers to keep them equal in digits. For example: 0.303 +4.230 4.533

11. Multiplying Decimals by Decimals When multiplying decimals, we do not need to line up the decimal points before we work the problem. We need to multiply the problem as if we were multiplying whole numbers. After we have the problem worked, we need to count all the places to the right of each decimal point. Then, that is the amount of places we put in the answer. For example: 12.3 x 1.5 = ??? 12.3 X 1.5 613 +1230 18.45 As we see, we have one place to the right of each number. We add them up, and we have two decimal places. Therefore, our answer must have two decimal places in it.

12. Multiplying Decimals by 10, 100, 1000 In our number system, the places have value. The value of each place is 10 times greater each time we move one place to the left. When we multiply a number by 10, the digits all shift one place to the left. When we multiply 0.34 by 10, the three shifts from the tenths place to the ones’ place, and the four shifts from the hundredths place to the tenths place. 0.34 3.4

13. Dividing Decimals by Decimals When dividing a decimal number by a decimal number, we move the decimal point of the divisor so that it becomes a whole number. Then we move the decimal point in the dividend the same number of places. The decimal point in the quotient is straight up from the new location of the decimal point in the division box. The memory cue for dividing by a decimal number is “over, over, and up.” For example: 0.3 0.12 0.4 3 1 . 2 1 2

14. Decimals Click Here Sandy Denson, 2003