1. Math Review
Chapter 3: Decimals

2. The system of numbers that you use is called the decimal system and is based on powers of ten (base ten system). Each place in the place value grid is ten times the value of the place to the right of it. Every number to the right of the decimal point is a decimal fraction ( a fraction with a denominator of 10, 100, 1,000, and so on).
On the place value grid notice that 1/10 can be written as ten to a negative exponent. 10 to the negative first power.

4. Expanded Notation Write .365 in expanded notation
.65 =
(3 x .1) + (6 x .01) + (5 x .001)
(3 x 10 ) + (6 x 10) + (5 x 10 )
Write 5.26 in expanded notation
5.26 =
(5 x 1) + (2 x .1) + (6 x .01)
(5 x 10 ) + (2 x 10 ) + (5 x 10 )

5. Writing Decimals
To read a decimal or write a decimal in words, you start at the left and end with the place value of the last number on the right. Where a whole number is included, use the word “and” to show the position of the decimal point.
Ex. Read the number .75
seventy-five hundredths
Ex. Read the number
forty-five and three hundred twenty-one thousandths

6. Comparing Decimals
If you want to compare decimals, that is, find out if one decimal is greater than another, simply make sure that each decimal goes out to the same number of places to the right.
Ex. Which is greater, .37 or .365?
When you align the two decimals you can easily see that the .37 is greater.
You can also align the decimals first and then add the zeros. The number of digits to the right of the decimal point does not determine the size of the number (.5 is greater than .33).

7. Rounding Decimals
1. Underline the place value to which you’re rounding.
2. Look to the immediate right (one place) of your underlined place value.
3. Identify the number (the one to the right). If it is 5 or higher, round your underlined place value up 1 and drop all the numbers to the right of your underlined number. If the number (the one to the right) is 4 or less, leave your underlined place value as it is and drop all the numbers to the right of your underlined number.
Ex. Round off .478 to the nearest hundredth
Ex. Round off to the nearest thousandth

8. Decimal Computation
To add or subtract decimals, just line up the decimal points and then add or subtract in the same manner you would add or subtract whole numbers.
Ex. Add =
Ex. Subtract =
Ex. Subtract 78.9 – =
Ex. Subtract 17 – 8.43 =

9. Multiplying Decimals
To multiply decimals, just multiply as usual. Then count the total number of digits above the line which are to the right of all decimal points. Place your decimal point in your answer so there is the same number of digits to the right of it as there was above the line.

10. Dividing Decimals
Dividing decimals is the same as dividing other numbers, except that if the divisor (the number you’re dividing by) has a decimal, move it to the right as many places as necessary until it is a whole number. Then move the decimal point in the dividend (the number being divided into) the same number of places. Sometimes, you may have to add zeros to the dividend (the number inside the division sign).

11. Dividing Decimals

12. Estimating Sums, Differences, Products, and Quotients
When working with decimals, it is easy to make a simple mistake and misplace the decimal point. Estimating an answer can be a valuable tool in helping you avoid this type of mistake.

13. Estimating Sums
Estimate and 5.07 by rounding to the nearest tenth.
= 24.7
So is approximately equal to 24.7
Estimate by rounding to the nearest whole number
= 25
is approximately equal to 25

14. Estimating Differences
Estimate – by rounding to the nearest whole number.
12 – 5 = 7
– approximately equal to 7

15. Estimating Products
Estimate the product of 4.7 x 5.9 by rounding to the nearest whole number.
5 x 6 = 30
4.7 x 5.9 approximately equal to 30
Again, in decimals, as in whole numbers, if both multipliers end in .5, or are halfway numbers, rounding one number up and one number down will give you a better estimate of the product.
Try estimating 7.5 x 8.5 to the nearest whole number.

16. Estimating Quotients
Estimate the quotient of divided by 3.12 by rounding to the nearest whole number.
27 divided by 3 = 9
27.49 divided by 3.12 is approximately equal to 9

17. Repeating Decimals Terminating decimals Repeating decimals
A vinculum (a horizontal line over the number or numbers) is the standard notation used to show that a number or group of numbers is repeating.