1. Bell Ringer

2. Bell Ringer

3. Chapter 4
Decimals Review

4. Writing Decimals Another way to represent part of a whole
A number that is written in a system based on multiples of 10.
You need to use a decimal point to separate the whole number and the decimal.

5. Example The decimal three and fifty-two thousandths is shown. 3.052
The decimal three and fifty two thousandths is shown in expanded form:
3 + 5/ /1000
The same decimal is shown as powers of ten: 3 ones + 0 tenths + 5 hundredths + 2 thousandths

6. Representing Decimals on a Tenths Grid and a Hundredths Grid
Tenths grids and hundredths grids can be used to model decimals and show the connection between fractions and decimals. An entire hundredths grid represents one whole. Each small square represents one- hundredth. An entire tenths grid also represents one whole. Each bar represents one-tenth.

7. Example

8. Representing Decimals on a Number Line

9. Comparing and Ordering Decimals
To compare two decimals, compare the digits in each place value from left to right. If the digits in a place value are the same, then move to the right and compare the next place value until you find two different digits to compare.
Example
The decimals 43.27, , 43.58, are ordered from least to greatest.

10. Estimating Decimals Using Benchmark Decimals
Benchmark decimals, such as 0, 0.5, and 1, are common decimals that can be used to estimate the value of decimals.
Example
Because the digit in the tenths place is a nine, the decimal is close to 1.

11. Rounding Decimals
To round a decimal to a given place value, look at the digit to the right of the place where you want to round the decimal. If the digit to the right is 4 or less, round down. If the digit to the right is 5 or greater, round up.
Example
To round to the nearest hundredth, look at the digit in the thousandths place. The digit in the thousandths place is 6. Because 6 is greater than 5, round up. So, rounded to the nearest hundredth is

12. Writing Fractions as Decimals

13. Estimating Sums and Differences of Decimals
To estimate the sum or difference of decimals, first round each decimal to the nearest whole number. Then, add or subtract.
Example
Estimate
= – 99
= 71

14. Adding and Subtracting Decimals
When adding or subtracting decimals, be sure to line up the decimal points. Doing so helps to ensure that the digits in the same place value are being added or subtracted correctly.
a b

15. Multiplying Decimals
When multiplying decimals, the number of decimal places in the product is equal to the sum of the decimal places in the factors. Estimating the product helps to check if a product is reasonable.
Example
The estimate of the product for the expression 6.13 × 9.87 to the nearest whole number is shown. Then, the product of the multiplication expression is shown.
Estimate: 6.13 X 9.87 ≈ 6 x 10
= 60

16. Actual product:
6.13 X x 9.87 = Estimating first made it easier to determine where to place the decimal point in the product.

17. Dividing Whole Numbers

18. First estimate how many eights are in 41,816. Think: 5000 x 8 = 40,000
First estimate how many eights are in 41,816. Think: 5000 x 8 = 40,000. Therefore, take the difference of 41,816 and 40,000. The difference is 1816.
Next, estimate how many eights are in Think: 200 x 8 = Therefore, take the difference of 1816 and The difference is 216.
Then, estimate how many eights are in Think: 20 x 8 = x 8 =5 240 — that’s too much! Therefore, take the difference of 216 and 160. The difference is 56.
You know that 8 x 7 = 56.
Finally, add the factors to find the quotient.
The quotient is 5227.

19. Dividing Whole Numbers with Quotients that Have Remainders
Not all numbers divide evenly into other numbers. When a divisor does not evenly divide into the dividend, the quotient contains a remainder. Remainders can be written as fractions, decimals, or as a whole number. Depending on the situation, the remainder can be ignored because all that needs to be calculated are whole numbers.

20. Dividing Decimals
When dividing decimals, first multiply the dividend and the divisor by the power of ten that makes the divisor a whole number. Then divide. Be sure to line up the decimal point in the quotient with the decimal point in the dividend. Estimating the quotient helps to check if the quotient is reasonable.
Example
The estimate of the division expression ÷ 4.9 to the nearest whole number is shown. Then, the quotient of the division expression is shown.
Estimate: ÷ 4.9 ≈ 15 ÷ 5
= 3

21. Actual quotient: