Math 6 Honors Periods 1, 6 & 7 ( Yosemite Week in review)

Comparing Decimals 3-4

We have used number lines to compare whole numbers. Number lines can be used to show comparisons of decimals. As with whole numbers, a larger number is graphed to the right of a smaller number.

In order to compare decimals, we compare the digits in the place farthest to the left where the decimals have different digits.

Compare the following:

1. 0.64 and 0.68 since 4 < 8 then 0.64 < 0.68.

2. 2.58 and 2.62 since 5 < 6 then 2.58 < 2.62 .

3. 0.83 and 0.833

To make it easier to compare, first express 0.83 to the same number of decimal places as 0.833

0.83 = 0.830 Then compare

0.830 and 0.833 since 0 <3 Then 0.830 < 0.833.

Write in order from least to greatest

4.164, 4.16, 4.163, 4.1

First, express each number to the same number of decimal places Then compare. 4.164, 4.160, 4.163, 4.100

The order of the numbers from least to greatest is

4.1, 4.16, 4.163, 4.164

Rounding 3-5

A method for rounding may be stated as follows: Find the place to which you wish to round, mark it with an underline ___ Look at the digit to the right. If the digit to the right is 5 or greater, add 1 to the marked digit. If the digit to the right is less than 5, leave the marked digit unchanged. Replace each digit to the right of the marked place with a 0

Round 32,567 to (a) the nearest ten thousand, (b) the nearest thousand, (c) the nearest hundred, and (d) the nearest ten

(a)32, 567: since 2 is less than 5, we leave the 3 unchanged, and replace 2, 5, 6, and 7 with zeros

30,000

(b) 32,567: since the digit to the right of 2 is 5, we add a 1 to 2 and get 3 and we replace 5, 6, and 7 with zeros

33,000

(c)32,567: since 6 is greater than 5, we add 1 to 5 and replace 6 and 7 with zeros

32,600

(d) 32,567: since 7 is greater than 5, we add 1 to 6 and replace 7 with a zero

32,570

A similar method of rounding can be used with decimals. The difference between the two methods is that when rounding decimals, we do not have to replace the dropped digits with zeros.

Round 4.8637 to (a) the nearest thousandth, (b) the nearest hundredth, (c) the nearest tenth, and (d) the nearest unit

a. 4.8637: Since 7 is greater than 5, we add 1 to 3 --get 4 & drop the 7

4.864

b. 4.8637: Since 3 is less than 5, we leave 6 unchanged and drop 3 & 7

4.86

c. 4.8637: Since 6 is greater than 5, we add 1 to 8 and drop 6,3, &7

4.9

d. 4.8637: Since 8 is greater than 5, we add 1 to 4 and drop 8, 6, 3, & 7

5

Adding and Subtracting Decimals 3-6

Decimals may be added or subtracted using the same rules as whole numbers

Write the given numbers one above the other with the decimal points in line.

Annex zeros to get the same number of decimal places and then add or subtract as if the numbers were whole numbers.

Place a decimal point in the number for the sum or difference in position under the decimal points in the given numbers.

Add 6.47 + 340.8 + 73.523

STEP 1	STEP 2	STEP 3
0006.47	006.470	006.470
0340.8	340.800	340.800
+ 073.523	+ 73.52	+ 73.523
	420 793	420.793

The use of rounded numbers to get an approximate answer is called estimation. We use estimates to check actual answers. Use estimates as a habit to check if your answer is reasonable. To find an estimate, first round the highest place value of the smallest number, then compare.

Add 8.574 + 81.03 + 59.432. Then estimate to check your answer. What is the highest place value of the smallest number? 9 + 81 + 59 = 149