### Topics:

1) Rounding Decimals

2) Comparing Fractions and Decimals

3) Even, Odd, Composite, and Prime Numbers ### Introduction to Digits

The following images shows all the different digits from thousands to ten thousandths. The digits are centered about the decimal point but remember when counting from the right you start with tenths.

REMEMBER: Starting at the right of the decimal point the first digit is tenths, and an easy way to remember is that you add -ths to the digits when you go to the right of the decimal oneths sounds a bit weird to say.

### Rounding Decimals

Rounding Decimals

for 5 and above round up

Example 1.7677 ~ 1.768

for below 5 round down

Example 1.8421 ~ 1.842

### Round the Following to the nearest:

1) 1.676 to the nearest tenth

2) 0.578 to the nearest hundredth

3) 19.35511 to the nearest thousandth

4) 6.992232 to the nearest hundred thousandth

5) 5.53411 to the nearest ten

1) 1.7

2) 0.58

3) 19.355

4) 6.99223

5) 10

### 1) 1.676 to the nearest tenth

The first step is to identify the tenths digit:

1.676

Then look to the number to the right of the tenths digit

• If it is above 5 we round the tenths digit up

• If it is below a 5 we leave the tenths digit unchanged

1.676 <--------- because 7>5 we will round up

### 2) 0.578 to the nearest hundredth

The first step is to identify the hundredths digit:

0.578

Then look to the number to the right of the hundredths digit

• If it is above 5 we round the tenths digit up

• If it is below a 5 we leave the tenths digit unchanged

0.578<--------- because 8>5 we will round up

### 3) 19.35511 to the nearest thousandth

The first step is to identify the thousandth digit:

19.35511

Then look to the number to the right of the thousandth digit

• If it is above 5 we round the tenths digit up

• If it is below a 5 we leave the tenths digit unchanged

19.35511<--------- because 1<5 we will not round up

### 4) 6.992232 to the nearest hundred thousandth

The first step is to identify the hundred thousandth digit:

6.992232

Then look to the number to the right of the tenths digit

• If it is above 5 we round the tenths digit up

• If it is below a 5 we leave the tenths digit unchanged

6.992232<--------- because 2<5 we will not round up

### 5) 5.53411 to the nearest ten

The first step is to identify the ten digit:

_5.53411

Then look to the number to the right of the tens digit

• If it is above 5 we round the tenths digit up

• If it is below a 5 we leave the tenths digit unchanged

_5.53411<--------- because 5=5 we will round up

### Comparing Fractions and Decimals

In order to compare fractions and decimals you have to make them easily comparable:

1. You can convert simple fractions into decimals

3/4 --> 0.75

1. You can convert simple decimals into fractions

1.75 --> 7/4

1. You can convert simple fractions into mixed fractions and compare the non fractional part

19/2 --> 9 1/2

1. You can approximate the decimal form of more complex fractions using long division

3/7 --> 0.429

1. You can easily tell negative numbers will be less than positive numbers

-102.233423 --> OH NO what a big scary negative number

### Example: Order 1.72, 4/5, -1/5, 7/4 from least to greatest

Steps:

1) -1/5 is the lowest because it is the only negative

2) 4/5 = 0.8 and 7/4 = 1.75

3) 7/4>1.72

### Order the Following from least to greatest:

1) 3/8, 1 5/8, 75%, 0.33, -1/8

2) 2, 3/4, 8/12, 3 5/8, -12/16

3) 1.6, 6/4, 9/12, 3 5/8, -12/16

Hint: Try converting fractions into decimals and vice-versa(Try not to use a calculator unless you are stuck)

1) -1/8 < 0.33 < 3/8 < 75% < 1 5/8

2) -12/16 < 8/12 < 3/4 < 2 < 3 5/8

3) -12/16 < 9/12 < 6/4 < 1.6 < 3 5/8

More Practice:Real Numbers

### 1) 3/8, 1 5/8, 75%, 0.33, -1/8

1) We can see that -1/8 will be the lowest number

2) We can see that 1 will be the greatest because the rest are decimals and fractions below 1

3) We can see that:

3/8 < 5/8

4) Now the hardest part is to compare the following:

3/8 and 0.33

3/8 = 0.375 <-- by long division

0.375 > 0.33

5) Now to compare the following:

5/8 and 75%

5/8 = 0.625

75% = 0.75

0.75>0.625

### Even, Odd, Prime, and Composite Numbers

Even: Divisible by 2

Example: 92, 4, 56

Odd: Not divisible by 2

Example: 97, 121, 1

Prime: Only divisible by 1 and the number itself:

Example: 13, 29, 31

Composite: Divisible by other whole number(not prime)

Example: 6, 8, 10

Exceptions: Numbers that are neither prime nor composite

Example: 0 and 1

### Categorize the Following(2 terms each):

1) 2

2) 0

3) 1

4) 5

5) 9

6) 192

7) 23

8) Final Boss: 1231231231321487953457230495273894523123123123122

1. even, prime

2. even (neither prime nor composite)

3. odd (neither prime nor composite)

4. odd, prime

5. odd, composite

6. even, composite

7. odd, prime

8. even, composite