Kindly visit my site to give your child a bright future!!!!!

https://skypeonlinetution.wixsite.com/skypeonlinetution

# Skype Online Tution

Check out my site! Come visit and tell me what you think. https://https://skypeonlinetution.wixsite.com/skypeonlinetution

# Ordering of Decimals

# Ordering Decimals

*“Could I have a 3.65 and an 0.8, please … ?”
NO, not THAT type of ordering. I mean putting them in order …*

Ordering Decimals can be tricky. Because often we look at 0.42 and 0.402 and say that 0.402 must be bigger because there are more digits. But no!

We can use this method to see which decimals are bigger:

- Set up a table with the
**decimal point in the same place**for each number. - Put in each number.
- Fill in the
**empty squares with zeros**. - Compare using the
**first column**on the left - until one number If the digits are equal move to the
**next column**to the right wins.

If you want |
||

If you want descending order you always pick the largest first |

## Example: Put the following decimals in ascending order:

1.506, 1.56, 0.8

In a table they look like this:

Units | Decimal Point |
Tenths | Hundredths | Thousandths |

1 | . | 5 | 0 | 6 |

1 | . | 5 | 6 | |

0 | . | 8 |

### Fill in the empty squares with zeros:

Units | Decimal Point |
Tenths | Hundredths | Thousandths |

1 | . | 5 | 0 | 6 |

1 | . | 5 | 6 | 0 |

0 | . | 8 | 0 | 0 |

### Compare using the first column (Units)

Two of them are “1”s and the other is a “0”. Ascending order needs smallest first, and so “0” is the winner:

Answer so far: **0.8**

Now we can remove 0.8 from the list:

Units | Decimal Point |
Tenths | Hundredths | Thousandths |

1 | . | 5 | 0 | 6 |

1 | . | 5 | 6 | 0 |

– | . | – | – | – |

### Compare the Tenths

Now there are two numbers with the same “Tenths” value of 5, so move along to the “Hundredths” for the tie-breaker

### Compare the Hundredths

One of those has a 6 in the hundredths, and the other has a 0, so the 0 wins (remember we are looking for the smallest each time). In other words 1.506 is less than 1.56:

Answer so far: **0.8, 1.506**

Remove 1.506 from the list:

Units | Decimal Point |
Tenths | Hundredths | Thousandths |

– | . | – | – | – |

1 | . | 5 | 6 | 0 |

– | . | – | – | – |

Only one number left, it must be the largest:

Answer: **0.8, 1.506, 1.56**

Done!

## Example: Put the following decimals in DESCENDING order:

0.402, 0.42, 0.375, 1.2, 0.85

In a table they look like this:

Units | Decimal Point |
Tenths | Hundredths | Thousandths |

0 | . | 4 | 0 | 2 |

0 | . | 4 | 2 | |

0 | . | 3 | 7 | 5 |

1 | . | 2 | ||

0 | . | 8 | 5 |

And we want to go from **highest to lowest** (descending).

### Fill in the empty squares with zeros:

Units | Decimal Point |
Tenths | Hundredths | Thousandths |

0 | . | 4 | 0 | 2 |

0 | . | 4 | 2 | 0 |

0 | . | 3 | 7 | 5 |

1 | . | 2 | 0 | 0 |

0 | . | 8 | 5 | 0 |

### Compare using the first column (Units):

There is a 1, all the rest are 0. Descending order needs largest first, so 1.2 must be the highest. (Write it down in your answer and cross it off the table).

Answer so far: **1.2**

Units | Decimal Point |
Tenths | Hundredths | Thousandths |

0 | . | 4 | 0 | 2 |

0 | . | 4 | 2 | 0 |

0 | . | 3 | 7 | 5 |

– | – | – | – | – |

0 | . | 8 | 5 | 0 |

### Compare the Tenths.

The 8 is highest, so 0.85 is next in value.

Answer so far: **1.2, 0.85**

Units | Decimal Point |
Tenths | Hundredths | Thousandths |

0 | . | 4 | 0 | 2 |

0 | . | 4 | 2 | 0 |

0 | . | 3 | 7 | 5 |

– | – | – | – | – |

– | – | – | – | – |

Now there are two numbers with the same “Tenths” value of 4, so move along to the “Hundredths” for the tie-breaker

One number has a 2 in the hundredths, and the other has a 0, so the 2 wins. So 0.42 is bigger than 0.402:

Answer so far: **1.2, 0.85, 0.42, 0.402**

Units | Decimal Point |
Tenths | Hundredths | Thousandths |

– | – | – | – | – |

– | – | – | – | – |

0 | . | 3 | 7 | 5 |

– | – | – | – | – |

– | – | – | – | – |

Only 0.375 left, so the answer is:

**Answer: 1.2, 0.85, 0.42, 0.402, 0.375**

Kindly visit my Profile to give your child a bright Future and Deep knowledge

http://TutorIndia.net/Tutor_Profiles-NDYxNjA-Mr_Rajeev_Tripathi

# What is Function?

# What is a Function?

A function relates an input to an output.

It is like a machine that has an input and an output.
And the output is related somehow to the input. |

f(x) |
“f(x) = … ” is the classic way of writing a function.And there are other ways, as you will see! |

## Input, Relationship, Output

We will see many ways to think about functions, but there are always three main parts:

- The input
- The relationship
- The output

### Example: “Multiply by 2” is a very simple function.

Here are the three parts:

Input | Relationship |
Output |
---|---|---|

0 | × 2 | 0 |

1 | × 2 | 2 |

7 | × 2 | 14 |

10 | × 2 | 20 |

… | … | … |

For an input of 50, what is the output?

## Some Examples of Functions

**x**(squaring) is a function^{2}**x**is also a function^{3}+1- Sine, Cosine and Tangent are functions used in trigonometry
- and there are lots more!

## Names

First, it is useful to give a function a **name**.

The most common name is “* f*“, but we can have other names like “

*” … or even “*

**g***” if we want.*

**marmalade**But let’s use “f”:

We say *“f of x equals x squared”*

what goes **into** the function is put inside parentheses () after the name of the function:

So ** f(x)** shows us the function is called “

**“, and “**

*f***” goes**

*x***in**

And we usually see what a function does with the input:

** f(x) = x^{2}** shows us that function “

*” takes “*

**f***” and squares it.*

**x**

Example: with **f(x) = x ^{2}**:

- an input of 4
- becomes an output of 16.

In fact we can write** f(4) = 16**.

## The “x” is Just a Place-Holder!

Don’t get too concerned about “x”, it is just there to show us where the input goes and what happens to it.

It could be anything!

So this function:

f(x) = 1 – x + x^{2}

Is the same function as:

- f(q) = 1 – q + q
^{2} - h(A) = 1 – A + A
^{2} - w(θ) = 1 – θ + θ
^{2}

The variable (x, q, A, etc.) is just there so we know where to put the values:

f(**2**) = 1 – **2** + **2**^{2} = 3

## Sometimes There is No Function Name

Sometimes a function has no name, and we see something like:

y = x^{2}

But there is still:

- an input (x)
- a relationship (squaring)
- and an output (y)

## Relating

At the top we said that a function was **like** a machine. But a function doesn’t really have belts or cogs or any moving parts – and it doesn’t actually destroy what we put into it!

** A function relates an input to an output**.

Saying “**f(4) = 16**” is like saying 4 is somehow related to 16. Or 4 → 16

to get more information, kindly Subscribe……….!!

or, Add me on Skype:- Prof. Rajeev Tripathi