__Introduction Approximate Value__-

Approximate value is that means Not exact value, but close enough to be used.

#### __Examples__

• the cord measures 1.91, and you round it to "2", as that is good enough.• the bus ride takes 27 minutes, and you say it is "a 30 minutes bus ride".

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__ Estimate__-

Estimate can give us the rough idea about something. Sometimes, we need to calculate something but do not have a calculator or paper and pen. We must use mental mathematics to get the answer. That's where estimation comes in handy. Estimation can allow us to see whether our answer is reasonable. Consider the following example.

5 + 8 = 60

By estimating the answer of 5 + 8 = 60, we find that the answer is unreasonable and incorrect.

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__ Approximation__

The answer is approximation. Approximation is the science of making numbers simpler. However, approximation is a crucial element of estimation. In a broad sense, estimation means guessing some kind of value and trying to be as close to the real value as we want. Sometimes the result can be really far off, however, as we will see later.

We can use approximation to remember something more easily.

__Some Rule to Solve the Problems__-

• the value is less than 5 consider it as zero for example 4.04 will be written as 4.0. Here the second number of decimal is less than 5 so it is consider as 0.

• If the value is equal to or greater than 5 increase, 1 in left digit for example 4.06 will be written as 4.1. If we further apply approximation to this number than we get 4.0, because this time 1 is less than 5 .

__Note-__

After approximation our numbers are : 1268 + 21 = 1289,

You can also apply approximation to the result in same way :

The number will be modified as – 1180

Again approximation – 1200 ( Final value )

__ In Addition__-

Give an example -

Add 1758.005 + 18.886
In this example first digit is 1758.005 here the 3rd digit of decimal is 5 that means we can neglect it by increasing 1 in the left side. After approximation the new number is 1758.01. Now we can apply another step of approximation, but this time the second decimal digit 1 is lower than 5. So we will neglect it and our number will become 1758.0 .

__In Multification-__

Give an example-

19.86 × 31.268
In this example first number is 19.86 here the first right term from decimal is 9 i.e. greater than 5. So we can directly add 1 to left side after neglecting decimal digits . The number will become 20.
But still you can use another approximation to simplify it 20 to make it 20.

__In Division-__

Give an example-

889.056 ÷ 9.466
Here first number is 779.056, in this case you can easily visualize 0 is coming in first right digit of the decimal. So neglect the all decimal numbers and write the number as 779.0, Still you can apply another approximation and make it780.