How many hours in a year

Do you know how many hours are there in a year

How many hours in a year is nothing but the total hours we have in 1 year. Hours in a year can be calculated by using the multiplication of arithmetic process. We know that 24 hours is equal to 1 day. With the help of this we can find the hours in a year. We know that one normal year is equal to 365 days and one leap year is equal to 366 days.

Also get more details on days of our lives comings and goings

Important Terms to Calculate How many Hours in a Year

1 minute = 60 seconds
1 hour = 60 minutes
1 day = 24 hours
1 week = 7 days
1 year = 12 months
1 year = 365 days
1 leap year = 366 days

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How to find an Area of a Circle

The area of a circle is a simple shape of Euclidean geometry consisting of those points in a plane which are equidistant from a given point called the center. The common distance of the points of a circle from its center is called its radius.



Finding area of a circle

Example: 1Find the area of the circle with radius 14 meter

Solution:
We know the formula for finding the area of the circle = r²
Here r = 14 meter, = 3.14, substitute r and value in the above formula we get

Area = 3.14 * 14²

Area = 3.14 *14*14

Simplify the above we get

Area = 615.44 meter square

Therefore the area of the circle is 615.44 meter ²

More details about area of a circle formula.

Errors: Absolute and Relative Errors

Absolute Errors

Since no measurement is exact, there will always be the possibility of an error. Numbers are often rounded off to a certain number of significant figures or decimal places, and in such instances an absolute error can be calculated.

If the number 1200 is given to the nearest 100, for example, then the number can be anything between 1150 and 1250. It can therefore be written as 1200 ± 50. In this instance, the absolute error is 50.

In general, if a number is a ± b, then the absolute error is b.

Relative Errors

The absolute error doesn"t really tell us much about how big the error really is. For example, an absolute error of 1000 is very big if the number we are talking about is 3000, but it is small if we are talking about 100 000 000 000. The relative error incorporates the number that we are talking about.

If a number is a ± b, then the relative error is b/a

Example

If 200 is correct to 2 significant figures, what is the relative error?
This can be written as 200 ± 5, since the highest number it could be is 205 and the lowest is 195. The relative error, therefore, is 5/200 = 1/40 = 0.025 .

Percentage Error

Percentage error = relative error × 100

Absolute and Relative Error - Example Problems:

Absolute and relative error - Problem 1:

Student calculates the mass of a sample to be 5.65 g. Actual mass of the sample is 7.75 g. Determine the absolute error and relative error.

Solution:

Experimental calculated Value = 5.65 g

Known Value = 7.75 g

Absolute Error = Experimental calculated value - Known Value
= 5.65 g - 7.75 g
Absolute Error = - 2 g

Relative Error =

Relative Error =

Relative Error = - -0.29629 g.

Absolute and relative error - Problem 2:

Student calculates the mass of a sample to be 6.45 g. Actual mass of the sample is 8.42 g. Determine the absolute error and relative error.

Solution:

Experimental calculated Value = 6.45 g

Known Value = 8.42 g

Absolute Error = Experimental calculated value - Known Value
= 6.45 g - 8.42 g
Absolute Error = - 1.97 g

Relative Error =

Relative Error =

Relative Error = -0.233 g.

Hope you like the above definition and examples of Absolute and Relative Errors.Kindly leave your comments.

Logarithms

Introduction

Logarithms were invented by Napier. Before we had calculators, logarithms made calculation easier because they reduced multiplication and divisions to addition and subtraction. These days, logarithms are less important for this purpose.

Logarithms

A logarithm is writen as log_a(x) where a is a number called the base. Usually logarithms are written to the base 10 or sometimes base 2 for binary numbers, but it can be any number. If the logarithm is to the base e= 2.71828..., then we call it a natural logarithm because it is the only logarithm base which has a rate of change equal to the thing which is changing. Natural logs are also written, ln(u). The ln comes from the Latin, log naturalis.

Rules of Logarithms

log_a(0) is undefined(1)

log_a(1) = 0(2)

log_a(u v) = log_a(u) + log_a(v)(3)

log_a(u/v) = log_a(u) - log_a(v)(4)

log_a(u)ⁿ = n log_a(u)(5)

log_b(u) = log_a(u)/log_a(b) - change of base(6)

Where b is the old base, a is the new base, u is the argument of the logarithm.

log_a(1/u) = - log_a(u) from (2) and (4).(7)

With these rules we can manipulate the exponential functions. Logs are the inverse functions of

Exponential Function

We have seen how to convert a number into a logarithmic number but how about if we are given a logarithm of a number and want to know what the original number was? This is achieved using exponential functions. The exponential function is the inverse function of a logarithmic function.

That is to say, that a^log_a(u) = u or log_a(a^u)=u

If we have a log to the base 10, the inverse function is 10^u.

For natural logarithms, the inverse function is e^u or exp(u). In particular, log₁₀(10^u) = u

and 10^log₁₀(u)= u(8)

ln(e^u) = u or e^ln(u) = u(9)

Example

What is the value of the number the gives the following logs to the base 10:

i) 1, ii) 12, iii) -2, iv) 2.6, v) -5.43

Answers

1. log₁₀ x = 1
   x=10¹ = 10
2. log₁₀ x = 12
   x=10¹² = 1x10¹²
3. log₁₀ x = -2
   x=10^-2 = 0.02
4. log₁₀ x = 2.6
   x=10^2.6 = 501.187
5. log₁₀ x = 12
   x=10^-5.43 = 3.71535 x 10^-6