Mathematical Programming Algorithms Assignment

 

Introduction 

This module will have been given to you as a condition of admittance into one of the programmes. This brochure includes both guidelines and exercises for each module. This module has a total of nine activities for you to complete and submit. Before attempting the activities, you should read through each guide.

This module will have been given to you as a condition of admittance into one of the programmes.

This brochure includes both guidelines and exercises for each module. This module has a total of nine activities for you to complete and submit. Before attempting the activities, you should read through each guide.

Decimal Guide

A decimal is a way of writing a non-integer number. A decimal number is a number that falls between two other numbers.

 

7.465 is a number that falls between the digits 7 and 8. As a result, it is greater than 7, but less than 8.

 

Value headers such as tenths, hundredths, and so on can be utilised to figure out what a decimal number means.

Units tenths of a millionth of a 7 4 6 5 7 4 6 5 7 4 6 5 7 4 6 5 7 4 6

 

Ordinary whole numbers are to the left of the decimal point. Parts of whole numbers are represented by the numbers to the right of the decimal point.

Rounding

It might be difficult to interpret and deal with decimal fractions because they are made up of strings of numbers. This is made easy by rounding.

 

So, regardless of how many decimal places we’re rounding to, we determine the value of the final rounded number depending on the consecutive digits – if they round to a digit less than 5, we round down; if they round to a digit more than 5, we round up, as seen in the examples below: 3.46 = 3.457 to 2 decimal places

Long Division Guide

 

Below is a brief ‘how to’ guide to help you brush up on your long division skills. For this task, no remainders should be left in your long division; you must continue to use the decimal point.

Fractions Guide

Written Fractions

 

The numerator is the fraction’s top number, and it reflects the proportion of equal parts that the whole is divided into.

The denominator is the fraction’s bottom number, and it reflects the total number of parts that the whole is divided into.

In the above example, the purple segment would be displayed as 1/6, one of six segments that make up the entire unit.

If we wanted to represent all of the segments save the purple one as a fraction, we’d write 5/6, which is five segments of six segments.

 

Proper and Improper Fractions

The numerator is less than the denominator in a suitable fraction. As a result, 1/6 and 5/6 are both correct fractions. The numerator of an incorrect fraction is greater than the denominator. As a result, 7/6 and 10/6 are both incorrect fractions. This indicates that the percentage is more than one.

 

A mixed fraction is a fraction that contains both a whole number and a proper fraction. As a result, the improper fractions 11/6 and 14/6 can also be represented as 11/6 and 14/6.

 

Comparing Fractions

 

It’s simple to compare fractions with the same denominator. Let’s compare 1/6 with 5/6, for example.

 

We can tell that 5 is more than 1 by looking at the numerators. As a result, 5/6 is greater than 1/6.

 

When the denominators differ, such as 1/6 and 3/5, a common denominator (or one that can be divided by both 6 and 5) must be found.

 

The simplest method is to multiply 6 x 5 = 30.

 

As a result, the new numerator will be 30.

 

After that, you must calculate the corresponding number of 1/30 for each fraction.

Simplifying Fractions

 

The numerator and denominator of a fraction must be divided by the same value at the same time when simplifying it.

 

Consider the following scenario:

 

20/30 Because both are divisible by ten, the answer is 2/3.

 

Because 2/6 and 2 are both divisible by 2, this can be reduced to 1/3.

Volume

We move the point to the right when we MULTIPLY by numbers like 10, 100, or 1000.

 

The multiplier is off by the same number of places as the number of zeros in the multiplier. For example, 2.3 x 100 = 230, 58 x 1000 = 58 000, and 0.06 x 10 = 0.6.

 

We move the point LEFT by the same number of places when we DIVIDE by such quantities.

 

For example, 43.7 10 = 4.37 360 100 = 3.60 9.5 1000 = 0.0095

 

We also need two other measurements when it comes to volumes. These are widely utilised in the continent on a daily basis.

Keep in mind that deci…means “one tenth of…”

 

“One hundredth of…” is what centi signifies.

 

“One thousandth of…” is what milli…means.

 

It’s a lot easier to measure very small weights correctly than it is to measure volumes. As a result, we have names for weights less than one gramme. You’re undoubtedly familiar with the first one.

 

One thousandth of a gramme is equal to one milligramme. We can express the link in a variety of ways:

 

0.001g Equals 1mg 1 gramme equals 1000 milligrammes

 

It’s possible you’ve never heard of the next tiniest one.

 

One millionth of a gramme equals one microgram. It is one thousandth of a milligramme in size. The prefix “micro” is represented by the sign m in science.

 

As a result, 1000mg equals 1mg. When written rapidly or sloppily, however, this symbol m can resemble the letter m, causing confusion and possibly harm.

Percentage Guide

 

The symbol for percent is percent, which means “per hundred” or “out of a hundred.”

So, if 34% of the population is over 60 years old, then means 34% of the population is over 60 years old.

 

One important principle is that 100 percent refers to the entire quantity.

 

Since 34 percent of the population is over the age of 60, it can be deduced that 66 percent of the population is not over the age of 60.

 

Because a percentage may be represented as 34/100, it is effectively a fraction with 100 as the denominator. This fraction can be simplified and/or written as a decimal as necessary.

Converting percentages to decimals

 

We divide a percentage by 100 to convert it to a decimal. 7 percent equals 7/100.

 

By moving the decimal point two positions to the left, you can achieve this. Remember that adding zeros to a number does not change the value; rather, it aids us in our calculations.

 

0.07 = 007.0 /100

Converting fractions to percentages

 

We multiply a fraction by 100 to turn it to a percentage. By placing a full number above 1, it can be written as a fraction.

 

1/8*100

 

1/8*100/1 = 1/8*100/1

 

12.5 percent =100/8

 

Percentages are a common way of representing proportions of numbers or quantities, which facilitates comparisons and our perception of size.

 

Percentage of a quantity to be calculated

 

To compute, multiply the number by the required percentage. What is the percentage of 96 that is 30 percent?

 

30/100*96

 

=2880/100

 

=28.8