project2

Problem Solving

name

Institution

Problem Solving

1. Explain how to ROUND a number to any   place. Give at least three examples. Why is this important? 

Only numbers with decimals can be rounded off. Rounding off numbers depends on the decimal places. Decimal places are determined based on the number of digits that fall on the right hand side of the decimal. For instance, if there are three digits to the right of the decimal, then the number is said to have three decimal places, for example 23.654. Rounding numbers depends on the number of decimal places required. For instance, if a number is to be rounded to 1 decimal place but has three digits to the right, the first digit after the zero is considered. When rounding off, the number falling in the place required is left while the rest are discarded. However, the number immediately after the one falling in the place required determines the value of the place. If the number is 0 to 4, the rest of the digits are discarded without making any change to the digit in the place required. If the number is 5 to 9, then the number falling in the place required is increased by one value. For example, 23.654 to 2 decimal places becomes 23.65 while 23.655 becomes 33.66. Learning to round numbers is important when performing estimations.

2. Make up a new problem similar to   this one: “The cost of renting a boat from Estes Rental is $9 per 15 minutes.   The cost from Ship and Shore Rental is 20 per half-hour. If you plan to rent the boat for three   hours, which business offers the better deal and by how much.”

It costs $50 to rent a car with Toyota on a daily basis whereas it takes &250 to rent the same car at Mercedes for a whole week. A client plans to rent the car for a week. Therefore, at Toyota he will pay &50 times 7 which is a total of $350. At Mercedes, he will have to pay a one-time fee of $200. Therefore, Mercedes offers a better deal for him by a margin of $100.

3. Convert each of the following base   ten numerals to a numeral in the given base:

Convert 67 to base three

2111

Convert 1544 to base five

22134

Convert 59 to base two

111011

Explain why it is important to understand the base for a number as well as the value. 

A base or a radix in mathematics represent the number of digits that a system sues to represent a number. The most common base used today in mathematics is decimal system. Decimal system is also called base 10 since the term “dec” refers to 10. Moreover, a base can be any whole number that is larger than 1. The most common practice is to write the base number next to the number itself, for instance, 10 to base 5 is written as 105. The most importance uses of bases is in computer science. Binary is used to refer to base 2 and is commonly used since at the most simplest level, a computer only uses zeros and ones. In addition, bases are used in measurements for instance in making markings on the wall. Here, numbers are often expressed to base 1.

4. Explain why a symbol for zero is needed in a positional system, but NOT in other systems. Given an example of each type of system.

In the positional system, the position occupied by a number is more important than the value of the number itself. Therefore, positional system expresses numbers in a sequence and the importance of a number is based on the position it occupies in the sequence. Zero is thus important since it offers a point of transition between one number to the next. For instance, when counting numbers, upon reaching 9, one starts again all over at zero before going to 1. The base system does not need a zero since all numbers are often expressed to base 1. The Egyptian system, Roman system and Babylonian system all do not need zeros in their numerical since it does not play any importance.