Side panel FYE1600-24 Learning Unit 3 LEARNING UNIT 3: NUMBERS PAGE LEARNING UNIT 3: NUMBERS Completion requirements A number is a mathematical object used to count, measure, and label. Different types of numbers have many different uses. Numbers such as natural numbers and real numbers can be classified into sets, called number systems. The same number can be written in many different ways. Numbers are very interesting. There are different types of numbers with different characteristics, which make them amenable to being used in many different ways. For instance, exponential numbers can be used to represent very large and/or very small standard numbers, whereas fractions can be changed into decimals and vice versa. Exponential numbers are written as a product of either a decimal or an integer and as a power of ten. This works because of the way our base-10 place value system is set up. Each place value column is 10 times larger than the one before it as you move from right to left. As you move from left to right, each place value is ten times smaller than the one before it. This “times 10” relationship between the columns lets us show numbers in exponential notation. The base number 10 is written as a regular-sized number. An exponent is a smaller number written up and to the right of the 10. The exponent tells how many place value columns are being shown. The number 10 can be shown 10¹. This is like saying 1 x 10. The number 100 can be shown as 1 x 10². This is like saying 1 x 10 x 10. The number 1 000 can be shown as 1 x 10³. This is like saying 1 x 10 x 10 x 10. The number 10 000 can be shown as 1 x 10⁴. This is like saying 1 x 10 x 10 x 10 x 10. For each place value column, add one more number to the exponent. So far, our multiplier has been 1. It can be another number, such as 4. The number 4 000 000 can be shown in exponential notation as 4 x 10⁶. This is a shorter way of saying 4 x 10 x 10 x 10 x 10 x 10 x 10. The exponent matches the number of zeroes in the original number. The multiplier can even be a decimal. Be careful when you change the number 4.5 x 10⁴ from the exponential to the standard notation. Standard notation is writing the number in regular form. The number 4.5 x 10⁴ does NOT become 450 000, but rather 45 000. There are only three zeroes in the correct answer. The decimal point replaces one of the zeroes. The exponential notation allows us to write very large numbers in a short way. The more you use exponential notation, the more fun it will become. Fractions and decimals are two different ways to show the same values: parts of wholes. Knowing both systems well and being able to change from one system to the other will help you succeed. Succeed in what? Remember that we have a base-10 place value system. The first space to the right of the decimal point is called the tenth place. The second space is called the hundredth place. For each column that you move to the left, you are multiplying the previous column by ten. Because of this predictable pattern, one easy way to turn a fraction into a decimal is to check and see if the denominator can easily be turned into a ten, a hundred, or a thousand. For example, if you need to write the fraction as a decimal, you can simply multiply the numerator and the denominator by 25 to get a new fraction. Since the second decimal place is the hundredth place, your decimal is simply 0.25. The digit 5 lands in the hundredths place and gives the decimal its name: twenty-five hundredths. With practice, you will become skilled at converting standard numbers to exponential numbers as well as fractions to decimals and vice versa.....What is the target audience of text 3?
a.
foundation phase and FET learners
b.
intermediate phase and FET learners
c.
foundation and senior phase learners
d.
senior phase and FET learners
