Business Maths: Learning Decimal Numbers
In this article, we shall learn a bit about handling maths at our workplace. We shall learn about decimal numbers in this part and in second part we shall learn about percentages.
Decimals: Whole Numbers & Fractions
People, who need to communicate in numeric terms, need to understand decimal numbers, or decimals. Decimal numbers provide a convenient means for describing quantities that contain both whole numbers and fractions. Decimal numbers, which have a set of values ranging from 0 to 9, are the basis of our whole tens number system. Monetary values are stated in terms of decimals, and decimals are generally used for precise measurements.
Decimals are widely used in business for counting bills and coins, valuing stocks, calculating averages and interest rates, using calculators, reading odometers, and measuring time, depth, temperature, height, and weight. Decimals are also used in numerous calculations for analysis purposes. Decimals, like fractions, describe parts of a whole number, in units of tenths, hundredths, thousandths, and so on. The decimal point separates the whole number from the fractional value. Decimals are used in a variety of ways every day by most people.
Understanding decimals in the workplace is important to:
- Read quantities or measurements expressed as decimals
- Write numbers that include fractional parts
- Simplify mathematical operations-including addition, subtraction, division and multiplication.
With an understanding of decimals, you can make quick, accurate calculations. You will, therefore, be better equipped to make critical business decisions that rely upon calculation or analysis of numbers. Because decimal numbers are common in the workplace, knowing what they mean and how to work with them is an important skill. Understanding Decimals
A decimal is basically a fraction with a denominator that is a power of ten. The period, or decimal point (.), marks the place where the whole numbers end, and the decimal fractions begin. In other words, digits to the left of a decimal point indicate a number greater than or equal to one, digits to the right of a decimal point indicate a fraction (a value less than one). Decimals are a way of writing fractions without cumbersome numerators and denominators. For example, 3/10 is written as the decimal "0.3". The decimal point between the 0 and the 3 indicates that this number is a decimal fraction. Any fraction can be expressed as a decimal simply by dividing the numerator by the denominator.
There are three parts to a decimal number:
1. A digit or digits representing the whole number
2. A decimal point
3. A digit or digits representing the fraction.
Like the mixed numbers, decimals include both whole numbers (to the left of the decimal point) and fractions (to the right of the decimal point). For example, the decimal 1.1, includes the whole number one and the fraction one-tenth. Decimal numbers have digits before and after the decimal point- even if that digit is just zero. Whole numbers have no fractional part, so that part is expressed as point zero. For example, the whole number eight would be 8.0, expressed as a decimal. Some decimal numbers have only fractions, and no whole numbers. Whole numbers have no fractional part, so that part is expressed as point zero. For example, the whole number eight would be 8.0,expressed as a decimal. Placement of the decimal point in a decimal number is based on the concept of place value. Decimal numbers are organized into groups of one's or multiples of ten (to the left of the decimal) or multiples of one-tenth (to the right of the decimal). In decimal numbers, the value of each digit depends on its place, or position, in the number. Values to the left of the decimal point are whole numbers. Values to the right of the decimal point are fractions. Adding and Subtracting Decimals
Adding and subtracting decimals is basically the same as adding and subtracting whole numbers. You work from right to left, adding or subtracting numbers of the same place value. The only tricky part is placement of the decimal. You must be sure to line up the numbers being added or subtracted, so that all the decimal points are in a vertical line. Then add or subtract each column of digits, starting on the right and working left. You will need to borrow and carry, the same as you do when adding and subtracting whole numbers.
The steps to add decimal numbers are explained below. As an example, consider the problem 8.2+0.97+1.34.
1. Align the decimal points
2. Add trailing zeroes
3. Add each column
4. Place decimal point
Adding zeroes to the end of a decimal makes it easier to perform operations with decimals that have different numbers of digits to the right of the decimal point. That way, the digits line up, and the digits of the same place value can easily be added.
As already seen, the rule in addition and subtraction is that the decimal points must always be lined up. Adding zeroes at the beginning of a whole number or at the end of a decimal number to get them to line up correctly doesn't change the value of the number. Never put a 0 between the decimal point and any other digit, however. That would change the value!
Decimals often show up on the job, since they allow precise measurement of fractional values—and are easier to work with than fraction with numerators and denominators. Decimals appear in numerous problems in the workplace, in expressions of distance, money, measurements, and volume. Adding and subtracting decimal numbers isn't very much different from adding or subtracting whole numbers. Mastering the skill only requires an understanding of place values and decimal points. Once you have mastered the addition and subtraction of decimals, you will be able to handle many new job tasks, and make existing tasks easier. Just remember to put the numbers in vertical arrangement with the decimal points lining up, add zeroes as necessary, and add or subtract as indicated. Multiplying Decimals
If your business deals with decimal numbers, you will find it very useful to be able to multiply them. For example, say your company hires an administrative assistant from a temporary help agency to fill in for part of a workday. The time clock says she worked 3.9 hours, and she earns £11.70 an hour. How much does the business have to pay? The answer (3.9 x £11.70 = £45.63) requires you to multiply decimals. If you can multiply whole numbers, you can multiply decimals. The answer in a multiplication problem is called the "product".
The steps in the process are as follows:
1. Delete trailing zeroes
2. Multiply the numbers
3. Count the total number of decimal places in both numbers
4. Insert the decimal point in the product.
Notice that the first step in multiplying decimal numbers is to delete trailing zeroes. You can do this only if the zero is the last digit, and it is to the right of the decimal point. Deleting trailing zeroes like this doesn't change the value of the number, but it does simplify the multiplication problem. Never delete a zero to the left of the decimal point, or a zero that occurs between the decimal point and any other digit, however. That would change the value. The trickiest part of multiplying decimals may be counting the total number of decimal places in the problem, so you can put the decimal point in the right place in the answer. Once you have a good understanding of where to place the decimal point in your product, multiplying decimals is a straightforward process.
When you multiply decimal numbers, temporarily disregard the decimal points and multiply the numbers like multiplying any whole numbers. Then just count up the decimal places and move the decimal point to its proper location. Putting a decimal in the wrong place in a multiplication problem makes a big difference. Moving a decimal one place to the left reduces the product by one-tenth. Moving it one place to the right multiplies the answer by ten. In many jobs, workers use decimals all the time. You may not have to multiply decimals every day in your workplace, but it's a valuable skill when the need arises. Multiplying decimals is used on the job to calculate money values, dimensions, volume, and trends. Next time you use your calculator to figure costs or expenses, think about the math, and how the process works. Dividing Decimals
The process of dividing decimals is very similar to the process of dividing whole numbers. It can be a useful skill in many situations. For example, a contractor might bill your firm £277.75. You know the contract calls for payments of £25.25 an hour, and you want to know how many hours the contractor worked. The answer is to divide £277.75 by £25.25, which shows that the contractor worked 11 hours.
If you can divide whole numbers, you can divide decimals. There are two situations to consider-
Dividing a decimal by a whole number, and dividing a decimal by a decimal number. The steps below explain how to divide decimals by whole numbers (numbers that include no fraction):
1. Place the divisor before the division bracket and place the dividend under it
2. Proceed with the division
3. Put the decimal point in the answer (quotient).
Whole numbers have implied decimal points(.0), so they should be considered decimal numbers. Sometimes, when you divide numbers (1.0 divided by 3.0, for example), the quotients have infinite decimal places. That means you have to decide how precise your answer needs to be, then use the principles of rounding to round your answer. To round a decimal number, find the digit occupying the place value you need (the rounding digit). Then look at the digit to the right of that digit. If the digit to the right of the rounding digit is less than 5, leave the rounding digit unchanged. If it is five or more, then add one to the rounding digit. Remove all digits following the rounding digit. When division produces answers with decimals that go on forever, you need to round your quotient to some place value. The place value you round to depends upon the degree of accuracy required in your particular application.
Dividing a decimal number by another decimal number is basically the same process, except there is one more step. You must convert the divisor (the decimal you are dividing in to the other decimal) to a whole number. Division is often required in business situations where you know two numbers (consumption per hour versus total consumption, unit size versus total area, price versus quantity, for example) and have to calculate a third. In fact, division is a critical skill for business analysis purposes. You can divide decimals to define important relationships between costs and expenses in your organization. Many of the financial figures that are commonly used to analyze financial statements are derived from dividing decimal numbers.
Dividing decimal numbers becomes quite manageable—if you just remember to move the decimal points the same number of places in the divisor and the dividend, and put the decimal point in your answer directly above the decimal in the dividend. Even if you routinely use a calculator, practicing division problems with pen and paper will sharpen your skills, making you more likely to realize your mistake if you punch in a wrong number or put a decimal point in the wrong place. Being able to divide decimal numbers is an important skill in dealing with business finance, productivity, and other areas. When you can do the math, you can perform analyses and solve problems that improve performance profits—and make yourself a more valuable member of the workforce.
We shall learn about percentages in the next section:-
Business Maths Part II: Learning Percentages