Decimals In Daily Life

Decimals are a shorthand way to write fractions and mixed numbers with denominators that are powers of 10, like 10, 100, 1000, 10000, etc. If a number has a decimal point, then the first digit to the right of the decimal point indicates the number of tenths. For example, if we take a number like 643.125, it can be expressed as:

If we start from the left-hand side, 6 hundred, 4 tens, 3 units, 0.1 tenths, 0.02 hundredths, and 5 thousandths place. Apart from this, students should be able to:

• Read and write decimals accurately, 

• Move between the written, spoken, and symbolic forms of decimals,

• Understand the role of the decimal point and the relationship among tenths, hundredths, and thousandths.

Types of Decimal Numbers

1. Terminating Decimal Numbers:

The terminating decimal numbers have a finite number of digits just after the decimal point.

For example, 12.30000 can be written as 12.30 or 12.3 as 0 is repeated many times. Such decimals are termed terminating decimals.  

2. Non-terminating Decimal Numbers:

These decimals are also called non-repeating decimals as these numbers are not repeated.

For example, 234.6574 in which numbers after decimals are not repeated. These types of decimals are called irrational numbers and they cannot be written in fraction form.

3. Recurring Decimal Numbers:

Recurring decimals are those decimals in which two or more numbers are repeated in a particular pattern or at repeated intervals. For example, 234.4545645456 in which the numbers like 4, 5, and 6 are repeated in a pattern. Hence, such kinds of decimals are called as recurring or repeated decimals.

4. Non-recurring Decimal Numbers:

These decimals are termed as non-terminating decimals as these decimals' value does not repeat. For example, 23.5467.

What are Decimal Numbers?

A decimal is any number from the base-ten number framework. In this unit, we'll be explicitly focusing on the numbers that have at least one digits to the directly of the point. The decimal point helps in isolating the ones spot from the tenths spot in the number.

In cash, the fact of the matter is utilised to isolate dollars from pennies. When we move directly to the point, each number spot is isolated by 10. Along these lines, presently we'll express the number.

5749100

In the decimal structure and the extended structure, the number is 5749100.

Initially, we should compose the blended number in the extended structure = (5 x 10) + (7 x 1) + (4 × 110) + (9 × 571100).

Subsequently, the decimal type of this number is '57.49'. It is extremely certain that the composition of the number in a decimal structure is essentially less demanding. Presently, we'll compose this number in the spot esteem outline to give you a superior comprehension of how the decimals work.

Let’s start with an example.

Order the numbers underneath from least to most prominent: 58, 57, and 5749100. As you definitely realise that, 5749100 is a mixed number. It includes a fraction and a whole number. Presently, let us utilise the place value that will enable you to think about these numbers. in this way,

57 = (5 × 10) + (7 × 1)

5749100 = (5 × 10) + (7 × 1) + (4 × 110) + (9 × 1100 )

58 = (5 × 10) + (8 × 1)

Answer: Ordering these numbers from least to most prominent, we get 57, 5749100, and 58. In any case, that resembles a great deal of composing! Things being what they are, what do we do now? So as to keep away from this circumstance, we can utilise decimals to compose, 5749100.

Value and Decimals 

When you move directly in this spot value chart, each number is divided by 10. For example, thousands are divided by 10 to give you hundreds. This likewise stands valid for the digits that are on the directly of the decimal point. For example, tenths, when divided by 10, give you hundredths. In any case, remember that when you read the decimals, the decimal point must be read as "and”.

Along these lines, if the decimal number is 57.49, it is read as "fifty-seven and forty-nine hundredths." However, in everyday life, we read the decimal point as "point" and not "and". Along these lines, the decimal number 57.49 is perused as "fifty-seven point four nine." However, this utilisation isn't scientifically right. How about we comprehend this with an example.

Write each phrase as a fraction as well as a decimal number

How Long can a Decimal be? 

A figure can have any number of decimal spots to the directly of the point. Presently, we'll clarify this with the assistance of a case of the numerical value of Pi. We have abbreviated it to 50 decimal digits. Let’s take a look.

Pi = 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510

Decimal Digits 

In the event that the number is 1.0897, at that point the digits, 0, 8, 9 and 7 are the decimal digits. In this way, the digits that are on the directly of the point are known as the decimal digits.

Use of Decimals in Our Daily Lives 

Clearly, every typical person has ten fingers. Since we have ten fingers, our numbering depends on products of ten which is called decimal. Would you be able to envision how life would be unique if every person were brought into the world with eight fingers and not ten? Perhaps our numbering framework would be founded on products of eight. A numbering framework dependent on eight exists and is called octal. Octal numbering is used in the background in PC frameworks.

Yet, obviously, in regular day-to-day existence, we use decimal numbers. The possibility of decimal numbering comes to us from the old civic establishments regardless we use the numbering dependent on tens from the Romans. The Roman numeral for ten is X and 20 is XX or multiple times 10. Regardless you see Roman numerals in dates on structures and motion pictures and every year the Super Bowl gets the following Roman number.

Our decimal numbering, utilising Arabic numerals and not Roman numerals, additionally uses products of 10, so 40 implies multiple times 10. In any case, you definitely realise that! The other intriguing piece of decimals is the way decimals are utilised to speak about portions. Route, in 1616, a Scottish mathematician named John Napier, recommended that decimal numbering could be used to show parts and he included the decimal point. Numbers to one side of the decimal point would represent entire numbers and numbers on the other side would show the fragmentary part.

So, the number 1 would be 1.5 in decimal. Hold up a moment, how could we get a 5 for? Since we're utilising 10 as the base of decimal, half of 10 meets 5. So also, the division winds up 0.25 and ends up 0.75. The image is somewhat more confounded when you take a gander at 1/3. In the event that you isolate 1 by 3 on your adding machine, you get the decimal esteem 0.333 with three filling the screen. That is on the grounds that there is anything but a total identical decimal number for 1/3. You need to see what number of digits to the directly of the decimal point, called the exactness of the decimal number, to use.

Researchers and specialists use decimal numbers all the time in counts. When you ponder propelled science themes in secondary school, you will realise why the exactness of a decimal number is so vital in figuring.

For you however decimals are simpler to use in number juggling tasks than divisions are. Consider multiplying 1 by 6. It's simpler to increase 1.75 by 6.5! Truth be told, consider your adding machine. You never see divisions on a mini-computer. When you do calculations on the adding machine, you generally use decimal numbers.

We use decimals consistently while managing cash, weight, length, and so forth. Decimal numbers are utilised in circumstances where more exactness is required than the entire numbers can give. For instance, when we compute our load on the gauging machine, we don't generally discover the load equal to an entire number on the scale. So as to know our correct weight, we should comprehend what the decimal incentive on the scale implies. This segment manages the idea of decimals in three vital fields of our day to day life.

• Use of decimal to represent money

Cash, cash, cash! There are 100 pennies in a dollar and a half dollar is 50 pennies or .50. Each time you purchase a thing and make change, you are working with decimals. Have you at any point seen what number of costs end in .98 or .99? That is so you believe that the thing costs short of what it does. For instance, which appears less cash 1.99 or 2?

Obviously, 1.99 dollar is less cash by a penny yet when organisations endeavour to motivate you to purchase something, that penny has any kind of effect since you think about what is to one side of the decimal to be progressively essential. So, you will contrast 1 and 2 and that appears to be a major distinction.

Managing decimal numbers is unavoidable when managing cash. As a rule, when we need to change over paisa into rupee. Assume we go to a neighbourhood shop to buy 500 gm of turmeric, where, one kg of turmeric costs Rs 51. All in all, what amount of cash would it be a good idea for us to hand over to the businessperson? We isolate Rs 51 by 2 which are equal to 25.5. So as to hand over the definite sum, we should comprehend what 25.5 methods of rupees are. Give us a chance to become familiar with this with the help of a basic example.

Example 1: Converting 165 paisa to Rs.

As we know, 1 paisa = 1/100 Rs

So, 165 paisa = Rs 165*1/100 = Rs 165/100 = Rs 1.65

Example 2: Converting 450 paisa to Rs.

As we know, 1 paisa = Rs 1/100

So, 450 paisa = 450*1/100 = Rs 450/100 = Rs 4.50 = Rs 4 and 50 paisa.

• Use of decimal to represent the length

While estimating the length of a thing, it isn't fundamental that the length of an item is several of the given graduations. For instance, while estimating the length of a table with a meter scale, the length may not be an entire number; it might lie between two graduations on the meter scale. In such circumstances, decimal numbers are utilized. 

Investigate the vehicle's odometer; the miles on it is constantly seemed decimal too. Talking about vehicles and mileage, have your people anytime utilized MapQuest to get headings? All mileage in this standard course seems decimal too.

From the conversion of units, we know

1 km = 100 m 

1 m = 100 cm 

1 cm = 10 mm

Presently, let the length of the table best be 2 m and 75 cm, and after that, it tends to be spoken to as (2+ 75/100) m.

Example 3: Converting 276 cm into metres.

As we probably are aware, 100 cm = 1 m

Along these lines, 1 cm = 1/100 m

276 cm = 276 * 1/100 m = 276/100 m = 2.76 m

• Use of decimal to speak to weight

We use decimal numbers while managing weight. For instance, when we are purchasing a watermelon, it can't generally say something entire numbers, it very well may be under 2 kg however more than 1kg. In such circumstances, the retailer needs to compute the amount to charge for a watermelon, in light of its weight. As we probably are aware,

1 kg = 1000 gm 

1 gm = 1000 mg

Presently assume that it is 1kg and 750 gm. At that point, he will charge according to the cost of 1kg + (750/1000) kg of the watermelon. We will become familiar with the transformation of load into decimal in the accompanying precedents:

Example 4: Converting 250 gm to kg.

As we probably are aware, 1000 gm = 1 kg.

In this way, 1 gm = 1/1000 kg.

250 gm = 250 * 1/1000 kg = 250/1000 kg = 0.250 kg

Numerous people use decimals consistently when they manage cash. Decimals are likewise usually found on gas siphons and on a vehicle's odometer. Every one of these employments of decimals is an approach to prove a small amount of an entire unit, such as, a dollar or gallon of fuel.

Each time somebody purchases a thing and makes a change, they are working with decimals. Moreover, many stores value things at 1.99, or comparative, in light of the fact that 1.99 appears less cash than $2. This is on the grounds that people think about the number on the left half of the decimal to be increasingly imperative.

Decimal numbering, which is numbering dependent on sets of 10, originated from antiquated human advancements, such as, the Romans'. Today Arabic numerals are more normally used than Roman numerals, yet regardless they use decimal numbering. In 1616, John Napier, a Scottish mathematician, proposed that decimal numbering could be used to speak to portions if a decimal point was included. Numbers on the left half of the point would be entire numbers, and those on the privilege would show the part. To figure out what decimal numbers speak to the part, the best number of the part is isolated by the base number. This implies one-half winds up 0.5, and one-quarter ends up 0.25.

Properties of Decimals

Important properties of decimal numbers under multiplication and division operations are as follows:

• If any two decimal numbers are multiplied in any order, the product remains the same.

• If a whole number and a decimal number are multiplied in any order, the product remains the same.

• If a decimal fraction is multiplied by 1, the product is the decimal fraction itself.

• If a decimal fraction is multiplied by 0, the product is zero (0).

• If a decimal number is divided by 1, the quotient is the same decimal number.

• If a decimal number is divided by the same number, the quotient is 1. 

• If 0 is divided by any decimal, the quotient is 0, not exist.

• The division of a decimal number by 0 is not possible, as the reciprocal of 0 does exist.