Decimals

Decimals are an important part of math that we use in our everyday lives. They are necessary when we need to describe something that is not a whole number. For example, when we talk about money, we often use decimals. If you have one dollar and fifty cents, you can write it as $1.50, which includes a decimal point.

What is a decimal?

Decimals are a way of writing numbers that include fractions of an integer. A decimal number has an integer part and a fractional part, separated by a point called the decimal point. For example, the number 3.75 has an integer part of 3, and a fractional part of 75.

The decimal point is like a sign that says "Here comes the part of the number that is less than one." Anything to the right of the decimal point represents numbers that are less than one. Here's how we can divide 3.75 into its parts:

Whole Number Division : 3
decimal point : .
Fractional part : 75

Place value in decimal

In decimals, the position of each number is very important, just like in whole numbers. This is how it works:

hundreds tens units tens hundredths thousandths
100 10 1 . 0.1 0.01 0.001

For the number 45.678, we can match each digit with its place value:

tens units tenths hundreds thousandths
4 5. 6 7 8

• 4 is in the tens place, so it represents 40.
• 5 is in units place, so it represents 5.
• 6 is in the tenths place, so it represents 0.6.
• 7 is in the hundredths place, which means 0.07.
• 8 is in the thousandth place, that is, 0.008.

Viewing decimals

Let's imagine a simple decimal number, such as 0.5. Imagine a pie that is divided into 10 equal parts (tenths). 0.5 looks like this:

Here, 5 out of 10 pieces are shaded grey, which represents 0.5.

Decimal addition

Adding decimals is very similar to adding whole numbers. The most important thing is to line up the decimal points. For example, if you want to add 2.5 and 3.75, it would look like this:

2.50
+ 3.75
,
6.25

You start adding from the digit farthest to the right and move to the left, just as with whole numbers.

Decimal subtraction

Subtracting decimals also requires lining up the decimal points. Let's look at an example where we subtract 1.4 from 5.2:

5.2
- 1.4
,
3.8

Notice how we line up the digits according to the decimal point before subtracting.

Decimal multiplication

When multiplying decimals, the numbers are first multiplied as normal without taking into account the decimal points. Finally, the decimal is placed in the result. Here is an example with 0.3 x 0.2:

Multiply as usual: 3 x 2 = 6
Decimal places for total count: 2 (0.3 and 0.2 have one decimal place each)
Place a decimal place: 0.06

Now let's look at what happens when you multiply a whole number by a decimal, such as 4 x 0.5:

Multiply as usual: 4 x 5 = 20
Decimal places: 1 (0.5 has one decimal place)
Place decimal place: 2.0

Decimal division

The principle of division with decimals is the same as for division with whole numbers:

Consider dividing 0.8 by 4:

Convert to whole numbers: 8 ÷ 4 = 2
Since you moved the decimal point forward one place for the numerator, do the same for the result: 0.2

Let's try dividing a large decimal number, such as 6.3, by 3:

Perform the division as usual: 63 ÷ 3 = 21
Adjust for decimal places: Since the original number had one decimal place, the result will be 2.1

Uses of decimals in daily life

Decimals are used everywhere in everyday life. Here are some examples of when decimals are used:

• Money: Money is usually represented through decimals. For example, $4.25 represents four dollars and twenty-five cents.
• Measurement: Distances are often measured in decimal metres or centimetres. For example, something might measure 1.75 metres.
• Time: Time can be represented using decimals. For example, 1.5 hours is equivalent to 1 hour and 30 minutes.
• Weight: Weights in grocery items are often expressed in decimals, such as 2.5 kilograms.

As you can see, decimal numbers are an important part of understanding, calculating, and expressing quantities in many aspects of daily life.

Conclusion

Decimals are interesting, versatile, and very useful. They take us beyond whole numbers and allow us to describe fractions of a whole using a position-based system that is clear and easy to use. When learning about decimals, it's important to remember to focus on the location of the decimal point. Understanding the difference in place value will make adding, subtracting, multiplying, and dividing decimals much easier and ensure accuracy. The more you practice, the more this complex system will become second nature!

Comments