Tenths and Hundredths as Decimals

In the world of mathematics, decimals are another way of representing fractions. This concept is very important in our daily lives, helping us understand things like money, measurements, and much more. In this detailed guide, we will explore how to convert tenths and hundredths to decimal numbers.

Understanding decimals

Before moving on to tenths and hundredths, let's first understand what a decimal is. A decimal is a number that has a whole number part and a fractional part separated by a decimal point. For example:

    3.5
    12.72
    0.08

Here 3.5 is a decimal number where 3 is the whole number and .5 is the fractional part. Similarly in 12.72 12 is the whole number and .72 is the fractional part.

Decimals as decimals

Let's start with tenths. When a whole is divided into ten equal parts, each part is called a tenth. We write tenths as decimals by placing one digit after the decimal point. Here are some examples:

    1 decimal = 0.1
    2 tenths = 0.2
    5 tenths = 0.5
    9 tenths = 0.9

In each example, the number after the decimal point represents the number of tenths. Let's understand this visually:

The above visualization shows a rectangle divided into ten equal parts. One part is filled in, representing 0.1 or 1/10.

Hundredths as a decimal

Now learn about hundredths. When a whole is divided into one hundred equal parts, each part is called a hundredth part. We write hundredths as decimals by placing two digits after the decimal point. Here are some examples:

    1 hundredth = 0.01
    25 hundredths = 0.25
    50 hundreds = 0.50
    75 hundreds = 0.75

Each example shows how the hundredths appear as a decimal, with two digits after the decimal point. Check out this visual example:

In the above visualization, the rectangle is divided into one hundred equal parts, and only a small portion is filled, representing 0.01 or 1/100.

Converting fractions to decimals

Now that we understand tenths and hundredths, let's learn how to convert fractions to decimals.

Example 1: Converting 1/10

To convert 1/10 to a decimal, divide the numerator by the denominator:

    1 ÷ 10 = 0.1

Example 2: Converting 1/4

For a fraction like 1/4, it's a little different. Since the denominator is 4, which isn't 10 or 100, you multiply the two parts to get 100:

    (1 × 25) / (4 × 25) = 25/100 = 0.25

The fraction 1/4 is converted to 25 hundredths, or 0.25.

Practical applications of tenths and hundredths

Decimals are especially useful in real life. Let's take a look at some practical applications:

Wealth

Money is usually divided into whole units and fractions. For example, if you have 3 dollars and 50 cents, you can say that you have a total of 3.50. Here, 0.50 represents fifty hundredths or 50/100.

Measurement

Decimals are often used in measurements such as length, weight, and volume. For example, the length of a pencil might be 7.6 cm, where 0.6 represents six-tenths of a centimeter.

Sports scores

Decimals show exact numbers, such as times in a race. A runner might complete a course in 9.81 seconds, which indicates that he or she completes the course in nine seconds and eighty-one hundredths of a second.

Exercises and drills

For a better understanding, let's solve some exercises:

Exercise 1

Write 6/10 as a decimal:

    6 ÷ 10 = 0.6

Exercise 2

Convert 3/100 to decimal:

    3 ÷ 100 = 0.03

These exercises show how to express fractions and hundredths as decimals.

Conclusion

Understanding tenths and hundredths as decimals is a foundational skill in math that leads to more complex concepts in the future. With practice, these conversions become intuitive, making decimals an essential part of mathematical literacy.

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