Reading and Writing Decimals

Introduction to decimals

Decimals are a way of representing numbers that are not whole. They use a point, known as a decimal point, that separates the whole number from the fractional part. Decimals are essential to understand because they are used daily in various aspects of life, such as in money, measurements, and scientific data.

Decimal point

A decimal point is a point or period that separates the whole number part of a number from the fractional part. For example, in the number 12.34, "12" is the whole number, and "34" is the fractional part.

Place value in decimal

Just like whole numbers, decimals also have place values that help us determine the value of each digit in a number. Place value tells us what each digit represents, depending on its place in the number. Here are the place values of decimals:

whole number division decimal fraction division
hundreds tens units | tenths hundredths thousandths
1 2 3 | 4 5 6
|<--3---|<--2-| <--|---0.4------|

For example, in the number 123.456:

• 1 is in the hundreds place (100).
• 2 is in the tens place (10s).
• 3 is in the ones place (1s).
• 4 is in the tenths place (0.1).
• 5 is in the hundredths place (0.01).
• 6 is in the thousandths place (0.001).

Reading decimals

Decimals can be easier to read if we follow the place value system. Let's start with some simple examples:

• 0.3 is read as "three tenths".
• 0.45 is read "forty-five hundredths".
• 2.76 is read "two and seventy-six hundredths."

When reading a decimal, the part before the decimal point is read as a whole number, while the part after the decimal point is read as its place value. Here's a more complex example:

• 45.678 is read "forty-five and six hundred seventy-eight thousandths".

Writing decimals

Writing decimals involves placing the decimal digits according to their place values. Suppose you need to write the number "five and three hundred twenty one thousandths."

• First, write the whole number part before the decimal point: 5.
• Next, decide the digits that come after the decimal point: 321.
• Place these digits into their correct place values as shown: 5.321.

Another example: Write "two hundred seventeen and four hundred nine thousandth."

• The complete number is 217.
• The fractional part is "four hundred nine thousandths": 409.
• Combine and write: 217.409.

Comparing decimals

Decimals are compared digit by digit from left to right. If the decimal parts are equal, compare as whole numbers. Let's look at some examples:

• Compare 3.67 and 3.672. Here, 3.67 is less than 3.672 because 670 is less than 672.
• Consider 1.234 and 1.23. Here, 1.234 is larger than 1.23, even though the first few digits are the same, because an extra digit makes it larger.

Viewing decimals

Decimals can be visualised using models or number lines to understand their size and the space they occupy. Let's use a number line to visualise some decimals:

In this view, the number line displays values from 0 to 4. Decimals, such as 1.5, lie between 1 and 2.

Uses of decimals in real life

Decimals are used everywhere in real life around us. Here are some examples:

• Money: Dollars and cents use decimals. If something costs $2.75, that means 2 dollars and 75 cents.
• Measurement: In the metric system, decimals are used to measure length, weight, or volume. For example, 1.5 meters is halfway between 1 meter and 2 meters.
• Sports: In racing, times may be measured to the nearest hundredth of a second, such as 9.87 seconds in a sprint.

Practice problems

To get more comfortable with decimals, let's practice some problems.

Problem 1

Write the following in decimal form: "Seven and twenty-three hundredths."

Solution: 7.23 is the decimal form.

Problem 2

Which is greater: 0.8 or 0.75?

Solution: 0.8 is greater than 0.75.

Problem 3

Compare and arrange in descending order: 3.5, 3.15, 3.51.

Solution: The descending order is 3.51, 3.5, 3.15.

Problem 4

Which decimal lies between 1 and 2 on the number line?

Solution: 1.5 lies between 1 and 2.

Conclusion

Reading and writing decimals may seem difficult at first, but with practice, it becomes more accessible. Understanding decimals is important in dealing with many real-world scenarios that involve numbers that are not whole, such as money, measurement, and science. Keep practicing, and soon decimals will become second nature!

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