Decimals Place Value Worksheet

Understanding Decimals and Place Value

Decimals are a way of expressing fractions in a more compact form. They are used to represent numbers that have a fractional part, which is less than one whole. In this worksheet, we will explore the concept of place value in decimals and provide exercises to help you understand and apply this concept.

What is Place Value in Decimals?

In decimals, each digit has a specific place value, just like in whole numbers. The place value of a digit in a decimal number depends on its position relative to the decimal point. The decimal point is the point that separates the whole part from the fractional part of the number.

Here’s a breakdown of the place values for each digit in a decimal number:

• Tenths: The digit to the right of the decimal point represents tenths.
• Hundredths: The digit to the right of the tenths place represents hundredths.
• Thousandths: The digit to the right of the hundredths place represents thousandths.
• Ten-thousandths: The digit to the right of the thousandths place represents ten-thousandths.

And so on.

Reading and Writing Decimals

When reading decimals, we say the decimal point as “point” or “decimal”. For example, the decimal number 4.56 is read as “four point five six” or “four decimal five six”.

When writing decimals, we use a decimal point to separate the whole part from the fractional part.

Comparing Decimals

To compare decimals, we need to compare the digits in each place value. Here are the steps:

1. Compare the whole part of each number.
2. If the whole parts are equal, compare the tenths place.
3. If the tenths place is equal, compare the hundredths place.
4. Continue this process until you find a difference.

Adding and Subtracting Decimals

To add or subtract decimals, we need to line up the decimal points and perform the operation as usual.

Here’s an example:

Addition

4.56 + 2.34 =?

Line up the decimal points:

4.56

+ 2.34

6.90

Subtraction

4.56 - 2.34 =?

Line up the decimal points:

4.56

- 2.34

2.22

Multiplying Decimals

To multiply decimals, we multiply the numbers as usual and then place the decimal point in the product.

Here’s an example:

4.56 x 2.34 =?

Multiply the numbers:

4.56 x 2 = 9.12 4.56 x 0.3 = 1.368 4.56 x 0.04 = 0.1824

Add up the products:

9.12 + 1.368 + 0.1824 = 10.6704

Round the answer to the correct number of decimal places.

Dividing Decimals

To divide decimals, we divide the numbers as usual and then place the decimal point in the quotient.

Here’s an example:

4.56 ÷ 2.34 =?

Divide the numbers:

4.56 ÷ 2 = 2.28 4.56 ÷ 0.3 = 15.2 4.56 ÷ 0.04 = 114

Find the average of the quotients:

(2.28 + 15.2 + 114) / 3 = 43.82

Round the answer to the correct number of decimal places.

Exercises

Reading and Writing Decimals

1. Write the decimal number 4.56 in words.
2. Read the decimal number 2.34 aloud.
3. Write the decimal number 1.98 in words.

Comparing Decimals

1. Compare the decimals 4.56 and 4.57.
2. Compare the decimals 2.34 and 2.35.
3. Compare the decimals 1.98 and 1.99.

Adding and Subtracting Decimals

1. Add 4.56 and 2.34.
2. Subtract 2.34 from 4.56.
3. Add 1.98 and 0.34.

Multiplying Decimals

1. Multiply 4.56 and 2.34.
2. Multiply 2.34 and 1.98.
3. Multiply 1.98 and 0.34.

Dividing Decimals

1. Divide 4.56 by 2.34.
2. Divide 2.34 by 1.98.
3. Divide 1.98 by 0.34.

Notes

• When adding or subtracting decimals, make sure to line up the decimal points.
• When multiplying decimals, make sure to place the decimal point in the product.
• When dividing decimals, make sure to place the decimal point in the quotient.

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