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Expanded Notation Decimals

A number can be expressed in the expanding notation to emphasize the place value for each digit. Depending upon the place value we can write the expanded form of decimal form of numbers. Decimal notation is a way of expressing numbers in any base-10 system. Expanded notation, in mathematics, is used to show the value of each digit of a number. Decimal place values are represented with decimals 0.1, 0.01, 0.001 and so on.


Expanded Notation Decimals

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Expanded Notation with Decimals

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As we convert from denominate numbers to expanded notation, the focus shifts to a different way of expressing place value. Let us see with the help of example how to wrote whole numbers and decimals using place value and expanded notation.

Whole number

Decimal number

Place value of decimal

Ten thousands

thousands

hundreds

tens

ones

Decimal point

tenths

hundredths

thousandths

Ten thousandths

Hundred thousandths

Number

4

6

9

2

7

.


0

3

8

9

4


Hence, given number 46927.03894 can be written in expanded notation as follows:

46927.03894 = (4 × 10,000) + (6 × 1000) + (9 × 100) + (2 × 10) + (7 x 1) + (0 × $\frac{1}{10}$) + (3× $\frac{1}{100}$) + (8× $\frac{1}{1000}$) + (9× $\frac{1}{10000}$) + (4× $\frac{1}{100000}$)

Examples of Expanded Decimals

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Below are the examples on expanded notation with decimals:

Solved Examples

Question 1: Write the expanded notation with decimals 9685.5183
Solution:
(9 x 1000) + (6 x 100) + (8 x 10) + (5 x 1) + (5 x 0.1) + (1 x 0.01) + (8 x 0.001) + (3 x 0.0001)

Question 2: Write the expanded notation of 563.31
Solution:
(5 x 100) + (6 x 10) + (3 x 1) + (3 x 0.1) + (1 x 0.01)

Question 3: Write the expanded notation of 59.795
Solution:
(5 x 10) + (5 x 1) + (3 x 0.1) + (9 x 0.01) + (5 x 0.001)

Question 4: Write the expanded notation of 5390.778
Solution:
(5× 1000) + (3 x 100) + (9 x 10) + (0 x 1) + (7 x 0.1) + (7 x 0.01) + (8 x 0.001)

Expanded Notation Decimals Practice Problems

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Practice Problems

Question 1: Write the expanded notation with decimals 834.84
Question 2: Write the expanded notation with decimals 976.782
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