### Maths Expanded Form

##### Expanded Form

The expanded form of a number is the sum of the place values of each digit in the number. For example, the expanded form of 345 is 300 + 40 + 5.

##### How to Write a Number in Expanded Form

To write a number in expanded form, follow these steps:

- Start with the leftmost digit in the number.
- Multiply this digit by the place value of its position.
- Write the product of this multiplication.
- Move to the next digit to the right and repeat steps 2 and 3.
- Continue until you have written all the digits in the number.

##### Examples of Expanded Form

Here are some examples of numbers written in expanded form:

- 345 = 300 + 40 + 5
- 1,234 = 1,000 + 200 + 30 + 4
- 10,001 = 10,000 + 1

##### Uses of Expanded Form

Expanded form is used for a variety of purposes, including:

- Teaching place value
- Adding and subtracting large numbers
- Multiplying and dividing large numbers
- Converting between different number systems

Expanded form is a useful way to represent numbers. It can be used for a variety of purposes, including teaching place value, adding and subtracting large numbers, multiplying and dividing large numbers, and converting between different number systems.

##### Writing Numbers in Expanded Form

Expanded form is a way of writing numbers that shows the value of each digit in the number. For example, the number 123 can be written in expanded form as 100 + 20 + 3.

##### Steps to Write a Number in Expanded Form

- Start with the leftmost digit in the number.
- Write the digit followed by a zero and the place value of the digit.
- Repeat steps 1 and 2 for each digit in the number.
- Add the numbers together to get the expanded form of the number.

##### Examples of Numbers Written in Expanded Form

- 123 = 100 + 20 + 3
- 456 = 400 + 50 + 6
- 789 = 700 + 80 + 9
- 1,234 = 1,000 + 200 + 30 + 4
- 5,678 = 5,000 + 600 + 70 + 8

##### Benefits of Writing Numbers in Expanded Form

Writing numbers in expanded form can be helpful for understanding the place value of each digit in a number. It can also be helpful for adding and subtracting numbers.

For example, if you want to add the numbers 123 and 456, you can first write them in expanded form:

- 123 = 100 + 20 + 3
- 456 = 400 + 50 + 6

Then, you can add the numbers in each column:

- 100 + 400 = 500
- 20 + 50 = 70
- 3 + 6 = 9

The sum of the two numbers is 579.

Writing numbers in expanded form can be a helpful way to understand the place value of each digit in a number. It can also be helpful for adding and subtracting numbers.

##### Expanded Form Examples

The expanded form of a number is the sum of the place values of each digit in the number. For example, the expanded form of 123 is 100 + 20 + 3.

Here are some more examples of expanded form:

**456**= 400 + 50 + 6**789**= 700 + 80 + 9**1,234**= 1,000 + 200 + 30 + 4**5,678**= 5,000 + 600 + 70 + 8**10,000**= 10,000 + 0 + 0 + 0

##### How to Write a Number in Expanded Form

To write a number in expanded form, follow these steps:

- Start with the leftmost digit in the number.
- Write the digit followed by a zero and the place value of the digit.
- Repeat steps 1 and 2 for each digit in the number.
- Add the terms together to get the expanded form of the number.

For example, to write 123 in expanded form, we would follow these steps:

- Start with the leftmost digit, which is 1.
- Write 1 followed by a zero and the place value of the digit, which is hundreds.
- Repeat steps 1 and 2 for the remaining digits, which are 2 and 3.
- Add the terms together to get the expanded form of 123, which is 100 + 20 + 3.

##### Uses of Expanded Form

Expanded form is a useful way to represent numbers because it shows the place value of each digit. This can be helpful for understanding how numbers work and for performing operations on numbers.

For example, expanded form can be used to add and subtract numbers. To add two numbers in expanded form, simply add the terms that have the same place value. For example, to add 123 and 456, we would add 100 + 400, 20 + 50, and 3 + 6. This gives us 500 + 70 + 9, which is 579.

Expanded form can also be used to subtract numbers. To subtract two numbers in expanded form, simply subtract the terms that have the same place value. For example, to subtract 456 from 123, we would subtract 400 from 100, 50 from 20, and 6 from 3. This gives us 600 - 30 - 3, which is 567.

Expanded form is a useful way to represent numbers because it shows the place value of each digit. This can be helpful for understanding how numbers work and for performing operations on numbers.

##### Expanded Form of Numbers with Decimals

The expanded form of a number with decimals represents the number as a sum of its individual place values. It provides a detailed breakdown of the number’s composition, making it easier to understand and compare numbers.

##### Understanding Expanded Form

Consider the number 345.678. Its expanded form can be written as:

345.678 = 300 + 40 + 5 + 0.6 + 0.07 + 0.008

In this expanded form:

- 300 represents the hundreds place.
- 40 represents the tens place.
- 5 represents the ones place.
- 0.6 represents the tenths place.
- 0.07 represents the hundredths place.
- 0.008 represents the thousandths place.

##### Expanded Form with Decimals

When working with decimals, the expanded form includes place values to the right of the decimal point. These place values are powers of 10, with each place value being 1/10th of the previous one.

For example, the expanded form of 23.456 can be written as:

23.456 = 20 + 3 + 0.4 + 0.05 + 0.006

In this expanded form:

- 20 represents the tens place.
- 3 represents the ones place.
- 0.4 represents the tenths place.
- 0.05 represents the hundredths place.
- 0.006 represents the thousandths place.

##### Benefits of Expanded Form

The expanded form of numbers with decimals offers several benefits:

**Clarity:**It provides a clear and detailed representation of a number, making it easier to understand its composition.**Comparison:**Expanded form allows for easy comparison of numbers, especially when they have decimals.**Estimation:**It helps in estimating values and performing mental calculations.**Rounding:**Expanded form simplifies rounding numbers to a specific place value.**Place Value Understanding:**It reinforces the concept of place value and helps students develop a strong understanding of the decimal number system.

The expanded form of numbers with decimals is a valuable tool for representing and understanding numbers. It provides a detailed breakdown of the number’s composition, making it easier to compare, estimate, and round numbers. By understanding the expanded form, individuals can develop a strong grasp of the decimal number system and perform mathematical operations with greater accuracy and confidence.

##### Expanded Form with powers of 10

The expanded form of a number with powers of 10 is a way of writing the number as a sum of its individual digits, each multiplied by a power of 10.

##### How to Write a Number in Expanded Form with Powers of 10

To write a number in expanded form with powers of 10, follow these steps:

**Identify the place value of each digit in the number.**The place value of a digit tells you how many times 10 it is worth. For example, the digit 3 in the number 345 is in the hundreds place, so it is worth 300.**Write each digit as a product of its place value and a power of 10.**For example, the digit 3 in the number 345 would be written as 3 × 100.**Add the products of all the digits to get the expanded form of the number.**For example, the expanded form of the number 345 would be 3 × 100 + 4 × 10 + 5 × 1.

##### Examples of Expanded Form with Powers of 10

Here are some examples of numbers written in expanded form with powers of 10:

**2345**= 2 × 1000 + 3 × 100 + 4 × 10 + 5 × 1**12,345**= 1 × 10,000 + 2 × 1000 + 3 × 100 + 4 × 10 + 5 × 1**123,456**= 1 × 100,000 + 2 × 10,000 + 3 × 1000 + 4 × 100 + 5 × 10 + 6 × 1

##### Uses of Expanded Form with Powers of 10

Expanded form with powers of 10 is useful for a variety of purposes, including:

**Comparing numbers.**Expanded form can make it easier to compare numbers by showing how many times 10 each number is worth. For example, the number 345 is greater than the number 234 because 345 is worth 300 + 40 + 5, while 234 is worth 200 + 30 + 4.**Rounding numbers.**Expanded form can be used to round numbers to a specified place value. For example, the number 345 rounded to the nearest ten is 350, because 345 is closer to 350 than it is to 340.**Estimating calculations.**Expanded form can be used to estimate the results of calculations. For example, the product of 345 and 234 can be estimated by multiplying the expanded forms of the two numbers: (3 × 100 + 4 × 10 + 5 × 1) × (2 × 100 + 3 × 10 + 4 × 1) = 6 × 10,000 + 15 × 1000 + 42 × 100 + 60 × 10 + 20 × 1 = 80,420.

Expanded form with powers of 10 is a useful way to represent numbers and perform calculations. It can be used to compare numbers, round numbers, and estimate calculations.

##### Expanded Form Solved Examples

The expanded form of a number is the sum of the place values of each digit in the number. For example, the expanded form of 123 is 100 + 20 + 3.

**Example 1:**

**Problem:** Write the expanded form of 456.

**Solution:**

456 = 400 + 50 + 6

**Example 2:**

**Problem:** Write the expanded form of 7,890.

**Solution:**

7,890 = 7,000 + 800 + 90

**Example 3:**

**Problem:** Write the expanded form of 123,456.

**Solution:**

123,456 = 100,000 + 20,000 + 3,000 + 400 + 50 + 6

**Example 4:**

**Problem:** Write the expanded form of 9,876,543,210.

**Solution:**

9,876,543,210 = 9,000,000,000 + 800,000,000 + 70,000,000 + 6,000,000 + 500,000 + 40,000 + 3,000 + 200 + 10

**Example 5:**

**Problem:** Write the expanded form of 0.123.

**Solution:**

0.123 = 0.1 + 0.02 + 0.003

**Example 6:**

**Problem:** Write the expanded form of 0.000456.

**Solution:**

0.000456 = 0.0004 + 0.00005 + 0.000006

##### Expanded Form FAQs

**What is the expanded form of a number?**

The expanded form of a number is a way of writing a number by adding the values of each digit separately. For example, the expanded form of 123 is 100 + 20 + 3.

**Why is the expanded form of a number useful?**

The expanded form of a number can be useful for understanding the place value of each digit in a number. It can also be helpful for adding and subtracting large numbers.

**How do you write a number in expanded form?**

To write a number in expanded form, start by writing the number in standard form. Then, add the values of each digit separately. For example, to write 123 in expanded form, you would write 100 + 20 + 3.

**What are some common mistakes people make when writing numbers in expanded form?**

One common mistake people make when writing numbers in expanded form is to forget to add the values of the digits in the ones place. For example, when writing 123 in expanded form, some people might write 100 + 20, which is incorrect.

Another common mistake people make is to add the values of the digits in the wrong order. For example, when writing 123 in expanded form, some people might write 3 + 20 + 100, which is also incorrect.

**How can I avoid making mistakes when writing numbers in expanded form?**

To avoid making mistakes when writing numbers in expanded form, be sure to:

- Add the values of the digits in the ones place first.
- Add the values of the digits in the tens place next.
- Add the values of the digits in the hundreds place last.

You can also use a place value chart to help you write numbers in expanded form. A place value chart shows the value of each digit in a number.

**Here are some additional tips for writing numbers in expanded form:**

- Use parentheses to group the digits in each place value. For example, you could write 123 in expanded form as (100) + (20) + (3).
- Use commas to separate the digits in each place value. For example, you could write 123 in expanded form as 100, 20, 3.
- Use exponents to write large numbers in expanded form. For example, you could write 1,000,000 in expanded form as 1 x $10^6$.