# Place value

##### Intros

##### Examples

###### Lessons

- Write the value of the 5 in each number.
- Write each number in words.
- Margaret is starting a quilting project. She measured the lengths of her square pieces of fabric in cm. Write the given lengths in expanded form.

##### Practice

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###### Topic Notes

## What is the place value?

Place values are part of system where the position of a number can show us its value. The most common place value system is the decimal system, which has a base of ten. The decimal system is the system that you most commonly use in your everyday life.

In the decimal system, each position has a value that is a power of ten. Moving left or right on the system either moves a number up a non-negative power of 10 or down a negative power of 10 respectively. A decimal is used to separate the non-negatives and the negatives for numbers in the decimal system.

## How to find place value

Let's try some examples to figure out how to determine a number's value place.

**Question 1: **Write the value of 5 in the following number

6530

**Answer: **

All of the numbers in this number are on the non-negative side of the decimal system. Imagine a decimal placed behind the number (6530.) and you can correctly see how many positions to the left in the decimal system these non-negative powers of tens numbers are situated. You can find their decimal place value.

The lowest place value in this number is the 0 since it's at the far right of the number. This 0 is in the ones position since it is one digit before the decimal point. In other words, we have 0 ones in this number (0 x 1 = 0). The number 3 is in our tens position, meaning we have 3 tens in this number (3 x 10 = 30). We have the number 5 in the hundreds position (3 digits over to the left from the decimal). This can be written as 5 x 100 = 500.

Therefore, we've found that the value of 5 is 500.

**Question 2: **Write the value of 5 in the following number

53,694

**Answer: **

The lowest place value is 4, and being right before the decimal, it means we have 4 ones in this number. We can write this as 4 x 1, giving us 4. The 9 is in the tens position, and we have 9 tens in this number. Its value is 9 x 10, giving us 90. The number 6 is in our hundreds position, meaning we have 6 hundreds (6 x 100 = 600). Then we have 3 in our thousands position, which is 3 x 1000 = 3000.

Now we finally reach the 5. 5 in this number has the highest place value. The 5 is in the ten thousands position. 5 x 10,000 = 50,000. Therefore, the value of 5 is 50,000.

**Question 3: **Write the value of 5 in the following number

287,698,015

**Answer: **

Luckily for us, the place value of 5 in this number is in the lowest place value. Once again, by placing that imaginary decimal at the end of this number since all the place values are non-negative powers of 10, we can solve this problem. The 5 is one position over to the decimal, meaning it's in the ones position. This gives us the answer that there are 5 ones in this answer, and since that's 5 x 1, the answer for the value of 5 is 5.

**Question 4: **Write the value of 5 in the following number

2.5

**Answer: **

In this number, when we look to the right of the decimal point, the first digit that comes after the decimal is tenths. What is the value of 5 in this case? Since it's the first digit after the decimal, 5 is in the tenths position. In other words, we have 5 tenths which can be written as 5 x 0.1, giving us a final answer of 0.5. The 0.1 stands for tenths.

If you wanted to take a further look into place and place value, try inputting a number here and it can tell you what place value is!

###### Related Concepts

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