Place values
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 nonnegative power of 10 or down a negative power of 10 respectively. A decimal is used to separate the nonnegatives 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 nonnegative 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 nonnegative 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 nonnegative 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!
Place values
Related concepts:
 Prime factorization
 Introduction to Exponents
Lessons

1.
Write the value of the 5 in each number.

e)
2.75

2.
Write each number in words.

3.
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.