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Place values

Topic Notes
Why is the number 6 so scared? Because 7 ate 9! In this section, we will be learning how to determine the value of digits in whole and decimal numbers. We will do this by figuring out the place, or position, of a digit in a number using the place value system. Each place, or position, in the place value system has a value of 10 times the place to its right. In this section, we will show the value of each digit in a number by expressing the number in words and by writing the number in expanded form.

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!

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