Powers of ten are the superheroes of math, saving time and lots of space on every page!
Author
Amber Watkins
Published
March 2025
Powers of ten are the superheroes of math, saving time and lots of space on every page!
Author
Amber Watkins
Published
March 2025
Powers of ten are the superheroes of math, saving time and lots of space on every page!
Author
Amber Watkins
Published
March 2025
Key takeaways
Did you know the sun is 93,000,000 miles away from earth? Or that the earth is thought to be 4,500,000,000 years old? Just by seeing all those zeros, you know that’s got to be old.
In math, the powers of 10 come in handy when expressing big numbers like the age of the earth or the distance to the sun. Let’s learn more about the powers of ten and why they are important in math.
By definition, a ‘power’ in math is a number that is multiplied by itself a certain number of times. Therefore, the powers of 10 are how we express 10 multiplied by itself over and over. In fifth grade math, your child will learn the powers of ten along with scientific notation.
The powers of ten are most commonly written in exponential form where 10 is the base (the number being multiplied) and the exponent is how many times the base (in our case, 10) is multiplied by itself. When we write powers of ten with exponents, we read them as “10 to the power of ____” and fill in the blank with the exponent.
For example, 10 to the power of 2 is written as 102 in exponential form. The powers of ten can also be written in expanded and standard form.
Here are the first ten powers of 10:
| 101 = 10 | 101 = 10 |
| 102 = 100 | 102 = 100 |
| 103 = 1,000 | 103 = 1,000 |
| 104 = 10,000 | 104 = 10,000 |
| 105 = 100,000 | 105 = 100,000 |
| 106 = 1,000,000 | 106 = 1,000,000 |
| 107 = 10,000,000 | 107 = 10,000,000 |
| 108 = 100,000,000 | 108 = 100,000,000 |
| 109 = 1,000,000,000 | 109 = 1,000,000,000 |
| 1010 = 10,000,000,000 | 1010 = 10,000,000,000 |
By looking at the table, you’ll see a pattern arise—the number of zeros in the answer is the same as the number of tens you multiplied by. Isn’t that neat?
Here are two examples to explain these patterns to your child:
Now look at 10 to the power of 5 (shown as105). When you multiply five tens (10 x 10 x 10 x 10 x 10), the answer will have five zeros (100,000)..
Unlock unlimited maths questions
Put your skills to the test with fun exercises + maths games that are proven to boost ability!
Try DoodleMaths for free!
Select a year group
Explore the number 10 in a variety of different ways using counting frames and more!
Discover everyday language used to talk about time.
Learn all about recognising, creating and describing patterns.
In the examples above, we expressed the powers of ten in 3 ways:—expanded form, standard form, & exponential form. Practice each form with your child.
1,000 would be written as 103. Remember, in exponential form, the number 10 is always the base and the number of times you are multiplying 10 is used as the exponent. As we learned earlier, the exponent number is also the number of zeros in the answer.
Help your child see that since exponents tell us how many zeros are in each answer, we can easily multiply other numbers by the power of ten.
Multiply 4 x 104
Since 104 has 4 zeros, 104 is 10,000.
So 4 x 104 is the same as 4 x 10,000 or 40,000.
Scientific notation is a way to write large numbers using the powers of 10. Let’s take look with the following example:
Write 5,000,000 with the powers of 10.
First, count the number of zeros.
Since there are six zeros, 5 is being multiplied by 106.
So you can write 5,000,000 as 5 x 106.
Sometimes you will see negative powers of 10. Negative exponents can be written as decimals.
Write 10-3 as a decimal.
When a negative exponent is used, you must place the 10-3 on the bottom of a fraction to make it positive.
10-3 would become 1 / 103
Since 103 is the same as 10 x 10 x 10, you can rewrite the fraction as 1/(10 x 10 x 10) or 1/1000.
1/1000 can be written as the decimal .001.
If your child is struggling with this section, please see our converting fractions to decimals guide.
DoodleMaths is an award-winning app that’s filled with thousands of questions and games exploring multiplication, division and more! Plus, get free access to DoodleTables with any DoodleMaths subscription!
Designed by teachers, it creates each child a unique work programme tailored to their needs, doubling their progression with just 10 minutes of use a day. Try it for free!
Here are some beginner problems for your child to practice the powers of ten.
Answers:
For more practice with powers of ten, scientific notation, and other math topics for fifth graders, try the DoodleMath.
Ready to give it a go?
Put your knowledge to the test with these no-risk practice problems to get you ready for the classroom!
If you are counting in 10s, the tens place changes. If you are counting in 100s, the hundreds place changes. If you are counting in 1000s, the thousands place changes. If you are counting in 10000s, the ten thousands place changes.
Now try a few practice questions!
Ready to try some questions? Download the DoodleMaths app to practice questions for free today!
Want more practice? Our math help app is a great resource for times table practice!
Lesson credits
Amber Watkins
Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring primary through university level maths. "Knowing that my work in maths education makes such an impact leaves me with an indescribable feeling of pride and joy!"
Amber Watkins
Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring primary through university level maths. "Knowing that my work in maths education makes such an impact leaves me with an indescribable feeling of pride and joy!"
Parents, sign up for a DoodleMaths subscription and see your child become a maths wizard!
All rights reserved.
