A number in scientific notation is one digit, then a decimal part, times a power of ten.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
An example
4,300 is 4.3 × 10³. The first part is always between 1 and 10.
Small numbers use negative powers
0.00052 is 5.2 × 10⁻⁴.
Why bother
It makes wildly different sizes comparable at a glance, by looking at the exponent.
The standard form
Scientific notation writes a number as a value between 1 and 10 multiplied by a power of ten: 4,500 is 4.5 × 10³. The first factor must be at least 1 and less than 10, which makes the form unique.
Very small numbers use negative powers
0.00045 is 4.5 × 10⁻⁴. A negative exponent means dividing by that power of ten, which shifts the digits right. The same notation handles the size of a galaxy and the size of an atom.
Why scientists use it
Writing 0.000000000000000000000000001673 is unreadable and error-prone. As 1.673 × 10⁻²⁷ it is legible and comparable. The notation also makes the magnitude visible at a glance from the exponent alone.
Comparing numbers in this form
Compare the exponents first; only if they match do you compare the leading values. So 3 × 10⁸ beats 9 × 10⁷ despite 3 being less than 9. Reading the exponent first is what makes comparison instant.
Step 2: Try It Yourself
Tap and try it out.
Hundreds
4
Tens
3
Ones
0
4 hundreds, 3 tens and 0 ones is 430.
Step 3: Watch an Example
One step at a time.
Watch Leo Write 52,000
Leo writes a large number in scientific notation.
- Step 1
He places the point after the first digit, giving 5.2.
Step 4: Your Turn
Practice makes it stick.
The Big Number
Problem 1 of 2
7,000 is 7 × 10 to what power?
The Comparison
Problem 2 of 2
Which is bigger, 3 × 10⁵ or 9 × 10³?
Powers of Ten
1 of 4
60,000 is 6 × 10 to what power?
2 of 4
2 × 10³ written out. What is it?
3 of 4
4.5 × 10² written out. What is it?
4 of 4
Which is bigger, 8 × 10² or 2 × 10⁴?
Step 5: Quick Check
Show what you know.
Question 1 of 2
3 × 10⁴ written out. What is it?
Question 2 of 2
What must the first part of a scientific notation number be?
What You Learned
- Scientific notation is one digit, a decimal part, and a power of ten.
- The first part is at least 1 and less than 10.
- Compare the exponents first when comparing sizes.