Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for 8th grade scientific notation? Then this Grade 8 lesson on Scientific Notation for Huge and Tiny Numbers explains each idea step by step, with worked examples.
Quick answer: Scientific notation writes a number as a × 10ⁿ, with a between 1 and 10 and n an integer. Big numbers get a positive exponent, tiny numbers a negative one. It makes comparing sizes easy, and products and quotients follow the rules for powers of ten.
Standards: 8.EE.A.3, 8.EE.A.4 · Level: Grade 8
What is scientific notation?
A number is in scientific notation when it is written as a × 10n, where 1 ≤ a < 10 and n is an integer. Large numbers have a positive n; numbers between 0 and 1 have a negative n.
The exponent counts how far the decimal point travels. For a big number, slide the point left until one nonzero digit sits in front of it.
How do you write a very small number?
Slide the point right until one nonzero digit is in front of it. The number of places becomes a negative exponent.
| Operation | What to do | Example |
|---|---|---|
| Multiply | Multiply the a parts, add the exponents | (4 × 103)(2.5 × 105) = 10 × 108 = 1 × 109 |
| Divide | Divide the a parts, subtract the exponents | (6 × 107) ÷ (2 × 103) = 3 × 104 |
| Add or subtract | Give both the same power of 10 first | 3.5 × 104 + 0.5 × 104 = 4 × 104 |
How do you compare numbers in scientific notation?
Compare exponents first; the larger exponent wins when both coefficients are between 1 and 10. When exponents match, compare coefficients. To say how many times as large one number is, divide.
- Write each number as a × 10n.
- Apply the rule for the operation to the coefficients and to the powers of 10.
- If the coefficient leaves the range 1 to 10, shift the decimal point and adjust the exponent.
- Pick units that keep the numbers readable, such as micrometers for a cell.
Divide coefficients: 8.4 ÷ 2.1 = 4. Subtract exponents: 9 − 4 = 5.
Result: 4 × 105, or 400,000.
Calculators show 3.2E5 or 7.5E−3. The letter E means “times 10 to the power”, so 3.2E5 is 3.2 × 105 = 320,000. Never write E in a final answer.
Beep! A negative exponent means a small number, not a negative one. Check with a sanity test: 10−3 is 0.001, a tiny positive value.
- a × 10ⁿ with 1 ≤ a < 10 and n an integer.
- Move the decimal point left for big numbers (n positive) and right for small ones (n negative).
- Multiply: multiply coefficients and add exponents. Divide: divide coefficients and subtract exponents.
- To add or subtract, first match the powers of 10.
- Calculator display 3.2E5 means 3.2 × 10⁵.
Scientific Notation for Huge and Tiny Numbers: frequently asked questions
Why must the first number be between 1 and 10?
That rule gives every number exactly one scientific form. Without it, 45 × 10³ and 4.5 × 10⁴ would both describe 45,000, which makes comparing sizes harder.
What does a negative exponent in scientific notation mean?
It means the number is between 0 and 1. For example 4 × 10⁻³ equals 0.004. The value is still positive.
How do you multiply numbers in scientific notation?
Multiply the coefficients and add the exponents. Then adjust if the new coefficient is 10 or more. For instance, (5 × 10⁴)(6 × 10³) = 30 × 10⁷ = 3 × 10⁸.
How do you tell how many times larger one number is than another?
Divide the larger by the smaller. Since (9 × 10⁶) ÷ (3 × 10²) = 3 × 10⁴, the first is 30,000 times as large as the second.
What does 4.5E-3 on a calculator mean?
It is 4.5 × 10⁻³, which is 0.0045. The E stands for exponent of ten. Write it in full scientific notation when you copy it down.
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