Deal with the number parts and the powers of ten separately.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Multiplying
Multiply the number parts and add the exponents. (3 × 10⁴) × (2 × 10³) = 6 × 10⁷.
Dividing
Divide the number parts and subtract the exponents.
Tidying the answer
If the number part lands outside 1 to 10, shift it back. 40 × 10⁵ is written 4 × 10⁶.
Multiplying in scientific notation
Multiply the leading values and add the exponents: (3 × 10⁴) × (2 × 10³) = 6 × 10⁷. The two parts are handled separately, which is what makes calculations with enormous numbers manageable by hand.
Dividing
Divide the leading values and subtract the exponents: (6 × 10⁸) ÷ (2 × 10³) = 3 × 10⁵. Same structure, opposite operations, following directly from the exponent laws.
Fixing the leading value
If the leading value ends up outside 1 to 10 — say 40 × 10⁵ — rewrite it: 4 × 10⁶. The exponent absorbs the extra factor of ten. Answers should always be returned to standard form.
Adding is different
To add, the exponents must match first: 3 × 10⁴ + 2 × 10³ becomes 3 × 10⁴ + 0.2 × 10⁴ = 3.2 × 10⁴. Addition needs a common unit, exactly as with fractions and decimals. There is no shortcut.
Step 2: Try It Yourself
Tap and try it out.
Before: 4
After: 20
The factor is more than 1, so the bar got longer.
Step 3: Watch an Example
One step at a time.
Watch Leo Renormalise
Leo works out (5 × 10³) × (8 × 10²).
- Step 1
He multiplies the number parts: 5 × 8 = 40.
Step 4: Your Turn
Practice makes it stick.
The Product
Problem 1 of 2
(2 × 10³) × (4 × 10²). What is the number part?
The Exponent
Problem 2 of 2
Same product. What is the exponent?
Parts and Powers
1 of 4
(3 × 10²) × (3 × 10⁴). What is the exponent?
2 of 4
(8 × 10⁶) ÷ (2 × 10²). What is the number part?
3 of 4
Same division. What is the exponent?
4 of 4
60 × 10³ rewritten properly. What is the exponent?
Step 5: Quick Check
Show what you know.
Question 1 of 1
(4 × 10⁵) × (2 × 10³). What is the exponent?
What You Learned
- Handle the number parts and the powers of ten separately.
- Multiplying adds the exponents; dividing subtracts them.
- Renormalise so the number part sits between 1 and 10.