Standard Form Calculations

How to Add or Subtract Standard Form Numbers?

Step 1: Turn the standard form into an ordinary number.

Step 2: Add or subtract them.

Step 3: If needed, change your answer back to standard form.

Step 1: Change the numbers so both powers of 10 are the same

Step 2: Add or subtract the numbers in front

Step 3: Write the answer in standard form

(2.5 × 10⁵) + (3.5 × 10⁴) = ?

The powers are different: 10⁵ and 10⁴.

Step 1: Change 10⁵ to match 10⁴

We write: 2.5 × 10⁵ = 25 × 10⁴

Now we have: 25 × 10⁴ + 3.5 × 10⁴

Step 2: Add the front numbers : 25 + 3.5 = 28.5

So we get: 28.5 × 10⁴

Step 3: Change to standard form:

28.5 is bigger than 10, so move the decimal one place:2.85 × 10⁵

✅ Answer: 2.85 × 10⁵

How to Multiply or Divide Standard Form Numbers?

✅ Multiply or divide the numbers (a values) separately from the powers of 10.

✅ When multiplying powers of 10, add the indices (the little numbers).

✅ When dividing powers of 10, subtract the indices.

(3 × 10⁻²) × (4 × 10⁵)

Step-by-step:

Multiply the normal numbers: 3 × 4 = 12
Add the powers of 10: 10⁻² × 10⁵ = 10⁻²⁺⁵ = 10³
Put it together: 12 × 10³
But wait! In standard form, the first number must be between 1 and 10.
So: 12 = 1.2 × 10¹ Now multiply that with 10³:(1.2 × 10¹) × 10³ = 1.2 × 10⁴

Answer: 1.2 × 10⁴

(6 × 10⁶) ÷ (2 × 10⁻³) =?

Step-by-step:

Answer: 3 × 10⁹

🎯 Top Tips

🟡 Always check if the powers of 10 are the same before adding or subtracting.

🟡 If they’re different, either:

🟡 Multiply or divide the numbers (a values) separately from the powers of 10.

🟡 When multiplying powers of 10, add the indices (the little numbers).

🟡 When dividing powers of 10, subtract the indices.

✨ Always double-check if your final answer is in standard form!