Let's solve this step by step. The task is to
match each scientific notation number on the left with its correct
standard form (decimal) equivalent on the right.
---
🔍 Step 1: Understand Scientific Notation
Scientific notation is written as:
> $ a \times 10^n $
Where:
- $ a $ is a number between 1 and 10 (inclusive of 1, exclusive of 10),
- $ n $ is an integer.
To convert to standard form:
- If $ n $ is
positive, move the decimal point
right $ n $ places.
- If $ n $ is
negative, move the decimal point
left $ n $ places.
---
🔢 Let’s evaluate each one:
#### 1. $ 8.54 \times 10^{10} $
- $ 10^{10} $ means move decimal 10 places to the
right
- $ 8.54 \to 85400000000 $
- So,
85,400,000,000
✔ Match:
85400000000
---
#### 2. $ 4.5 \times 10^{-8} $
- Negative exponent → move decimal
left 8 places
- $ 4.5 \to 0.000000045 $
- So,
0.000000045
✔ Match:
0.000000045
---
#### 3. $ 6.02 \times 10^{23} $
- Move decimal 23 places to the
right
- $ 6.02 \to 602000000000000000000000 $
- That’s 6 followed by 23 digits →
602000000000000000000000
✔ Match:
602000000000000000000000
---
#### 4. $ 8.54 \times 10^{-10} $
- Move decimal 10 places to the
left
- $ 8.54 \to 0.000000000854 $
- So,
0.000000000854
✔ Match:
0.000000000854
---
#### 5. $ 8.85 \times 10^{-12} $
- Move decimal 12 places to the
left
- $ 8.85 \to 0.00000000000885 $
- So,
0.00000000000885
✔ Match:
0.00000000000885
---
#### 6. $ 4.5 \times 10^{-11} $
- Move decimal 11 places to the
left
- $ 4.5 \to 0.000000000045 $
- So,
0.000000000045
✔ Match:
0.000000000045
---
✔ Final Matching:
| Scientific Notation | Standard Form |
|----------------------------|----------------------------------|
| $ 8.54 \times 10^{10} $ |
85400000000 |
| $ 4.5 \times 10^{-8} $ |
0.000000045 |
| $ 6.02 \times 10^{23} $ |
602000000000000000000000 |
| $ 8.54 \times 10^{-10} $ |
0.000000000854 |
| $ 8.85 \times 10^{-12} $ |
0.00000000000885 |
| $ 4.5 \times 10^{-11} $ |
0.000000000045 |
---
🟩 Correct Pairs:
1. $ 8.54 \times 10^{10} $ →
85400000000
2. $ 4.5 \times 10^{-8} $ →
0.000000045
3. $ 6.02 \times 10^{23} $ →
602000000000000000000000
4. $ 8.54 \times 10^{-10} $ →
0.000000000854
5. $ 8.85 \times 10^{-12} $ →
0.00000000000885
6. $ 4.5 \times 10^{-11} $ →
0.000000000045
✔ All matched correctly!
Let me know if you'd like a visual or table version!
Parent Tip: Review the logic above to help your child master the concept of standard notation math.
