Let’s solve each problem step by step.
Scientific notation means a number like:
a × 10ⁿ, where
a is a decimal between 1 and 10, and
n is an integer (positive or negative).
To convert to ordinary number:
- If the exponent
n is
positive, move the decimal point in
a to the
right n places.
- If the exponent
n is
negative, move the decimal point in
a to the
left |n| places.
- Add zeros as needed when moving the decimal.
---
Let’s go one by one:
Left Column:
1.
2.181 × 10⁷ → Move decimal 7 places right → 21,810,000
2.
1.373 × 10⁵ → Move decimal 5 places right → 137,300
3.
3.84 × 10⁻⁸ → Move decimal 8 places left → 0.0000000384
4.
9.174 × 10⁵ → Move decimal 5 places right → 917,400
5.
5.9 × 10⁷ → Move decimal 7 places right → 59,000,000
6.
7.39 × 10⁻⁹ → Move decimal 9 places left → 0.00000000739
7.
3.04 × 10⁻⁵ → Move decimal 5 places left → 0.0000304
8.
5.418 × 10³ → Move decimal 3 places right → 5,418
9.
3.855 × 10⁻⁷ → Move decimal 7 places left → 0.0000003855
10.
4.689 × 10⁻⁴ → Move decimal 4 places left → 0.0004689
---
Right Column:
1.
3.98 × 10⁻⁷ → Move decimal 7 places left → 0.000000398
2.
9.23 × 10⁵ → Move decimal 5 places right → 923,000
3.
1.95 × 10⁷ → Move decimal 7 places right → 19,500,000
4.
2.199 × 10⁸ → Move decimal 8 places right → 219,900,000
5.
6.92 × 10⁻⁶ → Move decimal 6 places left → 0.00000692
6.
6.06 × 10⁶ → Move decimal 6 places right → 6,060,000
7.
4.25 × 10⁶ → Move decimal 6 places right → 4,250,000
8.
3 × 10⁷ → Move decimal 7 places right → 30,000,000
9.
7.12 × 10⁸ → Move decimal 8 places right → 712,000,000
10.
8.39 × 10³ → Move decimal 3 places right → 8,390
---
Double-checking a few tricky ones:
- 3.84 × 10⁻⁸ = 0.0000000384 → yes, 8 zeros after decimal before 384? Wait — let's count:
0.0000000384 → positions:
1st: 0
2nd: 0
3rd: 0
4th: 0
5th: 0
6th: 0
7th: 0
8th: 3 → so yes, correct.
- 7.39 × 10⁻⁹ → 0.00000000739 → 9 places: 8 zeros then 739 → correct.
- 3 × 10⁷ = 30,000,000 → yes, 7 zeros after 3.
All look good.
Final Answer:
21,810,000
137,300
0.0000000384
917,400
59,000,000
0.00000000739
0.0000304
5,418
0.0000003855
0.0004689
0.000000398
923,000
19,500,000
219,900,000
0.00000692
6,060,000
4,250,000
30,000,000
712,000,000
8,390
Parent Tip: Review the logic above to help your child master the concept of scientific notation to standard form worksheet.