Let’s go through each problem one by one. We’re comparing numbers in scientific notation — that means they look like:
a × 10^b, where “a” is a number between 1 and 10 (or sometimes negative), and “b” is the exponent.
How to compare:
- First, check if one number is positive and the other is negative →
positive is always bigger.
- If both are positive or both are negative:
- Compare the exponents first (the power of 10). The larger exponent usually means the bigger number — *unless* the coefficients are very different.
- If exponents are the same, then compare the coefficients (the “a” part).
- For negative numbers: the one with the smaller absolute value is actually bigger (e.g., -2 > -5).
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Let’s solve each:
1) 3 × 10⁵ vs 6 × 10⁻⁹
→ 10⁵ is huge, 10⁻⁹ is tiny (almost zero). So 3×10⁵ is way bigger.
✔ >
2) 8.5 × 10⁻⁵ vs 8.5 × 10⁻⁵
→ Exactly the same!
✔ =
3) 3.28 × 10¹⁷ vs 4.25 × 10¹⁷
→ Same exponent → compare 3.28 and 4.25 → 3.28 < 4.25
✔ <
4) 6.279 × 10⁵ vs 1.8 × 10⁷
→ 10⁷ is 100 times bigger than 10⁵ → even though 6.279 > 1.8, the exponent wins.
So 1.8×10⁷ = 18,000,000; 6.279×10⁵ = 627,900 → so second is bigger.
✔ <
5) 7.44 × 10⁹ vs 2.36 × 10⁹
→ Same exponent → 7.44 > 2.36
✔ >
6) -6.62 × 10² vs -3.21 × 10⁶
→ Both negative. Let’s think about their sizes:
-6.62×10² = -662
-3.21×10⁶ = -3,210,000 → this is MUCH more negative → so it’s smaller.
So -662 > -3,210,000
✔ >
7) -5.57 × 10² vs -6.97 × 10⁵
→ Again, both negative.
-5.57×10² = -557
-6.97×10⁵ = -697,000 → much more negative → so -557 is bigger.
✔ >
8) 1.28 × 10¹ vs 4.95 × 10²
→ 10² is 10 times bigger than 10¹ → 4.95×100 = 495; 1.28×10 = 12.8 → 495 is bigger.
✔ <
9) 8.22 × 10⁷ vs 4.64 × 10¹
→ 10⁷ is 10 million, 10¹ is 10 → no contest.
✔ >
10) 5.15 × 10⁻⁴ vs 6.35 × 10⁻⁵
→ Negative exponents mean small decimals.
5.15×10⁻⁴ = 0.000515
6.35×10⁻⁵ = 0.0000635 → so first is bigger.
Also, 10⁻⁴ is 10 times bigger than 10⁻⁵ → so even though 5.15 < 6.35, the exponent makes the first bigger.
✔ >
11) 3.27 × 10⁸ vs -1.59 × 10¹
→ Positive vs negative → positive is always bigger.
✔ >
12) -3.81 × 10² vs -7.34 × 10⁹
→ Both negative.
-3.81×100 = -381
-7.34×10⁹ = -7,340,000,000 → way more negative → so -381 is bigger.
✔ >
13) -3.79 × 10⁷ vs -3.40 × 10²
→ Both negative.
-3.79×10⁷ = -37,900,000
-3.40×10² = -340 → -340 is bigger (less negative).
✔ <
14) 2.08 × 10⁷ vs -9.20 × 10⁴
→ Positive vs negative → positive wins.
✔ >
15) 1 × 10⁸ vs 8.68 × 10⁵
→ 10⁸ = 100,000,000; 10⁵ = 100,000 → 8.68×100,000 = 868,000 → so first is bigger.
✔ >
16) 6.92 × 10¹ vs -2.04 × 10⁶
→ Positive vs negative → positive wins.
✔ >
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Final Answer:
1) >
2) =
3) <
4) <
5) >
6) >
7) >
8) <
9) >
10) >
11) >
12) >
13) <
14) >
15) >
16) >
Parent Tip: Review the logic above to help your child master the concept of ordering numbers in scientific notation worksheet.
