Let’s solve the first problem together:
6.2 × 10⁵ + 3.8 × 10⁴
Step 1: Make sure both numbers have the same power of 10.
We can change 3.8 × 10⁴ to match 10⁵.
To do that, move the decimal one place left → 0.38 × 10⁵
Step 2: Now add them:
6.2 × 10⁵ + 0.38 × 10⁵ = (6.2 + 0.38) × 10⁵ =
6.58 × 10⁵
✔ That matches answer choice A on the worksheet.
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Now let’s try the second one:
9.7 × 10³ – 4.2 × 10²
Step 1: Change 4.2 × 10² to match 10³.
Move decimal one place left → 0.42 × 10³
Step 2: Subtract:
9.7 × 10³ – 0.42 × 10³ = (9.7 – 0.42) × 10³ =
9.28 × 10³
✔ That matches answer choice B.
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Third problem:
5.1 × 10⁶ + 2.9 × 10⁶
Same power? Yes! Just add the front parts:
5.1 + 2.9 = 8.0 → so
8.0 × 10⁶
✔ That’s answer choice C.
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Fourth problem:
7.3 × 10⁴ – 1.5 × 10³
Change 1.5 × 10³ to 0.15 × 10⁴
Then subtract: 7.3 – 0.15 = 7.15 →
7.15 × 10⁴
✔ That’s answer choice D.
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Fifth problem:
4.6 × 10⁷ – 3.2 × 10⁶
Change 3.2 × 10⁶ to 0.32 × 10⁷
Subtract: 4.6 – 0.32 = 4.28 →
4.28 × 10⁷
✔ That’s answer choice E.
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Sixth problem:
8.9 × 10² + 6.1 × 10¹
Change 6.1 × 10¹ to 0.61 × 10²
Add: 8.9 + 0.61 = 9.51 →
9.51 × 10²
✔ That’s answer choice F.
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Seventh problem:
3.4 × 10⁵ – 1.7 × 10⁴
Change 1.7 × 10⁴ to 0.17 × 10⁵
Subtract: 3.4 – 0.17 = 3.23 →
3.23 × 10⁵
✔ That’s answer choice G.
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Eighth problem:
2.5 × 10³ + 7.5 × 10²
Change 7.5 × 10² to 0.75 × 10³
Add: 2.5 + 0.75 = 3.25 →
3.25 × 10³
✔ That’s answer choice H.
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Ninth problem:
6.8 × 10⁶ – 2.4 × 10⁵
Change 2.4 × 10⁵ to 0.24 × 10⁶
Subtract: 6.8 – 0.24 = 6.56 →
6.56 × 10⁶
✔ That’s answer choice I.
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Tenth problem:
1.2 × 10⁴ + 8.8 × 10³
Change 8.8 × 10³ to 0.88 × 10⁴
Add: 1.2 + 0.88 = 2.08 →
2.08 × 10⁴
✔ That’s answer choice J.
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Final Answer:
A, B, C, D, E, F, G, H, I, J
Parent Tip: Review the logic above to help your child master the concept of scientific notation coloring worksheet.
