Let’s solve each problem one by one. We’re multiplying numbers in scientific notation — that means we multiply the coefficients (the numbers before the “× 10^”) and then add the exponents.
---
Problem 1:
A newborn has about
3 × 10¹⁰ cells.
An adult has
1.5 × 10³ times as many cells.
So, to find the adult’s cell count:
→ Multiply the coefficients:
3 × 1.5 = 4.5
→ Add the exponents:
10¹⁰ × 10³ = 10^(10+3) = 10¹³
So, total =
4.5 × 10¹³
The coefficient is already to the nearest thousandth (it’s just 4.5), so no rounding needed.
✔ Answer for #1:
4.5 × 10¹³
---
Problem 2:
Rhode Island area =
1.2 × 10³ square miles
Alaska is
4.9 × 10² times larger.
Multiply coefficients:
1.2 × 4.9 = ?
Let’s calculate:
1.2 × 4.9
= 1.2 × (5 - 0.1)
= 1.2×5 - 1.2×0.1
= 6.0 - 0.12
=
5.88
Add exponents:
10³ × 10² = 10^(3+2) = 10⁵
So, Alaska’s area =
5.88 × 10⁵
Coefficient 5.88 is already to the nearest thousandth? Wait — thousandths would be three decimal places. But 5.88 is only two decimals. The instruction says “round the coefficient to the nearest thousandths, if necessary.” Since 5.88 is exact and doesn’t need more decimals, we leave it.
But let’s double-check: 1.2 × 4.9
Do it straight:
1.2
× 4.9
------
108 ← 1.2 × 9
+ 480 ← 1.2 × 40 (shifted)
= 588 → so 5.88 when you account for decimals (one from 1.2, one from 4.9 → total two decimals → 5.88)
Yes, correct.
✔ Answer for #2:
5.88 × 10⁵
---
Problem 3:
Kiddie pool holds
1.5 × 10² gallons
Olympic pool holds
4.4 × 10⁵ times as much.
Multiply coefficients:
1.5 × 4.4 = ?
Calculate:
1.5 × 4.4
= 1.5 × (4 + 0.4)
= 1.5×4 + 1.5×0.4
= 6.0 + 0.6
=
6.6
Add exponents:
10² × 10⁵ = 10^(2+5) = 10⁷
So, Olympic pool =
6.6 × 10⁷ gallons
Again, 6.6 is fine — no need to round further.
✔ Answer for #3:
6.6 × 10⁷
---
Final Answer:
1. 4.5 × 10¹³
2. 5.88 × 10⁵
3. 6.6 × 10⁷
Parent Tip: Review the logic above to help your child master the concept of scientific notation division worksheet.
