8.EE.3: Estimate with Powers of 10
Also written as 8.EE.A.3 and CCSS.MATH.CONTENT.8.EE.A.3 · Cluster: Work with radicals and integer exponents.
The Official Wording
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 10⁸ and the population of the world as 7 times 10⁹, and determine that the world population is more than 20 times larger.
Common Core State Standards, Grade 8, Expressions & Equations · Read it at the source · Checked October 14, 2026
What 8.EE.3 Means in Plain English
Eighth graders round a huge or tiny amount to one digit times a power of 10: a sand grain about 0.0005 m wide is 5 × 10⁻⁴ m. Then they compare: 8 × 10⁹ is 4 × 10³, or 4,000, times as much as 2 × 10⁶.
The point is quick judgment, not precision: an answer off by a power of 10 should look wrong at a glance. Exact digits and full calculation come in 8.EE.4, and high school asks students to choose a level of accuracy that fits the measurement (HSN-Q.3).
8.EE.3 I Can Statements
- I can round a big number to one digit times a power of 10.
- I can write a tiny decimal like 0.0005 as 5 × 10⁻⁴.
- I can say how many times larger one estimate is than another.
8.EE.3 Worked Example
A tiny length and a big one, each rounded to one digit times a power of 10, then compared by division.
A grain of sand is about 0.0005 meters across, and a soccer field is about 100 meters long. About how many grains, laid end to end, would stretch the length of the field?
- Write the grain as one digit times a power of 10. The decimal point jumps 4 places right to sit just after the 5.0.0005 m = 5 × 10⁻⁴ m
- Write the field the same way.100 m = 1 × 10² m
- “How many times as much” means divide. Divide the front digits and the powers of 10 separately.(1 ÷ 5) × (10² ÷ 10⁻⁴) = 0.2 × 10⁶
- 0.2 is not a single digit from 1 to 9, so move one factor of 10 into it.0.2 × 10⁶ = 2 × 10⁵
Check it: Work backward: 200,000 grains × 0.0005 m = 100 m. Or think in millimeters: a 0.5 mm grain means 2 grains per millimeter, and 100 m is 100,000 mm, so 200,000 grains.
Common Mistakes with 8.EE.3
Counting zeros instead of places
0.0005 = 5 × 10⁻³ (three zeros after the point)
Try this: Count the jumps the decimal point makes to sit just after the 5: four jumps right, so the exponent is -4.
Comparing the exponents only
“6 × 10⁵ is 100 times 3 × 10³ because 5 - 3 = 2.”
Try this: Divide the front digits too: 6 ÷ 3 = 2, and 10⁵ ÷ 10³ = 100, so it is 200 times as much.
Leaving two digits in front
4,200,000 ≈ 42 × 10⁵
Try this: Round to one nonzero digit before the power: 4,200,000 is about 4,000,000, which is 4 × 10⁶.
Where 8.EE.3 Fits
Practice 8.EE.3
Quick Check
- Round 0.00387 to a single digit times a power of 10.
- Round 61,000,000 to a single digit times a power of 10.
- About how many times larger is 9 × 10⁷ than 3 × 10⁴?