Thursday

Raven spreads a printed fact sheet on the bench. "Real numbers today, from a space agency table."

"Earth is about 149,600,000 kilometers from the Sun. Neptune is about 4,515,000,000."

"Too many zeros," Rocket says. "In scientific notation: 1.496 × 10⁸ and 4.515 × 10⁹."

"What do you notice when you compare them?" Raven asks.

"Round them. 1.5 × 10⁸ and 4.5 × 10⁹. Divide the fronts: 3. Divide the powers: 10¹. About 30 times as far."

Nova hovers over the sheet, her light resting on the Neptune row. "Does the table say that, or did you?"

"I did," Rocket says. "The table gives the distances. The comparing is my job."

"And the checking is ours," Raven says. "Puzzle Night gets a space puzzle."

To compare two numbers in scientific notation, divide the front numbers and subtract the exponents.

4.5 × 10⁹ ÷ 1.5 × 10⁸: the fronts give 4.5 ÷ 1.5 = 3, and 10⁹ ÷ 10⁸ = 10¹. So 3 × 10 = 30 times.

A rough estimate uses one digit times a power of ten. Neptune at 5 × 10⁹ km is between 10 and 100 times Earth's 1 × 10⁸.

These distances come from a published space agency fact sheet, in millions of kilometers, rounded as printed. They are the only real-world numbers in this course.

Multiply: multiply the fronts and add the exponents. (2 × 10³) × (3 × 10⁴) = 6 × 10⁷.

Add or subtract only when the powers match: 3 × 10⁴ + 2 × 10⁴ = 5 × 10⁴. If they differ, rewrite one first.

If the front leaves the 1 to 10 range, fix it. 5 × 10³ × 4 × 10² = 20 × 10⁵, which is 2 × 10⁶.

Mixed forms: 0.0032 + 1.8 × 10⁻³ is 3.2 × 10⁻³ + 1.8 × 10⁻³ = 5 × 10⁻³.

Pick a unit that fits. One sheet of paper is 1 × 10⁻² cm, or 1 × 10⁻⁴ m. Centimeters read more easily.

Sharp work with real numbers. Tomorrow you review the whole course and plan your Puzzle Night.