A city built on a number line. Every zoom is exactly 10 times finer — blocks, streets, houses, rooms.
REMEMBER: Each place in a number is worth 10 times the place to its
right and 1/10 of the place to its left — and that rule
keeps going straight through the decimal point. One block is 10 streets, one street is 10 houses, one house
is 10 rooms. When you multiply or divide by 10, the digits slide past the decimal point; the
point itself never moves. To compare or round decimals, zoom in one place at a time.
Part 1 · Zoom into the City
Type any number from 0 to 9.999. Then zoom in. At the Blocks level, the line shows ones.
Zoom once and the block splits into 10 streets (tenths). Zoom again: 10
houses (hundredths). Once more: 10 rooms (thousandths). Watch which
piece lights up — that is where your number lives.
Level 0 · Blocks (ones)
Your address
The Power-of-10 Elevator
A rider steps in with a number. Every floor up multiplies by 10; every floor
down divides by 10. Watch the digits: they slide past a decimal
point that is bolted to the floor.
Started with
3.472
Floors moved
0
Equation
3.472 × 100 = 3.472
Press a floor button. The equation updates with a power of 10 written with an exponent.
Part 2 · Comparison Duels & Rounding Rounds
Two decimals are dropped into the city. Decide first, lock in your answer, then watch the
city zoom until the numbers separate. Rounding rounds ask which landmark a number lives closest to.
Your first choice is the one that counts.
Part 3 · The Machines
Three step-by-step machines. Each step tells you what to do and why it works.
Read it, write it, break it apart
Multiply or divide by a power of 10
Round to any place with a number line
Part 4 · City Inspector Quiz
Ten questions. Each wrong answer tells you exactly which part of the city to revisit.
Question 1 of 10Score: 0
Word Box
Place value
The worth of a digit because of where it sits. In 3.472 the 4 is worth 4 tenths, not 4.
Tenth · Hundredth · Thousandth
The first three places to the right of the decimal point: 1/10, 1/100, 1/1000. Streets, houses, rooms.
10 times as much · 1/10 of
Every place is 10 times its right-hand neighbor and one-tenth of its left-hand neighbor.
Power of 10
10 multiplied by itself: 10¹ = 10, 10² = 100, 10³ = 1,000. The small raised number is the exponent — it counts the 10s.
Exponent
The small raised number that tells how many times to use 10 as a factor.
Expanded form
A number written as the sum of its digits times their place values: 3.472 = 3 × 1 + 4 × (1/10) + 7 × (1/100) + 2 × (1/1000).
Number name
The number in words. 3.472 is three and four hundred seventy-two thousandths. The word and marks the decimal point.
Compare
Decide which decimal is greater by checking places from left to right, stopping at the first place where the digits differ.
Round
Replace a number with the nearest landmark on the number line at a chosen place. The halfway point decides: halfway or more rounds up.