Real numbers

Practice 5 items →

Rationals versus irrationals: √2 is a point on the line, not a broken number. Students classify numbers, estimate square and cube roots between integers, operate on signed numbers, and write scientific notation with 1 ≤ a < 10.

Specification · for a parent or teacher

Part no.: reals-radicals-sci-notation
Course: Advanced Math 7 · Unit 2
Realm: Numbers
Difficulty: 3 of 4 — Grade 6–7 core. Multi-step, first symbolic work.
Qty: 5 items

Part no. is the node's id; the realm is the kind of math; qty is how many practice items it carries.

Students can

classify rational vs irrational; $\sqrt{n}$ , $\sqrt[3]{n}$ ; estimate $\sqrt{50}$ between 7 and 8; operate on signed numbers; scientific notation $a\times 10^k$ with $1\le a<10$ .

Ready when

they can classify $\sqrt{49}$ , $\sqrt{50}$ , $0.\overline{3}$ , $\pi$ and write $4{,}560{,}000$ in scientific notation.

Formulas

Scientific notation

a \times 10^k,\quad 1 \le a < 10

Watch for

$\sqrt{16/25}$ called irrational; $\pi=\frac{22}{7}$ ; $3.2\times 10^3$ written $32\times 10^2$ as “scientific.”

Before · requires

Decimals: terminating and repeatingdecimals-terminating-repeating · Math 6
Negative numbers and absolute valueintegers-absolute-value · Math 6
Whole numbers to one billionplace-value-billion · Math 5

After · used by

Introduction to algebraalgebra-foundations-7 · Math 7
Volume and surface area of solidsvolume-surface-3d · Math 7
Exponentslaws-of-exponents · Math 1
Coordinate geometrycoordinate-geometry · Math 1
Statistics: center and spreaddescriptive-stats-spread · Math 1

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