ACAP Grade 8 The Number System. Practice it free.

Knows that there are numbers that are not rational and works with numbers in scientific notation. This Grade 8 reporting domain maps to 7 practice skills and 8 representative questions from the playable bank.

Grade 87 mapped skills

What the test measures

The Number System skills

Know that there are numbers that are not rational and approximate them by rational numbers
Work with radicals and integer exponents
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities

Standards basis

Alabama Course of Study: Mathematics — Alabama

How the ACAP reports it

Alabama’s ACAP Summative is a state assessment tied to Alabama’s own K-12 mathematics standards and reporting structure rather than a national consortium blueprint. The publicly accessible assessment page does not expose a separate ACAP math blueprint in the fetched content, so the safest official coverage basis is Alabama’s mathematics standards organization into grade-level domains.

Blueprint & weighting

ACAP uses the Independent / state-specific framework (by grade domains structure).

Official sources

Alabama Department of Education - Assessment
Alabama Office of Mathematics Improvement

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playhard

Let $f(t) = 6e^{2t}$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(5)$ ?

Substitute $t = 5$ : $f(5) = 6e^{10}$ . Since $e^{10} \approx 22{,}026$ , $f(5) \approx 6(22{,}026) = 132{,}156 \approx 1 \times 10^{5}$ .

Practice playeasy

Which expression is $93{,}000{,}000$ in scientific notation?

$93{,}000{,}000 = 9.3 \times 10^{7}\textsf{.}$

Practice playeasy

Simplify: $y^{6} \cdot y^{3}$ .

The Product of Powers Property says that powers with the same base are multiplied by adding the exponents, written $y^{m} \cdot y^{n} = y^{m+n}\textsf{.}$ Both factors have base $y$ , so $y^{6} \cdot y^{3} = y^{6+3} = y^{9}\textsf{.}$

Practice playmedium

$\dfrac{6.3 \times 10^{-4}}{2.1 \times 10^{-9}}=$

Divide coefficients and subtract exponents: $6.3 \div 2.1 = 3$ and $-4-(-9)=5$ . So the quotient is $3 \times 10^{5}\textsf{.}$

Practice playeasy

Solve for all values of $x\textsf{.}$

$x^{3} = 125$

$5 \times 5 \times 5 = 125\textsf{,}$ so $x = 5\textsf{.}$

Practice playeasy

What is $\sqrt[\text{\scriptsize 3}]{1{,}000}\textsf{?}$

$10 \times 10 \times 10 = 1{,}000\textsf{,}$ so $\sqrt[\text{\scriptsize 3}]{1{,}000} = 10\textsf{.}$

Practice playeasy

Which is closest to $\sqrt{5}$ ?

$\sqrt{5} \approx 2.236$ .

Practice playhard

Let $f(t) = 5e^{3t} + 200$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(4)$ ?

Substitute $t = 4$ : $f(4) = 5e^{12} + 200$ . Since $e^{12} \approx 162{,}755$ , $f(4) \approx 5(162{,}755) + 200 = 813{,}975 \approx 8 \times 10^{5}$ .