NH SAS Grade 8 The Number System Practice

What the test measures

The Number System skills

Know that there are numbers that are not rational and approximate them by rational numbers
Use rational approximations of irrational numbers to compare the size of irrational numbers
Work with exponents and scientific notation in the context of very large and very small quantities

Standards basis

Common Core State Standards for Mathematics (CCSS-M) / New Hampshire mathematics standards — New Hampshire

How the NH SAS reports it

New Hampshire SAS is the state assessment system, but the official math reporting structure was not accessible from the state page in this session. In practice, New Hampshire’s math assessments are aligned to the state’s K-12 mathematics standards, which closely mirror Common Core grade-level domains and clusters.

Blueprint & weighting

Not published in the accessible source set used here.

Official sources

New Hampshire Department of Education – Assessments
Common Core State Standards for Mathematics
CCSS-M Grade 3 (Oregon ODE reprint)

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playhard

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

Substitute $t = 5$ : $f(5) = e^{15}$ . Since $e^{15} \approx 3{,}269{,}017$ , $f(5) \approx 3 \times 10^{6}$ .

Practice playeasy

Which is closest to $\sqrt{2}$ ?

$\sqrt{2} \approx 1.414$ .

Practice playeasy

Write $4500$ as $a \times 10^n$ where $1 \le a < 10$ . What is $n$ ?

$4500 = 4.5 \times 10^3$ , so $n = 3$ .

Practice playmedium

$(1.5 \times 10^{4})(8 \times 10^{3})$ equals

Multiply coefficients and add exponents: $1.5 \cdot 8 = 12$ and $4+3=7$ , giving $12 \times 10^{7}$ . Rewrite as $1.2 \times 10^{1} \times 10^{7}=1.2 \times 10^{8}\textsf{.}$

Practice playmedium

Let $f(t) = 8e^{3t} + 50$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(2)$ ?

Substitute $t = 2$ : $f(2) = 8e^{6} + 50$ . Since $e^{6} \approx 403.4$ , $f(2) \approx 8(403.4) + 50 = 3{,}277 \approx 3 \times 10^{3}$ .

Practice playeasy

Which is closest to $\sqrt{3}$ ?

$\sqrt{3} \approx 1.732$ .

Practice playeasy

$(2 \times 10^3)(3 \times 10^4) = 6 \times 10^n$ . What is $n$ ?

Multiply coefficients ( $2 \cdot 3 = 6$ ) and add exponents: $3 + 4 = 7$ , so $n = 7$ .

Practice playmedium

What is $(5 \times 10^{-3})(4 \times 10^{-2})$ in scientific notation?

Multiply coefficients and add exponents: $5 \cdot 4 = 20$ and $-3+(-2)=-5$ , giving $20 \times 10^{-5}$ . Rewrite $20=2 \times 10^{1}$ , so $2 \times 10^{1} \times 10^{-5}=2 \times 10^{-4}\textsf{.}$