Testinar Grade 8 math

Operations with Scientific Notation

Learn to reason about and solve Grade 8 problems involving Operations with Scientific Notation.

CH02-04 Exponents, Roots, and Scientific Notation

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Score: ____ / 8

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

A light-year is the distance light travels in one year, approximately \(9.46\times10^{15}\) meters. If a star is \(4.2\) light-years away, how many meters is it? (Express in scientific notation.)
1. \(39.7\times10^{14}\) m
2. \(4.2\times10^{15}\) m
3. \(3.97\times10^{16}\) m
4. \(2.25\times10^{16}\) m
A gold nucleus has a radius of about \(7\times10^{-15}\) meters. The electron cloud of a gold atom extends to about \(1.4\times10^{-10}\) meters. The atomic radius is how many times the nuclear radius?
1. \(0.5\times10^{5}\)
2. \(5\times10^{4}\)
3. \(2\times10^{4}\)
4. \(2\times10^{5}\)
A cubic container has side length \(1.5\times10^{-2}\) meters. What is its volume in cubic meters?
1. \(4.5\times10^{-6}\) m\(^3\)
2. \(3.375\times10^{-5}\) m\(^3\)
3. \(3.375\times10^{-6}\) m\(^3\)
4. \(6.75\times10^{-6}\) m\(^3\)
Which expression is NOT in proper scientific notation?
1. \(9.5\times10^{-3}\)
2. \(10.2\times10^{4}\)
3. \(1\times10^{6}\)
4. \(5.67\times10^{0}\)
What is the product \((3\times10^4)\times(2\times10^5)\) in scientific notation?
1. \(5\times10^9\)
2. \(6\times10^{10}\)
3. \(6\times10^{20}\)
4. \(6\times10^9\)
What is \((5\times10^7)\times(4\times10^3)\)?
1. \(2\times10^{10}\)
2. \(20\times10^4\)
3. \(9\times10^{10}\)
4. \(2\times10^{11}\)
Divide: \(\frac{8\times10^8}{2\times10^3}\)
1. \(10\times10^5\)
2. \(6\times10^5\)
3. \(4\times10^{11}\)
4. \(4\times10^5\)
Multiply: \((6\times10^2)\times(3\times10^4)\)
1. \(18\times10^5\)
2. \(18\times10^8\)
3. \(9\times10^6\)
4. \(1.8\times10^7\)

Teacher and parent reference

Answer key and explanations

C. \(3.97\times10^{16}\) m
Multiply: \(4.2\times(9.46\times10^{15})=(4.2\times9.46)\times10^{15}\approx39.7\times10^{15}=3.97\times10^{16}\) m.
C. \(2\times10^{4}\)
\(\frac{1.4\times10^{-10}}{7\times10^{-15}}=\frac{1.4}{7}\times10^{5}=0.2\times10^{5}=2\times10^{4}\).
C. \(3.375\times10^{-6}\) m\(^3\)
Volume \(=\) (side)\(^3=(1.5\times10^{-2})^3=(1.5)^3\times(10^{-2})^3=3.375\times10^{-6}\) m\(^3\).
B. \(10.2\times10^{4}\)
Scientific notation requires the coefficient to be in the range \([1, 10)\). In choice B, \(10.2\geq10\), so it is not in standard form. It should be \(1.02\times10^{5}\).
D. \(6\times10^9\)
Multiply the coefficients and add the exponents: \((3\times2)\times10^{4+5}=6\times10^9\).
D. \(2\times10^{11}\)
Multiply coefficients: \(5\times4=20\). Add exponents: \(10^{7+3}=10^{10}\). Rewrite \(20\times10^{10}=2\times10^{11}\).
D. \(4\times10^5\)
Divide coefficients: \(8\div2=4\). Subtract exponents: \(10^{8-3}=10^5\). Result: \(4\times10^5\).
D. \(1.8\times10^7\)
Multiply: \(6\times3=18=1.8\times10^1\). Add exponents: \(10^{2+4}=10^6\). Combine: \(1.8\times10^1\times10^6=1.8\times10^7\).