Testinar Grade 8 math

Understanding Scientific Notation

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

CH02-03 Exponents, Roots, and Scientific Notation

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

Which number is NOT in correct scientific notation form?
1. \(9.99\times10^{2}\)
2. \(1.0\times10^{0}\)
3. \(0.9\times10^{5}\)
4. \(5.05\times10^{-4}\)
Which number is equivalent to \(6.5\times10^{-3}\)?
1. \(6{,}500\)
2. \(65{,}000\)
3. \(0.065\)
4. \(0.0065\)
Convert \(42{,}000\) to scientific notation.
1. \(4.2\times10^{3}\)
2. \(4.2\times10^{5}\)
3. \(42\times10^{2}\)
4. \(4.2\times10^{4}\)
Which of the following equals \(3.8\times10^{2}\)?
1. \(38\)
2. \(38{,}000\)
3. \(3{,}800\)
4. \(380\)
The distance from Earth to the Sun is approximately \(1.496\times10^{8}\) km. What is this distance in standard form?
1. \(149{,}600\) km
2. \(1{,}496{,}000\) km
3. \(149{,}600{,}000\) km
4. \(1{,}496{,}000{,}000\) km
Write \(0.000284\) in scientific notation.
1. \(2.84\times10^{4}\)
2. \(2.84\times10^{-3}\)
3. \(28.4\times10^{-5}\)
4. \(2.84\times10^{-4}\)
The diameter of an atom is about \(2\times10^{-10}\) m. What is this in decimal form?
1. \(0.0000002\) m
2. \(0.00000002\) m
3. \(0.000000002\) m
4. \(0.0000000002\) m
Which number is written in correct scientific notation?
1. \(0.6\times10^{3}\)
2. \(60\times10^{-3}\)
3. \(60\times10^{2}\)
4. \(6.0\times10^{3}\)

Teacher and parent reference

Answer key and explanations

C. \(0.9\times10^{5}\)
The coefficient \(0.9\) is less than \(1\), violating the requirement that it must be in \([1, 10)\).
D. \(0.0065\)
A negative exponent shifts the decimal to the left. Move the decimal \(3\) places left: \(6.5\times10^{-3}=0.0065\).
D. \(4.2\times10^{4}\)
Move the decimal \(4\) places left to get \(4.2\); the exponent is positive \(4\). Thus \(42{,}000=4.2\times10^{4}\).
D. \(380\)
A positive exponent shifts the decimal to the right. Move the decimal \(2\) places right: \(3.8\times10^{2}=380\).
C. \(149{,}600{,}000\) km
Move the decimal \(8\) places right: \(1.496\times10^{8}=149{,}600{,}000\) km.
D. \(2.84\times10^{-4}\)
Move the decimal \(4\) places right to get \(2.84\); the exponent is negative \(4\) (because the original number is less than \(1\)).
D. \(0.0000000002\) m
A negative exponent means move the decimal to the left. With \(10^{-10}\), move \(10\) places left: \(2\times10^{-10}=0.0000000002\) m.
D. \(6.0\times10^{3}\)
Scientific notation requires the coefficient to be at least \(1\) but less than \(10\). Only \(6.0\times10^{3}\) meets this condition.