Testinar Grade 7 math

Introduction to Scientific Notation

Students will build Grade 7 mastery of introduction to scientific notation using models, equations, and test-style reasoning.

CH03-11 The Number System

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

Which number is equivalent to \(3.2\times10^4\)?
1. \(3{,}200\)
2. \(32{,}000\)
3. \(320{,}000\)
4. \(3{,}200{,}000\)
Express \(0.0056\) in scientific notation and identify which form is NOT equivalent.
1. \(5.6\times10^{-3}\)
2. \(56\times10^{-4}\)
3. \(0.56\times10^{-2}\)
4. \(5.6\times10^{-2}\)
When \(6.75\) is multiplied by a power of 10 to become \(0.000675\), what is the exponent?
1. \(10^{-2}\)
2. \(10^{-3}\)
3. \(10^{-4}\)
4. \(10^{-5}\)
The population of a city is \(1.5\times10^6\). How is this number written in standard form?
1. \(15{,}000\)
2. \(150{,}000\)
3. \(1{,}500{,}000\)
4. \(15{,}000{,}000\)
Express \(24{,}000{,}000\) in scientific notation.
1. \(2.4\times10^6\)
2. \(2.4\times10^7\)
3. \(24\times10^{7}\)
4. \(2.4\times10^{8}\)
A microscopic organism measures \(0.000003\) cm. What is this measurement in scientific notation?
1. \(3\times10^{-5}\)
2. \(3\times10^{-6}\)
3. \(3\times10^{5}\)
4. \(0.3\times10^{-5}\)
Which number is larger: \(4.1\times10^5\) or \(3.9\times10^6\)?
1. \(4.1\times10^5\)
2. \(3.9\times10^6\)
3. They are equal
4. Cannot be determined
Convert \(0.00042\) to scientific notation.
1. \(4.2\times10^{-4}\)
2. \(4.2\times10^{-5}\)
3. \(4.2\times10^{-3}\)
4. \(42\times10^{-4}\)

Teacher and parent reference

Answer key and explanations

B. \(32{,}000\)
\(3.2\times10^4=3.2\times10{,}000=32{,}000\). Move the decimal \(4\) places right.
D. \(5.6\times10^{-2}\)
\(0.0056 = 5.6 \times 10^{-3}\) (proper form). Check: \(56\times10^{-4}=5.6\times10^{-3}\) (equiv.), \(0.56\times10^{-2}=5.6\times10^{-3}\) (equiv.), but \(5.6\times10^{-2}=0.056 \neq 0.0056\).
C. \(10^{-4}\)
\(6.75 \times 10^{-4} = 6.75 \times 0.0001 = 0.000675\). The decimal moves 4 places left.
C. \(1{,}500{,}000\)
\(1.5\times10^6=1.5\times1{,}000{,}000=1{,}500{,}000\).
B. \(2.4\times10^7\)
Place the decimal after the first digit: \(2.4\). Count places moved: \(7\) places left, so exponent is \(7\). Proper scientific notation requires \(1\leq a<10\).
B. \(3\times10^{-6}\)
Move the decimal 6 places to the right to get \(3\). Exponent is \(-6\).
B. \(3.9\times10^6\)
\(3.9\times10^6=3{,}900{,}000\) and \(4.1\times10^5=410{,}000\). Since the exponent \(6\) is larger, \(3.9\times10^6\) is larger.
A. \(4.2\times10^{-4}\)
Move the decimal 4 places right from the first nonzero digit: \(0.00042 \to 4.2\). Exponent is \(-4\).