- \(10^4\) is NOT equal to which of the following?
- \(100,000\)
- \(0.1 \times 10^5\)
- \(10 \times 10 \times 10 \times 10\)
- \(10^2 \times 10^2\)
- \(10,000\)
The correct answer is A!
\(10^4\) is not equal to 100,000. To equal 100,000, you would need \(10^5\).
- Multiply 104 by 102.
- 108
- 102
- 106
- 10-2
- 103
The correct answer is C!
When multiplying terms with the same base, the exponents should be added. Thus, \(10^4 \times 10^2=10^6\).
- Divide \(x^5\) by \(x^2\).
- \(x^7\)
- \(x^4\)
- \(x^{10}\)
- \(x^3\)
- \(x^{2.5}\)
The correct answer is D!
When dividing terms with the same base, the exponents should be subtracted. Thus, \(\tfrac{x^5}{x^2}\) \(=x^3\).
- Multiply 8.23 by 109.
- 0.00000000823
- 0.000000823
- 8.23
- 8230000000
- 823000000000
The correct answer is D!
The decimal will be moved to the right nine places. Thus, seven zeros will be added to the right of 823, giving 8,230,000,000.
- Which of the following is equal to 83,000?
- \(83 \times 10^4\)
- \(8.3 \times 10^4\)
- \(8.3 \times 10^3\)
- \(83 \times 10^5\)
- \(83 \times 10\)
The correct answer is B!
Moving the decimal to the right of the digit 8 gives the equivalent expression \(8.3\times 10^4\), since there are four digits to the right of the 8.
- Which of the following is equal to 0.00875?
- \(8.75 \times 10^{-2}\)
- \(8.75 \times 10^{-3}\)
- \(8.75 \times 10^{-4}\)
- \(87.5 \times 10^{-3}\)
- \(875 \times 10^{-4}\)
The correct answer is B!
Moving the decimal to the right of the 8 gives \(8.75\times 10^{-3}\), since the decimal must be moved three places to the right.