Question

1. compare 2.01×10¹³ and 3.8×10¹¹.

a) circle the larger number. b) what is the magnitude of the larger number?

1. compare 1.815×10¹⁴ and 1.82×10¹⁴.

a) are the magnitudes the same or different?
b) circle the larger number.

1. compare 6.0×10⁻³ and 6.0×10⁻⁴.

a) circle the larger number. b) what is the magnitude of the larger number?

1. the wave length of the color red is about 6.5×10⁻⁹ meters. the wavelength of the color blue is about 4.75×10⁻⁹ meters.

a) what is the magnitude of the wave length of the color red?
b) what is the magnitude of the wave length of the color blue?
d) which is longer, the wavelength of red or the wavelength of blue?

1. circle the smaller number: 2.1×10⁻⁸ 1.2×10⁵
2. place the following numbers in order from least to greatest: 7.8×10⁶ 5.1×10⁴ 1.25×10⁵ 4.09×10⁴
3. which of the following numbers represents the least or smallest number?

a) 7×10⁸ b) 7×10⁹ c) 7.1×10⁸ d) 7.1×10⁹

1. which of these numbers has the greatest value?

a) 9×10⁹ b) 8×10⁹ c) 9×10⁸ d) 8×10⁸

1. which number is the greatest?

a) 5.25×10⁵ b) 5.55×10⁵ c) 2.55×10⁵ d) 5×10⁵

1. change 0.732×10⁹ into scientific notation.

Explanation:

Step1: Recall scientific - notation comparison rules

For numbers in scientific notation \(a\times10^{n}\) and \(b\times 10^{m}\), if \(n>m\), then \(a\times 10^{n}>b\times 10^{m}\) (assuming \(a,b> 0\)). If \(n = m\), then compare \(a\) and \(b\). The magnitude of a number in scientific notation \(a\times10^{n}\) is \(|n|\).

Step2: Solve problem 9

a) Compare \(2.01\times10^{13}\) and \(3.8\times10^{11}\). Since \(13>11\), \(2.01\times10^{13}\) is the larger number.
b) The magnitude of \(2.01\times10^{13}\) is \(13\).

Step3: Solve problem 10

a) The numbers are \(1.815\times10^{14}\) and \(1.82\times10^{14}\). The exponents are the same (\(14\)), so the magnitudes are the SAME.
b) Since \(1.82>1.815\), \(1.82\times10^{14}\) is the larger number.

Step4: Solve problem 11

a) Compare \(6.0\times10^{-3}\) and \(6.0\times10^{-4}\). Since \(- 3>-4\), \(6.0\times10^{-3}\) is the larger number.
b) The magnitude of \(6.0\times10^{-3}\) is \(3\).

Step5: Solve problem 12

a) The magnitude of the wavelength of red (\(6.5\times10^{-9}\) meters) is \(9\).
b) The magnitude of the wavelength of blue (\(4.75\times10^{-9}\) meters) is \(9\).
d) Since \(6.5>4.75\) and the exponents are the same, the wavelength of red is longer.

Step6: Solve problem 13

Compare \(2.1\times10^{-8}\) and \(1.2\times10^{5}\). Since \(-8 < 5\), \(2.1\times10^{-8}\) is the smaller number.

Step7: Solve problem 14

Rewrite the numbers: \(4.09\times10^{4}=40900\), \(5.1\times10^{4}=51000\), \(1.25\times10^{5}=125000\), \(7.8\times10^{6}=7800000\). In order from least to greatest: \(4.09\times10^{4},5.1\times10^{4},1.25\times10^{5},7.8\times10^{6}\).

Step8: Solve problem 15

Compare \(7\times10^{8}\), \(7\times10^{9}\), \(7.1\times10^{8}\), \(7.1\times10^{9}\). Since \(8 < 9\), among the numbers with exponent \(8\), \(7\times10^{8}\) is smaller than \(7.1\times10^{8}\). So the least number is \(7\times10^{8}\) (a).

Step9: Solve problem 16

Compare \(9\times10^{9}\), \(8\times10^{9}\), \(9\times10^{8}\), \(8\times10^{8}\). Since \(9>8\) and \(9\times10^{9}\) has the highest exponent among non - equal exponents, \(9\times10^{9}\) (a) has the greatest value.

Step10: Solve problem 17

Compare \(5.25\times10^{5}\), \(5.55\times10^{5}\), \(2.55\times10^{5}\), \(5\times10^{5}\). Since \(5.55>5.25>5>2.55\), \(5.55\times10^{5}\) (b) is the greatest.

Step11: Solve problem 18

For \(0.732\times10^{9}\), in scientific notation, it should be \(7.32\times10^{8}\) (move the decimal point one place to the right and decrease the exponent by 1).

Answer:

1. a) \(2.01\times10^{13}\)

b) \(13\)

1. a) SAME

b) \(1.82\times10^{14}\)

1. a) \(6.0\times10^{-3}\)

b) \(3\)

1. a) \(9\)

b) \(9\)
d) The wavelength of red

1. \(2.1\times10^{-8}\)
2. \(4.09\times10^{4},5.1\times10^{4},1.25\times10^{5},7.8\times10^{6}\)
3. a) \(7\times10^{8}\)
4. a) \(9\times10^{9}\)
5. b) \(5.55\times10^{5}\)
6. \(7.32\times10^{8}\)