Question

1. convert the following measurements from ordinary notation to scientific notation. dont forget your units! note: all numbers in scientific notation are expressed as a number between 1 and 10 (x) 10 raised to a power. a few more examples are: 314.15 = 3.1415 x 10² 0.00042 = 4.2 x 10⁻⁴ 234.5 x 10² = 2.345 x 10⁴ 1.350 = 1.35 x 10³ 0.002 = 2.0 x 10⁻³

Explanation:

Step1: Recall scientific - notation rule

Scientific notation is of the form \(a\times 10^{n}\), where \(1\leqslant a<10\) and \(n\) is an integer.

Step2: Convert Milky - Way diameter

The diameter of the Milky - Way is \(1000000000000000000000000\) miles. Move the decimal point 23 places to the left, so \(a = 1\) and \(n=23\). In scientific notation, it is \(1\times 10^{23}\) miles.

Step3: Convert tungsten melting - point

The melting point of tungsten is \(3410^{\circ}C\). Move the decimal point 3 places to the left, so \(a = 3.41\) and \(n = 3\). In scientific notation, it is \(3.41\times 10^{3}^{\circ}C\).

Step4: Convert Avogadro's number

Avogadro's number is \(602300000000000000000000\). Move the decimal point 23 places to the left, so \(a=6.023\) and \(n = 23\). In scientific notation, it is \(6.023\times 10^{23}\).

Step5: Convert atomic mass unit

The atomic mass unit is \(0.00000000000000000000000166\) g. Move the decimal point 24 places to the right, so \(a = 1.66\) and \(n=-24\). In scientific notation, it is \(1.66\times 10^{-24}\) g.

Step6: Convert uranium - 235 half - life

The half - life of uranium - 235 is \(710000000\) years. Move the decimal point 8 places to the left, so \(a = 7.1\) and \(n = 8\). In scientific notation, it is \(7.1\times 10^{8}\) years.

Step7: Convert speed of light

The speed of light in a vacuum is \(299793000\) m/s. Move the decimal point 8 places to the left, so \(a = 2.99793\) and \(n = 8\). In scientific notation, it is \(2.99793\times 10^{8}\) m/s.

Step8: Convert sodium light wavelength

The wavelength of sodium light is \(0.0000005893\) meters. Move the decimal point 7 places to the right, so \(a = 5.893\) and \(n=-7\). In scientific notation, it is \(5.893\times 10^{-7}\) m.

Answer:

Diameter of the Milky - Way: \(1\times 10^{23}\) miles
Melting point of tungsten: \(3.41\times 10^{3}^{\circ}C\)
Avogadro's number: \(6.023\times 10^{23}\)
Atomic mass unit: \(1.66\times 10^{-24}\) g
Half - life of uranium - 235: \(7.1\times 10^{8}\) years
Speed of light in a vacuum: \(2.99793\times 10^{8}\) m/s
Wavelength of sodium light: \(5.893\times 10^{-7}\) m