Question

Express the following measurements in scientific notation. (a) \(4020.6 \mathrm{~mL}\) (b) \(1.006 \mathrm{~g}\) (c) \(100.1^{\circ} \mathrm{C}\)

Short answer

Question: Express the following measurements in scientific notation: a) 4020.6 mL b) 1.006 g c) 100.1°C Answer: a) \(4.0206 \times 10^{3} \mathrm{~mL}\) b) \(1.006 \times 10^{0} \mathrm{~g}\) c) \(1.001 \times 10^{2} \, ^{\circ} \mathrm{C}\)

Step-by-step solution

Identify the decimal point position

In the given measurement, the decimal point is positioned after the 0 in 4020.6.

Move the decimal point

We will move the decimal point 3 places to the left to get a number between 1 and 10: \(4.0206\)

Write the number in scientific notation

After moving the decimal point, we can express the original number as a product of the new number and a power of 10: \(4.0206 \times 10^{3} \mathrm{~mL}\) #b)# Express 1.006 g in scientific notation.

Identify the decimal point position

In the given measurement, the decimal point is positioned between 1 and 0 in 1.006.

Move the decimal point

The decimal point is already in the correct position, so no movement is needed.

Write the number in scientific notation

As the decimal point did not move, we can express the original number as a product of the given number and a power of 10: \(1.006 \times 10^{0} \mathrm{~g}\) #c)# Express 100.1°C in scientific notation.

Identify the decimal point position

In the given measurement, the decimal point is positioned after the second 0 in 100.1.

Move the decimal point

We will move the decimal point 2 places to the left to obtain a number between 1 and 10: \(1.001\)

Write the number in scientific notation

After moving the decimal point, we can express the original number as a product of the new number and a power of 10: \(1.001 \times 10^{2} \, ^{\circ} \mathrm{C}\)