Question

Use scientific (exponential) notation to express the following quantities in terms of the SI base units in
0.13 g
232 Gg
5.23 pm
86.3 mg
37.6 cm
54 μm
1 Ts
27 ps
0.15 mK

Answer 1

Answer:

When a number is written in scientific notation (representing the number using powers of base ten) it is expressed so that it contains a digit in the place of the units and all other digits after the decimal point, multiplied by the respective exponent.  For example, the number $4.232(10)^{3}$.

On the other hand, it is known the units in the SI for mass, length, time and temperature are kilogram (kg), meter (m), second (s) and Kelvin (K), respectively. In addition, thera are prefixes of the International System (SI) that indicate a specific factor of 10.

For example:

-Giga (G) is a prefix that indicates a factor of $10^{6}$

-Pico (p) is a prefix that indicates a factor of $10^{-12}$

-Mili (m) is a prefix that indicates a factor of $10^{-3}$

-Micro ($\mu$) is a prefix that indicates a factor of $10^{-6}$

-Tera (T) is a prefix that indicates a factor of $10^{12}$

-Kilo (K) is a prefix that indicates a factor of $10^{3}$

Knowing this, let's express these quantities in terms of the SI base units:

$0.13 g=0.00013 kg=1.3 (10)^{-4}kg$

$232 Gg=232(10)^{6}g=232 (10)^{3}kg$

$5.23 pm=5.23(10)^{-12}m$

$86.3 mg=86.3(10)^{-3}g=8.63 (10)^{-5}kg$

$37.6 cm=0.376 m=3.76 (10)^{-1}m$

$54 \mu m=54 (10)^{-6}m$

$1 Ts=1 (10)^{-12}s$

$27 ps=27 (10)^{-12}s$

$0.15 mK=0.15(10)^{-3}K$