Question

a. How many kilograms are in 1 teragram? b. How many nanometers are in \(6.50 \times 10^{2}\) terameters? c. How many kilograms are in 25 femtograms? d. How many liters are in 8.0 cubic decimeters? e. How many microliters are in 1 milliliter? f. How many picograms are in 1 microgram?

Short answer

a. \(10^9\) kg b. \(6.50 \times 10^{23}\) nm c. \(25 \times 10^{-18}\) kg d. 8.0 L e. \(10^3\) µL f. \(10^3\) pg

Step-by-step solution

a. How many kilograms are in 1 teragram?

To convert from teragrams (Tg) to kilograms (kg), we need to know the conversion factor between the two. One teragram is equal to \(10^{12}\) grams, and since there are 1000 grams in a kilogram, we have to multiply by \(10^9\). 1 Tg = \(1 \times 10^9\) kg So, there are \(10^9\) kilograms in 1 teragram.

b. How many nanometers are in 6.50 × 10² terameters?

To convert from terameters (Tm) to nanometers (nm), we need to know the conversion factor between the two. One terameter is equal to \(10^{12}\) meters, and since there are \(10^9\) nanometers in a meter, we have to multiply by \(10^{21}\). 6.50 × 10² Tm = 6.50 × 10² × 10²¹ nm = 6.50 × 10²³ nm So, there are 6.50 × 10²³ nanometers in \(6.50 \times 10^2\) terameters.

c. How many kilograms are in 25 femtograms?

To convert from femtograms (fg) to kilograms (kg), we need to know the conversion factor between the two. One femtogram is equal to \(10^{-15}\) grams, and since there are 1000 grams in a kilogram, we have to divide by \(10^{18}\). 25 fg = 25 × 10⁻¹⁸ kg So, there are \(25 \times 10^{-18}\) kilograms in 25 femtograms.

d. How many liters are in 8.0 cubic decimeters?

To convert from cubic decimeters (dm³) to liters (L), we need to know that one cubic decimeter is equal to one liter. Therefore, the conversion factor is 1. 8.0 dm³ = 8.0 L So, there are 8.0 liters in 8.0 cubic decimeters.

e. How many microliters are in 1 milliliter?

To convert from milliliters (mL) to microliters (µL), we need to know the conversion factor between the two. One milliliter is equal to \(10^3\) microliters. 1 mL = \(1 \times 10^3\) µL So, there are \(10^3\) microliters in 1 milliliter.

f. How many picograms are in 1 microgram?

To convert from micrograms (µg) to picograms (pg), we need to know the conversion factor between the two. One microgram is equal to \(10^3\) picograms. 1 µg = \(1 \times 10^3\) pg So, there are \(10^3\) picograms in 1 microgram.

Key concepts

kilograms to teragrams

Converting kilograms (kg) to teragrams (Tg) involves understanding large scale measurements. A teragram is a massive unit used for extremely heavy objects. To grasp this, consider that one teragram equals one trillion grams. On the other hand, one kilogram equals 1,000 grams. Therefore, to convert from kilograms to teragrams, we should appreciate the scale of conversion:

• 1 Tg = \(10^{12}\) g
• 1 kg = 1,000 g

By dividing \(10^{12}\) grams by 1,000 (the number of grams in a kilogram), we see that 1 teragram is \(10^9\) kilograms. Such conversions are crucial when dealing with large estimates or scientific data involving significant mass calculations. Always remember that moving from a basic unit to a larger unit typically involves multiplying by a power of ten.

nanometers to terameters

When converting nanometers (nm) to terameters (Tm), it's essential to understand their place in the metric system. Nanometers are incredibly small, while terameters are vast. To visualize this:

• 1 Tm = \(10^{12}\) m
• 1 nm = \(10^{-9}\) m

Thus, moving from nanometers to terameters demands calculating a significant shift: a factor of \(10^{21}\), because a terameter is astronomically larger compared to a nanometer. This massive conversion factor helps with astronomical distances and nano-scale measuring simultaneously. For example, when dealing with scales like in scientific research or space measurement, it's important to confidently navigate these conversions for precise calculations.

femtograms to kilograms

Femtograms (fg) are used for measuring minuscule weights, while kilograms (kg) are a standard measurement for more everyday objects. Understanding the conversion between femtograms to kilograms requires a grasp of how tiny a femtogram is in relation to a kilogram:

• 1 fg = \(10^{-15}\) g
• 1 kg = 1,000 g

Thus, to convert a femtogram into kilograms, you need to understand that it involves dividing the femtogram value by \(10^{18}\). This division by a large factor represents the vast difference between these two units. Such conversions are very useful in fields like chemistry and materials science where extremely small quantities need measuring.

cubic decimeters to liters

The conversion from cubic decimeters (dm³) to liters (L) is straightforward because both units are equal in volume measurement. In daily usage and scientific contexts, it is beneficial to know these are interchangeable:

• 1 dm³ = 1 L

This means if you have any value in cubic decimeters, it is directly equal in liters. Such simplicity in conversions is helpful in practical applications like measuring fluids or gases. This equivalence saves time and reduces confusion, boosting fluidity in communication across scientific and everyday environments.

microliters to milliliters

Microliters (µL) and milliliters (mL) are used frequently in laboratory settings. Understanding the conversion factor between these units helps in precise measurements and solutions preparation:

• 1 mL = \(10^3\) µL

Thus, 1 milliliter is equal to 1,000 microliters. This conversion involves shifting the decimal point to accommodate smaller or larger samples easily. It helps in accuracy when dealing with solutions, reagents, or any fluid requiring exact quantities.

picograms to micrograms

Picograms (pg) and micrograms (µg) measure minute quantities of mass, essential in scientific fields like pharmacology or nanotechnology. Understanding their conversion is crucial for precision:

• 1 µg = \(10^6\) pg

Therefore, when converting micrograms to picograms, you multiply by \(10^3\). This conversion helps simplify mass calculations on a micro scale, ensuring research and experiments maintain accurate and consistent units.