Express Numbers Using Integers Power of 10

Lucy estimated that it would take 4,000 grains of sand to make a pound. That would mean that each grain of sand weighs 1/4000 of a pound. In decimal form, that weight would be 0.00025 of a pound. Express this in scientific notation?

• 2.5 × 10^–4 pounds

• 4 × 10^–3 pounds

• 2.5 × 10^–3 pounds

• 2.5 × 10^–5 pounds

Robert and Dora need to write 4,300,000,000 using scientific notation. Robert claims that 4,300,000,000 = 4.3 x 10⁸ and Dora claims that 4,300,000,000 = 4.3 x 10⁹. Whose number is correct and why?

• Robert’s number is correct because when converting 4,300,000,000, the decimal would be located between the 4 and the 3, and the original decimal point in the standard form moves to the left 8 places.

• Robert’s number is correct because when converting 4,300,000,000, the decimal would be located between the 4 and the 3, and the power of 10 is determined by the number of zeros.

• Dora’s number is correct because when converting 4,300,000,000, the decimal would be located between the 4 and the 3, and the original decimal point in the standard form moves to the left 9 places.

• Dora’s number is correct because when converting 4,300,000,000, the decimal would be located between the 4 and the 3, and the power of 10 is always the number of zeros plus 1.

A researcher measured approximately 0.005123 grams of bacteria in a sample. How is this number expressed in scientific notation?

• 5.123 × 10³ grams

• 5123 × 10^–6 grams

• 0.5123 × 10^–2 grams

• 5.123 × 10^–3 grams

A microscopic cell measures 3.8 x 10^-3 centimeters in diameter. What is this number in standard notation?

• 0.000038

• 0.00038

• 0.0038

• 0.038

One type of ant is 0.0063 meters long. What is this length in scientific notation?

How many zeros are needed to write the diameter of the nucleus of an atom in standard notation?

• 14

• 15

• 16

• 13

About how many times larger than the diameter of a red blood cell is the diameter of a grain of sand? Write your answer using a power of 10

Write the diameter of a red blood cell in standard notation

• 0.0000084

• 0.00000084

• 8400000

• 84000000