4/27The Perfect Partner for your Digital Business

ScienceMathematical Skills IIIScientific Notation

Pro. Ignacio AngueraColegio Real de Panamá

Scientific notation is a short way of representing such numbers without writing the place-holding zeros.

SCIENTIFIC NOTATION

Population of the world is around 7,500,000,000 people

Mass of a dust particle is 0.000000000753 kg

Approximate speed of light is 1,080,000,000 km/h

0.00000000000000000000000000000091093822 kg

Distance from the sun to the nearest star is

39,900,000,000,000 km

Mass of an electron is

Step 1: Identify the number without the place-holding zeros. → 653 Step 2: Place the decimal point after the leftmost digit. → 6.53 Step 3: Find the exponent by counting the number of places that you moved the decimal point

The decimal point was moved 8 places to the left. Therefore, the exponent of 10 is positive 8. Remember, if the decimal point had moved to the right, the exponent would be negative. Step 4: Write the number in scientific notation. → 6.53 x 108

Scientific notation is a short way of representing such numbers without writing the place-holding zeros.

SCIENTIFIC NOTATION

In scientific notation, we write the number as a product of two factors: the first is a number -m- between 1 and 10, and the second is a power of ten raised to the -n- power, written as 10exponent.

m x 10n

Sample Problem: Write 653,000,000 in scientific notation

Scientific notation is a short way of representing such numbers without writing the place-holding zeros.

SCIENTIFIC NOTATION

In scientific notation, we write the number as a product of two factors: the first is a number -m- between 1 and 10, and the second is a power of ten raised to the -n- power, written as 10exponent.

m x 10n

Original number Number inscientific notation

Population of the world is around 7,500,000,000 peopleApproximate speed of light is 1,080,000,000 km/hMass of a dust particle is 0.000000000753 kg Distance from the sun to the nearest star 39,900,000,000,000 Mass of an electron 0.000000000000000000000000

00000091093822 kg

Step 1: Multiply the decimal numbers. → 2.6 x 6.3 = 16.38 Step 2: Add the exponents. → 7 + 4 = 11 Step 3: Put the new decimal number with the new exponent in scientific notation form. → 16.38 x 1011

Step 4: Because the new decimal number is greater than 10, count the number of places the decimal moves to put the number between 1 and 10. Add this number to the exponent. In this case, the decimal point moves one place, so add 1 to the exponent. → 1 6.38 x 1011 → 1.638 x 1012

Scientific notation is a short way of representing such numbers without writing the place-holding zeros.

SCIENTIFIC NOTATION

Multiply in Scientific NotationMultiply their coefficients and add their exponents.r

a x 10n · b x 10m = (a · b) x 10 (n + m)

Sample Problem: Multiply (2.6 x 107) by (6.3 x 104).

• Step 1: Divide the decimal numbers. → 1.23 ÷ 2 .4 = 0.5125 • Step2: Subtract the exponents of the powers of 10. → 11 - 4 = 7 • Step 3: Place the new power of 10 with the new decimal in scientific notation form. → 0.5125 x 107

• Step 4: Because the decimal number is not between 1 and 10, move the decimal point one place to the right and decrease the exponent by 1. → 0.5 125 x 107 → 5.125 x 106

Scientific notation is a short way of representing such numbers without writing the place-holding zeros.

SCIENTIFIC NOTATION

Divide in Scientific NotationMultiply their coefficients and add their exponents.r

= x 10 (n - m)

Sample Problem: Divide (1.23 x 1011) by (2.4 x 104)

PRACTICE!

= x 10 (n – m))

Problem New decimal New exponent Answer

(5.76 x 109) x (3.2 x 103)

(3.72 x 108) x (1.2 x 105)

(6.4 x 10-4) ÷ (4 x 106)

(3.7 x 104) ÷ (5.2 x 105)

a x 10n · b x 10m = (a · b) x 10 (n + m)