Understanding Scientific Notation

Example: @@0.004@@ in Scientific Notation

• @@4 \times 10^{-3}@@

• @@4 \times 10^{3}@@

• @@0.4 \times 10^{-2}@@

• @@40 \times 10^{-4}@@

Negative Exponent

• A small number, decimal moves right.

• A large number, decimal moves left.

• A small number, decimal stays the same.

• A large number, decimal moves right.

Multiplying in Scientific Notation

• Multiply coefficients, add exponents

• Add coefficients, multiply exponents

• Multiply both coefficients and exponents

• Add both coefficients and exponents

Example: @@5000@@ in Scientific Notation

• @@5 \times 10^3@@

• @@5 \times 10^4@@

• @@50 \times 10^2@@

• @@500 \times 10^1@@

Adding/Subtracting in Scientific Notation

• Adjust to the same exponent, then add or subtract the coefficients.

• Multiply the coefficients and add the exponents.

• Add the coefficients and keep the exponent the same.

• Convert to decimal form before adding or subtracting.

Format of Scientific Notation

• latex="a \times 10^n", where 1 \leq |a| < 10 and n is an integer

• latex="a \times 10^n", where 0 \leq |a| < 10 and n is a real number

• latex="a \times 10^n", where 1 \leq |a| < 100 and n is an integer

• latex="a \times 10^n", where 1 \leq |a| < 10 and n is a rational number

Scientific Notation

• A method to express numbers in fractions

• A way to express very large or very small numbers using powers of 10.

• A technique for rounding numbers to the nearest whole number

• A system for converting numbers into binary format.

Positive Exponent

• A large number, decimal moves left.

• A small number, decimal moves right.

• A large number, decimal stays the same.

• A small number, decimal moves left.

Converting to Scientific Notation

• Move the decimal point to create a number between 1 and 10, then count the moves for the exponent.

• Multiply the number by 10 for each digit to the left of the decimal point.

• Add 1 to the exponent for each digit to the right of the decimal point.

• Divide the number by 10 for each digit to the left of the decimal point.

Dividing in Scientific Notation

• Multiply coefficients, add exponents.

• Divide coefficients, subtract exponents.

• Add coefficients, divide exponents.

• Subtract coefficients, multiply exponents.