Standard form (scientific notation) — KCSE Mathematics

Standard form, or scientific notation, is used to express very large or very small numbers conveniently. It is written as:
a × 10^n, where 1 ≤ a < 10 and n is an integer.
When performing operations, follow these steps:

• Addition/Subtraction: Ensure both numbers have the same exponent. Adjust if necessary.
• Multiplication: Multiply the coefficients and add the exponents.
• Division: Divide the coefficients and subtract the exponents.

Example: Add (3.2 × 10^5) and (4.5 × 10^5).

1. Both numbers have the same exponent (10^5).
2. Add coefficients: 3.2 + 4.5 = 7.7.
3. The result is 7.7 × 10^5.

Example: Divide (6.0 × 10^8) by (2.0 × 10^3).

1. Divide coefficients: 6.0 ÷ 2.0 = 3.0.
2. Subtract exponents: 8 - 3 = 5.
3. The result is 3.0 × 10^5.

Standard form, also known as scientific notation, is a way to express very large or very small numbers conveniently. It is written as a × 10^n, where:

• a is a number between 1 and 10,
• n is an integer.

This format is particularly useful in science and engineering, where measurements can vary greatly. For example:

• The mass of an electron is approximately 9.11 × 10^-31 kg.
• The distance to Proxima Centauri, the nearest star, is about 4.24 × 10^13 meters.

To convert a number into standard form, follow these steps:

1. Move the decimal point in the number until only one non-zero digit remains on the left.
2. Count the number of places moved; this becomes your exponent (n).
3. If you moved the decimal left, n is positive; if right, n is negative.

For example, to express 0.00056 in standard form:

• Move the decimal 4 places right: 5.6
• Therefore, it is 5.6 × 10^-4.

Standard form, also known as scientific notation, is a way to express very large or very small numbers conveniently. It is written as a × 10^n, where:

• a is a number greater than or equal to 1 and less than 10.
• n is an integer indicating the power of ten.

To convert a number into standard form:

1. Move the decimal point in the number until only one non-zero digit remains on the left.
2. Count how many places you moved the decimal point. This will be your n.
3. If you moved the decimal to the left, n is positive; if to the right, n is negative.

Example: Convert 45000 to standard form.

• Move the decimal point 4 places to the left: 4.5
• Count the moves: 4 (positive)
• Therefore, 45000 = 4.5 × 10^4.

Example: Convert 0.0045 to standard form.

• Move the decimal point 2 places to the right: 4.5
• Count the moves: 2 (negative)
• Therefore, 0.0045 = 4.5 × 10^-3.