ACT Math: Scientific Notation

What is scientific notation?

A method of expressing numbers as a product of a coefficient and a power of 10.

What is the general form of scientific notation?

The general form is a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.

What is the requirement for the coefficient in scientific notation?

The coefficient must be at least 1 but less than 10.

What is improper scientific notation?

When the coefficient is not between 1 and 10, such as 12 × 10².

How do you move the decimal for large numbers in scientific notation?

Move the decimal point to the left; each move increases the exponent by 1.

How do you move the decimal for small numbers in scientific notation?

Move the decimal point to the right; each move decreases the exponent by 1.

What is the difference between positive and negative exponents?

Positive exponents indicate large numbers, while negative exponents indicate small numbers.

Convert 356,000,000 to scientific notation.

3.56 × 10⁸

Convert 4,890,000 to scientific notation.

4.89 × 10⁶

Convert 0.0000489 to scientific notation.

4.89 × 10⁻⁵

How do you determine the exponent from decimal movement?

Count the number of places the decimal moves; left for positive, right for negative.

How do you convert scientific notation back to standard form?

Multiply the coefficient by 10 raised to the exponent.

What is 10³ in standard form?

1,000

What is 10⁻³ in standard form?

0.001

How does multiplying by 10 affect the decimal?

It moves the decimal one place to the right.

How does dividing by 10 affect the decimal?

It moves the decimal one place to the left.

What is the easiest memory rule for exponent signs?

Positive exponents mean large numbers, negative exponents mean small numbers.

Convert 72,000 to scientific notation.

7.2 × 10⁴

Convert 0.00072 to scientific notation.

7.2 × 10⁻⁴

Convert 5.6 × 10⁴ to standard form.

56,000

Convert 5.6 × 10⁻⁴ to standard form.

0.000056

How do you convert 15% to a decimal?

Divide by 100 or move the decimal two places left: 0.15.

How do you convert percentages?

By dividing by 100 or moving the decimal two places to the left.

Convert 6.35 × 10⁻⁴ to standard form.

0.000635

How do you find 15% of 6.35 × 10⁻⁴?

Calculate 0.15 × 6.35 × 10⁻⁴ = 0.0009525.

How do you handle percentages in scientific-notation problems?

Convert the percentage to a decimal and then multiply by the scientific notation value.

What are the biggest mistakes to avoid in scientific notation?

Not moving the decimal correctly, using improper coefficients, and miscalculating exponents.

What is the scientific notation for 0.0000005?

5 × 10⁻⁷

What is the scientific notation for 1,000,000,000?

1 × 10⁹

Convert 0.00000123 to scientific notation.

1.23 × 10⁻⁶

Convert 9,000 to scientific notation.

9 × 10³

Convert 0.005 to scientific notation.

5 × 10⁻³

What is the scientific notation for 0.00000000045?

4.5 × 10⁻¹⁰

Convert 2.5 × 10² to standard form.

250

Convert 3.0 × 10⁻² to standard form.

0.03

What is the scientific notation for 0.00000078?

7.8 × 10⁻⁷

Convert 0.0000001 to scientific notation.

1 × 10⁻⁷

What is the scientific notation for 100,000?

1 × 10⁵

Convert 0.00012 to scientific notation.

1.2 × 10⁻¹

Convert 0.0000003 to scientific notation.

3 × 10⁻⁷