Question

How does scientific notation with decimals work?

Answer 1

Scientific notation is the way that scientists handle large numbers and small numbers. For example, instead of writing 0.000 000 0056, they write 5.6 × 10⁻⁹.

We can think of 5.6 × 10⁻⁹ as the product of two numbers: 5.6 (the digits) and 10⁻⁹ (the power of 10).

Here are some examples of scientific notation.

1000 = 1 × 10³; 7354 = 7.354 × 10³

100 = 1 × 10²; 482 = 4.82 × 10²

10 = 1 × 10¹; 89 = 8.9 × 10¹

1 = 1 × 10⁰; 6 = 6 × 10⁰

1/10 = 0.1 = 1 × 10⁻¹; 0.32 = 3.2 × 10⁻¹

1/100 = 0.01 = 1 × 10⁻²; 0.053 = 5.3 × 10⁻²

1/1000 = 0.001 = 1 × 10⁻³; 0.0078 = 7.8 × 10⁻³

The exponent of 10 is the number of places we must shift the decimal point to get the scientific notation.

Each place the decimal moves to the left increases the exponent by 1.

Each place the decimal point moves to the right decreases the exponent by 1.

EXAMPLE:

Write the following numbers in scientific notation: 1001;
6 926 300 000; -392; 0.000 000 13; -0.0038

Solution:

1.001 × 10³; 6.9263 × 10⁹; -3.92 × 10²; 1.3 × 10⁻⁷; -3.8 × 10⁻³