Question

2,083,193 cm in scientific notation rounded into 2 sig figs

Answer 1

Answer:

$\boxed{2.1 \times 10^{6}\text{ cm}}}$

Explanation:

1. Rounding

2 083 193 cm

You want to round to two significant figures.

You replace all the underlined digits (all those after the first two digits) with zeroes.

The rule is: If the first figure dropped (8) is greater than 5, increase the last figure kept (0) by 1.

Then, 2 083 193 cm becomes 2 100 000 cm

2. Converting to scientific notation

A number in scientific notation has the form

N × 10ⁿ

where N is a decimal number called the mantissa and n is an integer called the exponent.

We must have 1 ≤ N < 10

(a) Determine the mantissa

Move the decimal place to the left to create a new number between 1 and 10.

2 100 000 ⟶ 2.100 000; N = 2.1

(b). Determine the exponent.

The exponent is the number of times you moved the decimal to get the mantissa.

You moved the decimal six places to the left, so the exponent n = 6.

(c). Write the number in scientific notation

$\text{The measurement in scientific notation is }\boxed{\mathbf{2.1 \times 10^{6} \textbf{ cm}}}.$