Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Oct 25, 2023

Write the elevation of a telescope, about 2500 meters above sea level, in scientific notation. $2500 = 2.5 \times 10^3$

STEP 1

Assumptions1. The elevation of the telescope is2500 meters above sea level. . We need to express this elevation in scientific notation.

STEP 2

Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. It is commonly used by scientists, mathematicians, and engineers. The format for writing a number in scientific notation is $a \\times10^n$ Where a is a number between1 and10 (including1 but excluding10), and n is an integer.

STEP 3

To convert the elevation of the telescope to scientific notation, we have to express2500 as a number between1 and10 multiplied by10 raised to an appropriate power.

STEP 4

We can write2500 as2. multiplied by1000. This is because2. is a number between1 and10 and1000 is a power of10.
$2500 =2. \\times1000$

STEP 5

We can express1000 as $10^3$ because10 raised to the power of3 equals1000.
$1000 =10^3$

STEP 6

Substitute $10^3$ for1000 in the equation from4.
$2500 =2.5 \\times10^3$ So,2500 in scientific notation is $2.5 \\times10^3$ .

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