QuestionExponents, Polynomials, and Radicals Converting between scientific notation and standard form in a real-world... Madely
Answer the following. (a) An astronomer's infrared telescope is able to detect radiation with a wavelength of $1.96 \times 10^{-5}$ meters. Write this number in standard notation. (b) The diameter of Pluto at its equator is approximately 2390 kilometers. Write this number in scientific notation. (a) $\square$ meters $\square$ $\times 10^{\circ}$ (b) $\square$ kilometers

Studdy Solution

STEP 1

1. Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.
2. Standard notation is the regular way of writing numbers.
3. To convert from scientific notation to standard notation, we move the decimal point to the right for positive exponents and to the left for negative exponents.
4. To convert from standard notation to scientific notation, we express the number as a product of a number between 1 and 10 and a power of 10.

STEP 2

1. Convert the scientific notation to standard notation for part (a).
2. Convert the standard notation to scientific notation for part (b).

STEP 3

Convert the number $1.96 \times 10^{-5}$ meters from scientific notation to standard notation.
- Since the exponent is $-5$ , move the decimal point 5 places to the left.
$1.96 \rightarrow 0.0000196$

STEP 4

Convert the number 2390 kilometers from standard notation to scientific notation.
- Identify the first non-zero digit and place the decimal point after it. - Count the number of places the decimal has moved to determine the exponent.
$2390 \rightarrow 2.390 \times 10^3$
The answers are: (a) $0.0000196$ meters (b) $2.390 \times 10^3$ kilometers

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms