Math Problem Statement

A color photograph taken with a digital camera is converted into digital format using [4\cdot10^0] bytes per pixel. Photographs taken with the camera each have [2.2\cdot10^6] pixels. How many bytes are there in one photo? Write your answer in scientific notation.

Solution

To calculate the number of bytes in one photo, we need to multiply the number of bytes per pixel by the number of pixels in the photo. The given values are:

  • 4 bytes per pixel
  • 2.2 × 10⁶ pixels

The total number of bytes in the photo is:

Total bytes=(4100)×(2.2106)\text{Total bytes} = (4 \cdot 10^0) \times (2.2 \cdot 10^6)

To multiply these, we combine the constants and powers of 10 separately:

Total bytes=(4×2.2)(100×106)\text{Total bytes} = (4 \times 2.2) \cdot (10^0 \times 10^6)

First, calculate the constants:

4×2.2=8.84 \times 2.2 = 8.8

Now, simplify the powers of 10:

100×106=10610^0 \times 10^6 = 10^6

Therefore, the total number of bytes in one photo is:

Total bytes=8.8106\text{Total bytes} = 8.8 \cdot 10^6

This is the final answer in scientific notation:

8.8106 bytes8.8 \cdot 10^6 \text{ bytes}

Let me know if you'd like further details or have any questions!

Here are some related questions you might find interesting:

  1. What is the total size in bytes for 1000 photos?
  2. How many kilobytes (KB) are in one photo, considering 1 KB = 1024 bytes?
  3. How many gigabytes (GB) would 1000 photos occupy?
  4. What would the total size of a photo be if it were taken with a camera that uses 8 bytes per pixel?
  5. If a photo were compressed to half its size, how many bytes would it then occupy?

Tip: When dealing with large numbers in scientific notation, always separate the constants (like 8.8) from the powers of 10. This makes multiplication and division easier.

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Math Problem Analysis

Mathematical Concepts

Multiplication
Scientific Notation

Formulas

Total bytes = (bytes per pixel) × (number of pixels)

Theorems

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Suitable Grade Level

Grades 6-8