After multiplying, a calculator screen displays 8.234 E^(14). How would you write this number in standard form
The Correct Answer and Explanation is:
Correct Answer:
The number 8.234 E^(14) (as shown on the calculator) means:8.234×10148.234 \times 10^{14}8.234×1014
To write this in standard form, we move the decimal point 14 places to the right because the exponent is positive. This gives:823,400,000,000,000823,400,000,000,000823,400,000,000,000
Explanation
When using scientific calculators or computers, large or small numbers are often displayed in a format called scientific notation. In this format, a number is written as:a×10na \times 10^na×10n
Where:
- aaa is a number greater than or equal to 1 and less than 10.
- nnn is an integer (positive or negative) showing how many times to move the decimal point.
In this case, the calculator shows 8.234 E^(14). The letter “E” (or sometimes “e”) is shorthand for “× 10^”, so 8.234 E14 means:8.234×10148.234 \times 10^{14}8.234×1014
The exponent 14 tells us how many places to move the decimal point to the right, since it’s a positive exponent, meaning the number is large.
Starting with 8.234, we move the decimal 14 places to the right. Here’s how it works step by step:
- Start: 8.234
- Move the decimal right 14 places
- After the decimal has been moved, we fill in the empty places with zeros
So:8.234→823,400,000,000,0008.234 \rightarrow 823,400,000,000,0008.234→823,400,000,000,000
This is the standard form, where all digits are written out without using exponents. Standard form is helpful when presenting numbers in everyday contexts, such as financial reports or written descriptions, where scientific notation might be confusing to general audiences.
In conclusion, 8.234 E14 written in standard form is:823,400,000,000,000823,400,000,000,000823,400,000,000,000
This format makes the scale of the number clear and easy to interpret without the need for scientific notation.
