Question

Express the following in numerals. Remember to leave a space after each period.

(a) Thirty-two thousand four hundred one
(b) Ninety thousand twelve
(c) Sixty-five thousand eight hundred ten
(d) One hundred thousand
A. 32,401; 90,012; 65,810; 100,000
B. 32,410; 90,120; 65,810; 100,000
C. 32,401; 90,012; 65,800; 100,000
D. 32,410; 90,120; 65,800; 100,000

Answer 1

Converting numbers to scientific notation involves adjusting the decimal point to create a new number between 1 and 10, and accordingly adjusting the exponent of ten. For example, 8,099 x 10^7 in scientific notation is 8.099 x 10^10. The process ensures the notation follows the format of a single non-zero digit followed by a decimal and any other significant digits, times a power of ten.

Step-by-step explanation:

To express the given numerals correctly, we need to convert them into scientific notation, which has the form of a single digit from 1 to 9, followed by a decimal point and the remaining significant figures, multiplied by a power of ten. Let's work through the given examples.

Converting to Scientific Notation

1. 8,099 x 107: First, locate the decimal point after the last digit (assuming it is after 8099). Then, count how many places to move the decimal left to get a number between 1 and 10. For 8,099, we move it three places to the left, resulting in 8.099. Finally, since we moved the decimal place, we add three to the exponent of 10, thus the scientific notation is 8.099 x 1010.
2. 34.5 x 100: Since 34.5 is already a number between 1 and 10 and the exponent is 0, the number is already in scientific notation. Therefore, it remains 34.5 x 100, which is simply 34.5.
3. 0.000332 × 104: Move the decimal point to the right to get a number between 1 and 10, which would be 3.32. Since we moved the decimal 3 places, we subtract 3 from the exponent, resulting in 3.32 x 101