Question

write the power of 10. identify the number between 1 and 10 to represent the original amount. write a decimal point after the digit in the greatest place - value column. write each digit that follows until only zeros remain. do not write the zeros. combine the power of 10 with the renamed number to express the original amount in scientific notation. 14,506,000,000,000 = 1.4506×10¹³. you can check your answer by multiplying. the product is. practice circle the letter of the correct scientific notation for each number. pay close attention to the exponents. 1. 634,000,000 a 6.34×10³ b 6.34×10⁻⁸ c 6.34×10⁹ d 6.34×10⁸ 2. 1,700,000,000 f 17×10⁹ g 1.7×10⁻⁹ h 1.7×10⁹ j 1.7×10¹³ 3. 608,000,000 a 608×10⁶ b 6.08×10⁶ c 6.08×10⁸ d 608×10⁸ 4. 7,589,000,000,000 f 7.589×10¹² g 7.589×10⁰ h 75.89×10⁷ j 7.58×10¹²

Explanation:

Step1: Recall scientific - notation rule

Scientific notation is of the form $a\times10^{n}$, where $1\leq a<10$ and $n$ is an integer. To convert a number to scientific notation, move the decimal point to get a number between 1 and 10, and the exponent $n$ is the number of places the decimal point is moved. If the decimal point is moved to the left, $n$ is positive; if to the right, $n$ is negative.

Step2: Convert 634,000,000

Move the decimal point 8 places to the left to get $a = 6.34$. So, $634000000=6.34\times10^{8}$.

Step3: Convert 1,700,000,000

Move the decimal point 9 places to the left to get $a = 1.7$. So, $1700000000 = 1.7\times10^{9}$.

Step4: Convert 608,000,000

Move the decimal point 8 places to the left to get $a = 6.08$. So, $608000000=6.08\times10^{8}$.

Step5: Convert 7,589,000,000,000

Move the decimal point 12 places to the left to get $a = 7.589$. So, $7589000000000=7.589\times10^{12}$.

Answer:

1. D. 6.34 × 10⁸
2. H. 1.7 × 10⁹
3. C. 6.08 × 10⁸
4. F. 7.589 × 10¹²