Questions: The Gross Domestic Product (GDP) for the United States in the first quarter of 2014 was approximately 1.71 times 10^13. If you wrote this number in standard notation, it would be the number 171 followed by how many zeros?

The Gross Domestic Product (GDP) for the United States in the first quarter of 2014 was approximately 1.71 times 10^13. If you wrote this number in standard notation, it would be the number 171 followed by how many zeros?

Transcript text: Sat Nov 9 @ knewton.com \$3) Knewton Alta 11584 MAT092 ELEMENTARY ALGEBRA MASTERY $13 \%$ 3.A.7.b. Scientific Notation CURRENT ObJECTIVE Convert from scientific notation to decimal notation Question The Gross Domestic Product (GDP) for the United States in the first quarter of 2014 was approximately $\$ 1.71 \times 10^{13}$. If you wrote this number in standard notation, it would be the number 171 followed by how many zeros? Provide your answer below:

Solution

Solution Steps

To convert a number from scientific notation to decimal notation, you need to move the decimal point to the right by the number of places indicated by the exponent. In this case, the exponent is 13, so you move the decimal point 13 places to the right. The number of zeros that follow the initial digits will be the difference between the exponent and the number of digits in the initial number.

Step 1: Convert Scientific Notation to Decimal Notation

The Gross Domestic Product (GDP) for the United States in the first quarter of 2014 is given in scientific notation as $ 1.71 \times 10^{13} $. To convert this to decimal notation, we move the decimal point 13 places to the right, resulting in $ 17100000000000 $.

Step 2: Count the Number of Zeros

The number $ 171 $ has 3 digits. The exponent in the scientific notation is $ 13 $. The number of zeros that follow the initial digits can be calculated as: \[ \text{Number of zeros} = 13 - 3 = 10 \]