Write 40,610,000 in scientific notation. (Section 1.7, Example 2)
Verified step by step guidance
1
Identify the significant digits in the number 40,610,000.
Place the decimal point after the first non-zero digit to form a number between 1 and 10. This gives us 4.061.
Count the number of places the decimal point has moved from its original position to its new position. In this case, it moves 7 places to the left.
Express the number in the form , where is the number formed in step 2 and is the number of places the decimal moved.
Combine the results to write the number in scientific notation as .
Recommended similar problem, with video answer:
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2m
Play a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Scientific Notation
Scientific notation is a way of expressing numbers that are too large or too small in a compact form. It is written as the product of a number between 1 and 10 and a power of ten. For example, the number 40,610,000 can be expressed as 4.061 x 10^7, where 4.061 is the coefficient and 7 is the exponent indicating how many places the decimal point has moved.
Place value refers to the value of a digit based on its position within a number. In the context of converting to scientific notation, understanding place value helps determine how many places the decimal point must be moved to create a number between 1 and 10. For instance, in 40,610,000, the digit '4' is in the ten-million place, which is crucial for identifying the correct exponent.
Exponent rules are mathematical guidelines that govern how to manipulate powers of ten. When converting to scientific notation, the exponent indicates how many times the base (10) is multiplied by itself. For example, moving the decimal point to the left increases the exponent, while moving it to the right decreases it. This understanding is essential for accurately expressing large numbers in scientific notation.