Table of contents

0. Review of Algebra4h 16m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 19m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

Previous problemNext problem

1:06 minutes

Problem 78a

Textbook Question

In Exercises 77–86, write each number in scientific notation. 64,000

Verified step by step guidance

Identify the significant figures in the number 64,000. Here, the significant figures are 6 and 4.

Determine the decimal point position to express the number as a value between 1 and 10. For 64,000, move the decimal point 4 places to the left to get 6.4.

Count the number of places the decimal point was moved. In this case, it was moved 4 places.

Express the number in scientific notation by multiplying the significant figure by 10 raised to the power of the number of places moved. This gives us 6.4 \times 10^4.

Verify that the scientific notation correctly represents the original number by considering the power of 10 and the significant figures.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

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 64,000 can be expressed as 6.4 x 10^4 in scientific notation.

Powers of Ten

Powers of ten are used in scientific notation to indicate how many times the base number 10 is multiplied by itself. Each power corresponds to a place value in the decimal system. For instance, 10^4 means 10 multiplied by itself four times, which equals 10,000, helping to scale the number appropriately in scientific notation.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. In scientific notation, only the digits in the coefficient (the number between 1 and 10) are considered significant. For example, in 6.4 x 10^4, the '6' and '4' are significant figures, indicating the precision of the measurement.