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Chapter 7: Problem 4

Convert each number into scientific notation. $$0.0125$$

Short Answer

Expert verified
1.25 \( \times \) 10^{-2}

Step by step solution

01

Identify the Decimal Placement

The given number is 0.0125. First, identify where the decimal point is currently located.
02

Move the Decimal Point

Move the decimal point in the number so that only one non-zero digit remains to the left of the decimal. By moving the decimal point 2 places to the right, the number becomes 1.25.
03

Determine the Exponent

Count the number of places the decimal point was moved. In this case, it was moved 2 places. Since the decimal was moved to the right, the exponent will be negative.
04

Write in Scientific Notation

Combine the digit from step 2 with the exponent from step 3. The number in scientific notation is written as \(1.25 \times 10^{-2}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Decimal Placement
Understanding decimal placement is crucial in scientific notation. The initial step is to pinpoint where the decimal point is located in the original number. For instance, in the number 0.0125, the decimal point is before all the digits and immediately after the zero. This position helps us know how far we need to move the decimal to convert the number into a more compact form.
Exponent
The exponent in scientific notation tells you how many places the decimal has moved, and in which direction. When you move the decimal point to the right, the exponent is negative, indicating that the original number is very small. Conversely, if you move it to the left, the exponent is positive, which means the original number is large. For the number 0.0125, the decimal point moved 2 places to the right, giving us an exponent of -2. Therefore, making it \(1.25 \times 10^{-2}\).
Convert Numbers
To convert any number into scientific notation, follow these steps systematically:
1. Identify the starting position of the decimal point.
2. Move the decimal point so that only one non-zero digit remains on the left.
3. Count how many places you moved the decimal.
4. Determine the exponent based on the direction of the movement.

Putting this into practice, for the number 0.0125, we:
  • Identify the decimal's starting position.
  • Move it 2 places to the right to make it 1.25.
  • Since we moved it to the right, our exponent is -2.

Finally, the scientific notation becomes \(1.25 \times 10^{-2}\).

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Most popular questions from this chapter

Estimate the answer without actually carrying out the computation and make the most appropriate choice. If you multiply \(7,250\) by \(0.004,\) the result is closest to (a) 0.3 (b) 3 (c) 30 (d) 300 (e) 3000

Convert each number into standard notation. $$3.5286 \times 10^{5}$$

Estimate the answer without actually carrying out the computation and make the most appropriate choice. If you multiply \(1.93 \times 10^{5}\) by \(5.12 \times 10^{-3},\) the result is closest to (a) 10 (b) 1000 (c) \(10,000\) (d) 0.01 (e) 0.001

Solve for x. $$-2<3 x+4 \leq 16$$

Do your computations using scientific notation. If the mass of one atom of iron is \(9.3 \times 10^{-23} \mathrm{gram},\) how many atoms are there in 1 gram?
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