Sure! Let's convert the scientific notation [tex]\(1.53 \times 10^{-8}\)[/tex] to its decimal form step by step.
### Step-by-Step Solution:
1. Understand the Scientific Notation:
- The number [tex]\(1.53 \times 10^{-8}\)[/tex] is in scientific notation. This means you need to multiply 1.53 by [tex]\(10^{-8}\)[/tex].
2. Interpret the Exponent [tex]\(-8\)[/tex]:
- The exponent [tex]\(-8\)[/tex] indicates that we need to move the decimal point 8 places to the left. If the exponent were positive, we would move the decimal point to the right.
3. Move the Decimal Point:
- Start with the number 1.53.
- Move the decimal point 8 places to the left. As you move the decimal point, you will need to add zeros as placeholders.
Let's visualize this step-by-step:
- Original number: [tex]\(1.53\)[/tex]
- Move the decimal point 1 place to the left: [tex]\(0.153\)[/tex]
- Move the decimal point 2 places to the left: [tex]\(0.0153\)[/tex]
- Move the decimal point 3 places to the left: [tex]\(0.00153\)[/tex]
- Move the decimal point 4 places to the left: [tex]\(0.000153\)[/tex]
- Move the decimal point 5 places to the left: [tex]\(0.0000153\)[/tex]
- Move the decimal point 6 places to the left: [tex]\(0.00000153\)[/tex]
- Move the decimal point 7 places to the left: [tex]\(0.000000153\)[/tex]
- Move the decimal point 8 places to the left: [tex]\(0.0000000153\)[/tex]
4. Write the Number in Decimal Form:
- After moving the decimal point 8 places to the left, we get the decimal form as [tex]\(0.0000000153\)[/tex].
So, [tex]\(1.53 \times 10^{-8}\)[/tex] in decimal form is:
[tex]\[ 0.0000000153 \][/tex]
That is the final answer.
