Answer :
To express \( 0.0000529 \times 10^4 \) in standard form, follow these steps:
1. Identify the given numbers:
- A decimal number: \( 0.0000529 \)
- An exponent: \( 10^4 \)
2. Understand the task:
- We need to multiply \( 0.0000529 \) by \( 10^4 \).
3. Break down the multiplication:
- The decimal \( 0.0000529 \) can be rewritten as \( 5.29 \times 10^{-5} \) since \( 5.29 \) is moved 5 places to the left of the decimal point to make it a standard form number (between 1 and 10).
- This gives us \( 5.29 \times 10^{-5} \times 10^4 \).
4. Combine the exponents:
- When multiplying powers of ten, you add the exponents: \( 10^{-5} \times 10^4 = 10^{-5+4} = 10^{-1} \).
5. Re-combine the numbers:
- Now we have \( 5.29 \times 10^{-1} \).
6. Simplify to standard form:
- \( 5.29 \times 10^{-1} \) can be simplified to \( 0.529 \).
Therefore, [tex]\( 0.0000529 \times 10^4 \)[/tex] expressed in standard form is [tex]\( 0.529 \)[/tex].
1. Identify the given numbers:
- A decimal number: \( 0.0000529 \)
- An exponent: \( 10^4 \)
2. Understand the task:
- We need to multiply \( 0.0000529 \) by \( 10^4 \).
3. Break down the multiplication:
- The decimal \( 0.0000529 \) can be rewritten as \( 5.29 \times 10^{-5} \) since \( 5.29 \) is moved 5 places to the left of the decimal point to make it a standard form number (between 1 and 10).
- This gives us \( 5.29 \times 10^{-5} \times 10^4 \).
4. Combine the exponents:
- When multiplying powers of ten, you add the exponents: \( 10^{-5} \times 10^4 = 10^{-5+4} = 10^{-1} \).
5. Re-combine the numbers:
- Now we have \( 5.29 \times 10^{-1} \).
6. Simplify to standard form:
- \( 5.29 \times 10^{-1} \) can be simplified to \( 0.529 \).
Therefore, [tex]\( 0.0000529 \times 10^4 \)[/tex] expressed in standard form is [tex]\( 0.529 \)[/tex].
