1Cademy - Converting $$96{,}000$$ and $$0.0078$$ to Scientific Notation

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Procedure for Converting from Decimal Notation to Scientific Notation

Example

Converting $96{,}000$ and $0.0078$ to Scientific Notation

Write $96{,}000$ and $0.0078$ in scientific notation by moving the decimal point to create a first factor between $1$ and $10$ , and multiplying by the appropriate power of $10$ .

Part ⓐ — Write $96{,}000$ in scientific notation.

Move the decimal point: Shift the implied decimal point in $96{,}000$ to the left until the first factor is between $1$ and $10$ . This gives $9.6$ .
Count the places moved: The decimal point was moved 4 places to the left.
Write as a product with a power of $10$ : Since the original number is greater than $1$ , the exponent is positive $4$ . The result is $9.6 imes 10^4$ .

Part ⓑ — Write $0.0078$ in scientific notation.

Move the decimal point: Shift the decimal point in $0.0078$ to the right to get $7.8$ .
Count the places moved: The decimal point was moved 3 places to the right.
Write as a product with a power of $10$ : Since the original number is between $0$ and $1$ , the exponent is negative $-3$ . The result is $7.8 imes 10^{-3}$ .