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slega [8]
3 years ago
11

Explain the steps for 0.000000001 in scientific notation

Mathematics
2 answers:
lawyer [7]3 years ago
8 0
If you count the zeros it’s
one billionth
RSB [31]3 years ago
3 0

Answer:

  • Find the place value of the most significant digit
  • Write the number using that place value as a multiplier
  • 1×10^-9

Step-by-step explanation:

It helps immensely if you understand how place value works in a decimal number system. It also helps if you understand the rules of exponents.

Around the decimal point, the place values are ...

  (hundreds) (tens) (ones) . (tenths) (hundredths) (thousandths)

Each location to the right of any given place has a place value that is 1/10 of the one to its left. When there get to be many factors of 10, it is useful to use exponents to represent the repeated multiplication.

  1/10 = 1/10^1

  1/100 = 1/10^2

  1/1000 = 1/10^3

If you count carefully, you find the the digit 1 in your number is in the 9th place to the right of the decimal point, so its multiplier is 1/10^9. That is ...

  0.000000001 = 1/10^9

By the rules of exponents, a positive exponent in the denominator is the same as its opposite exponent in the numerator, so this number can also be written as ...

  0.000000001 = 1×10^-9 . . . . scientific notation

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Combine the terms by multiplying into a single fraction.

\bf{\dfrac{5}{2}x-7=\dfrac{3}{4}x+14   }

Find the common denominator.

\bf{\dfrac{5x}{2}-7=\dfrac{3}{4}x+14   }

Combine fractions with the lowest common denominator.

\bf{\dfrac{5x(-7)}{2}=\dfrac{3}{4}x+14   }

Multiply the numbers.

\bf{\dfrac{5x-14}{2}=\dfrac{3}{4}x+14   }

Combine the multiplied terms into a single fraction

\bf{\dfrac{5x-14}{2}=\dfrac{3x}{4}+14   }

Find the common denominator.

\bf{\dfrac{5x-14}{2}=\dfrac{3x}{4}+\dfrac{4\cdot14}{4}    }

Combine fractions with the lowest common denominator.

\bf{\dfrac{5x-14}{2}=\dfrac{3x+4\cdot14}{4}   }

Multiply the numbers.

\bf{\dfrac{5x-14}{2}=\dfrac{3x+56}{4}   }

Eliminate the denominators of the fractions.

\bf{4\cdot\dfrac{5x-14}{2}=4\cdot\dfrac{3x+56}{4}   }

Cancel the multiplied terms that are in the denominator.

\bf{2(5x-14)=3x+56}

To distribute.

\bf{10x-28=3x+56 }

Add 28 to both sides.

\bf{10x-28+28=3x+56+28 }

Simplify

\bf{10x=3x+84 }

Subtract 3x from both sides.

\bf{10x-3x=3x+84-3x }

Simplify

\bf{7x=84 }

Divide both sides by the same factor.

\bf{x=\dfrac{84}{7} }

Simplify

\bf{x=12 \ \ \ === > \ \ \ Answer}

↓

<h3>Verification</h3>

Let x=12.

  1. \bf{\dfrac{5}{2}\times12-7=\dfrac{3}{4}\times12+14   }
  2. \bf{\dfrac{5\times12}{2}-7=\dfrac{3}{4}\times12+14   }
  3. \bf{\dfrac{60}{2}-7=\dfrac{3}{4}\times12+14   }
  4. \bf{30-7=\dfrac{3}{4}\times12+14   }
  5. \bf{30-7=\dfrac{3\times12}{4}+14   }
  6. \bf{30-7=\dfrac{36}{4}+14   }
  7. \bf{30-7=9+14   }
  8. \bf{23=9+14 }
  9. \bf{23=23}

Checked ✅

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Answer:3

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