0.000045 in Scientific Notation

0.000045 in scientific notation

0.000045 = 4.5 \times 10^{-5}

0.000045 in scientific notation is 4.5 × 10⁻⁵ – the decimal point moves 5 places to the right, so the power of ten is −5.

  • E-notation: 4.5E-5 (calculators, Excel, programming)
  • Engineering notation: 45 × 10⁻⁶ (the power is a multiple of 3)
  • Said aloud: four point five times ten to the power of negative five
  • Significant figures: 2
  • Order of magnitude: \displaystyle 10^{-5}
  • As a fraction: 9/200,000

Step-by-step solution

The problem

\text{Write } 0.000045 \text{ in scientific notation}
1

Find the coefficient

a = 4.5

Scientific notation is \displaystyle a \times 10^{n} with \displaystyle 1 \le a < 10. Put the decimal point just after the first non-zero digit (4).

2

Count the places the decimal point moves

  1. 0.000045
  2. 0.00045
  3. 0.0045
  4. 0.045
  5. 0.45
  6. 4.5

From \displaystyle 0.000045 to \displaystyle 4.5 the decimal point moves 5 places to the right.

3

Choose the sign of the exponent

n = -5

The number is less than 1, so the point moved right and the exponent is negative: each place right multiplies by 10, and \displaystyle 10^{-5} divides it back.

4

Write it in scientific notation

0.000045 = \textcolor{#0b5c56}{4.5 \times 10^{-5}}

Check

4.5 \times 10^{-5} = 4.5 \div 100{,}000 = 0.000045 \;\checkmark

Multiply the coefficient by the power of ten (a negative power divides) to get back the number.

The digits 45 at other powers of ten

Only the power changes when the decimal point moves – each place right is one more step of ten.

NumberScientific notationE-notation
0.454.5 × 10⁻¹4.5E-1
0.0454.5 × 10⁻²4.5E-2
0.00454.5 × 10⁻³4.5E-3
0.000454.5 × 10⁻⁴4.5E-4
0.0000454.5 × 10⁻⁵4.5E-5
0.00000454.5 × 10⁻⁶4.5E-6
0.000000454.5 × 10⁻⁷4.5E-7
0.0000000454.5 × 10⁻⁸4.5E-8
0.00000000454.5 × 10⁻⁹4.5E-9

Other numbers × 10⁻⁵

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