75000 in Scientific Notation

75000 in scientific notation

75{,}000 = 7.5 \times 10^{4}

75000 in scientific notation is 7.5 × 10⁴ – the decimal point moves 4 places to the left, so the power of ten is 4.

  • E-notation: 7.5E+4 (calculators, Excel, programming)
  • Engineering notation: 75 × 10³ (the power is a multiple of 3)
  • Said aloud: seven point five times ten to the power of four
  • Significant figures: 2 to 5 (the zeros at the end may or may not count)
  • Order of magnitude: \displaystyle 10^{4}
  • In words: seventy-five thousand

Step-by-step solution

The problem

\text{Write } 75{,}000 \text{ in scientific notation}
1

Find the coefficient

a = 7.5

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 (7); the zeros at the end only hold places, so they are left out.

2

Count the places the decimal point moves

  1. 75,000
  2. 7500
  3. 750
  4. 75
  5. 7.5

From \displaystyle 75{,}000 to \displaystyle 7.5 the decimal point moves 4 places to the left.

3

Choose the sign of the exponent

n = 4

The number is 10 or more, so the point moved left and the exponent is positive: each place left divides by 10, and \displaystyle 10^{4} multiplies it back.

4

Write it in scientific notation

75{,}000 = \textcolor{#0b5c56}{7.5 \times 10^{4}}

Check

7.5 \times 10^{4} = 7.5 \times 10{,}000 = 75{,}000 \;\checkmark

Multiply the coefficient by the power of ten to get back the number.

The digits 75 at other powers of ten

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

NumberScientific notationE-notation
7,5007.5 × 10³7.5E3
75,0007.5 × 10⁴7.5E4
750,0007.5 × 10⁵7.5E5
7,500,0007.5 × 10⁶7.5E6
75,000,0007.5 × 10⁷7.5E7
750,000,0007.5 × 10⁸7.5E8
7,500,000,0007.5 × 10⁹7.5E9

Other numbers × 10⁴

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