250000 in Scientific Notation

250000 in scientific notation

250{,}000 = 2.5 \times 10^{5}

250000 in scientific notation is 2.5 × 10⁵ – the decimal point moves 5 places to the left, so the power of ten is 5.

E-notation: 2.5E+5 (calculators, Excel, programming)
Engineering notation: 250 × 10³ (the power is a multiple of 3)
Said aloud: two point five times ten to the power of five
Significant figures: 2 to 6 (the zeros at the end may or may not count)
Order of magnitude: \displaystyle 10^{5}
In the Indian system: 2,50,000 – two lakh fifty thousand
In words: two hundred fifty thousand

Step-by-step solution

The problem

\text{Write } 250{,}000 \text{ in scientific notation}

Find the coefficient

a = 2.5

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

Count the places the decimal point moves

250,000
25,000
2500
250
25
2.5

From \displaystyle 250{,}000 to \displaystyle 2.5 the decimal point moves 5 places to the left.

Choose the sign of the exponent

n = 5

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^{5} multiplies it back.

Write it in scientific notation

250{,}000 = \textcolor{#0b5c56}{2.5 \times 10^{5}}

Check

2.5 \times 10^{5} = 2.5 \times 100{,}000 = 250{,}000 \;\checkmark

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

The digits 25 at other powers of ten

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

Number	Scientific notation	E-notation
2,500	2.5 × 10³	2.5E3
25,000	2.5 × 10⁴	2.5E4
250,000	2.5 × 10⁵	2.5E5
2,500,000	2.5 × 10⁶	2.5E6
25,000,000	2.5 × 10⁷	2.5E7
250,000,000	2.5 × 10⁸	2.5E8
2,500,000,000	2.5 × 10⁹	2.5E9

Other numbers × 10⁵

Any other number – or multiplying, dividing, adding and subtracting in scientific notation – use the Scientific Notation Calculator.