400000 in Scientific Notation

400000 in scientific notation

400{,}000 = 4 \times 10^{5}

400000 in scientific notation is 4 × 10⁵ – the decimal point moves 5 places to the left, so the power of ten is 5.

  • E-notation: 4E+5 (calculators, Excel, programming)
  • Engineering notation: 400 × 10³ (the power is a multiple of 3)
  • Said aloud: four times ten to the power of five
  • Significant figures: 1 to 6 (the zeros at the end may or may not count)
  • Order of magnitude: \displaystyle 10^{5}
  • In the Indian system: 4,00,000 – four lakh
  • In words: four hundred thousand

Step-by-step solution

The problem

\text{Write } 400{,}000 \text{ in scientific notation}
1

Find the coefficient

a = 4

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

2

Count the places the decimal point moves

  1. 400,000
  2. 40,000
  3. 4000
  4. 400
  5. 40
  6. 4

From \displaystyle 400{,}000 to \displaystyle 4 the decimal point moves 5 places to the left.

3

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.

4

Write it in scientific notation

400{,}000 = \textcolor{#0b5c56}{4 \times 10^{5}}

Check

4 \times 10^{5} = 4 \times 100{,}000 = 400{,}000 \;\checkmark

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

The digits 4 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
4,0004 × 10³4E3
40,0004 × 10⁴4E4
400,0004 × 10⁵4E5
4,000,0004 × 10⁶4E6
40,000,0004 × 10⁷4E7
400,000,0004 × 10⁸4E8
4,000,000,0004 × 10⁹4E9

Other numbers × 10⁵

Try different values

Frequently asked questions

Is 40 × 10⁴ the same as 4 × 10⁵?

It has the same value, but it isn’t scientific notation: the number in front must be at least 1 and less than 10, and 40 is not. Move the point one more place and add 1 to the power: 4 × 10⁵.

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