Is 15,300 in scientific notation 0.153*10^-5 or 1.53*10^-4

1 answer

To express the number 15,300 in scientific notation, we want it in the form \( a \times 10^n \), where \( 1 \leq a < 10 \) and \( n \) is an integer.

To convert 15,300 into scientific notation:

  1. Move the decimal point in 15,300 to the left until it is in the correct form. The decimal point moves 4 places to the left, so we get \( 1.53 \).
  2. Since we moved the decimal 4 places to the left, we multiply by \( 10^4 \).

This gives us: \[ 15,300 = 1.53 \times 10^4 \]

Now, let's analyze the two options given:

  1. \( 0.153 \times 10^{-5} \)
  2. \( 1.53 \times 10^{-4} \)

Both options appear to be incorrect for representing 15,300.

To verify:

  • \( 0.153 \times 10^{-5} = 0.153 \times 0.00001 = 0.00000153 \), which is significantly smaller than 15,300.
  • \( 1.53 \times 10^{-4} = 1.53 \times 0.0001 = 0.000153 \), which is also much smaller than 15,300.

The correct scientific notation for 15,300 is \( 1.53 \times 10^4 \).