8th Grade Math Scientific Notation

Important points of the scientific notation

The base should always be 10.

The exponent must be a non-zero integer, which means it can be either positive or negative.

The absolute value of the coefficient is greater than or equal to 1 but it should be less than 10.

Coefficients can be positive or negative numbers including whole and decimal numbers.

The mantissa carries the rest of the significant digits of the number.

When the scientific notation of any large numbers is expressed, then we use positive exponents for base 10.

When the scientific notation of any small numbers is expressed, then we use negative exponents for base 10.

Scientific Notation Example

Scientific notation problems include questions like below given examples.

1.    Convert 0.00000046 into scientific notation.

Ø  Move the decimal point to the right of 0.00000046 up to 7 places.

Ø  The decimal point was moved 7 places to the right to form the number 4.6.

Ø  Since the numbers are less than 10 and the decimal is moved to the right. Hence, we use a negative exponent here.

Ø  ⇒ 0.00000046 = 4.6 × 10^-7

2.    Convert 301000000 into scientific notation.

Ø  Move the decimal to the left 8 places so it is positioned to the right of the leftmost non-zero digit 3.01000000.

Ø  Remove all the zeroes and multiply the number by 10.

Ø  Now the number has become = 3.01.

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Sum Up

The primary reason why scientific notation is important is that it allows us to convert very large or very small numbers into much more manageable sizes. When these numbers are in scientific notation, it is much easier to work with them.